added the tutorial material - chapter 1.

Lab.bib

+
+@misc{mock-gw-data,
+      url = "home.icts.res.in/~ajith/Downloads/mock_gw_data.dat.gz"
+}
+@misc{ligo-data,
+	  note = "Download the file L1-STRAIN\_4096Hz-815045078-256.txt.gz from", 
+      url = "http://www.ligo.org/science/GRB051103/index.php"
+}
+@misc{rxte,
+	  note = "RXTE is an X-ray timing satellite", 
+      url = "https://heasarc.gsfc.nasa.gov/docs/xte/rxte.html"
+}
+@misc{rxte-data,
+      url = "http://home.icts.res.in/~ajith/Downloads/extracted_lightcurve_HerX-1.dat.gz"
+}
+@misc{rxte-data2,
+	url = "http://home.icts.res.in/~ajith/Downloads/4U1636-536_LC-extract.dat.gz"
+}
+@misc{nrdata,
+      url = "http://home.icts.res.in/~ajith/Downloads/nr_data.gz"
+}
+@misc{SXScatalog,
+      url = "http://www.black-holes.org/waveforms/"
+}
+
+@article{Porto:2010zg,
+      author         = "Porto, Rafael A. and Ross, Andreas and Rothstein, Ira Z.",
+      title          = "{Spin induced multipole moments for the gravitational
+                        wave flux from binary inspirals to third Post-Newtonian
+                        order}",
+      journal        = "JCAP",
+      volume         = "1103",
+      pages          = "009",
+      doi            = "10.1088/1475-7516/2011/03/009",
+      year           = "2011",
+      eprint         = "1007.1312",
+      archivePrefix  = "arXiv",
+      primaryClass   = "gr-qc",
+}
+
+@article{Ajith:2011ec,
+      author         = "Ajith, P.",
+      title          = "{Addressing the spin question in gravitational-wave
+                        searches: Waveform templates for inspiralling compact
+                        binaries with nonprecessing spins}",
+      journal        = "Phys. Rev. D",
+      volume         = "84",
+      pages          = "084037",
+      year           = "2011",
+      eprint         = "1107.1267",
+      archivePrefix  = "arXiv",
+      primaryClass   = "gr-qc",
+}
+
+@article{Harry:2011qh,
+      author         = "Harry, I.W. and Fairhurst, S.",
+      title          = "{A coherent triggered search for single spin compact
+                        binary coalescences in gravitational wave data}",
+      journal        = "Class.Quant.Grav.",
+      volume         = "28",
+      pages          = "134008",
+      doi            = "10.1088/0264-9381/28/13/134008",
+      year           = "2011",
+      note           = "* Temporary entry *",
+      eprint         = "1101.1459",
+      archivePrefix  = "arXiv",
+      primaryClass   = "gr-qc",
+}
+
+@article{Buonanno:2004yd,
+      author         = "Buonanno, Alessandra and Chen, Yan-bei and Pan, Yi and
+                        Vallisneri, Michele",
+      title          = "{A Quasi-physical family of gravity-wave templates for
+                        precessing binaries of spinning compact objects. 2.
+                        Application to double-spin precessing binaries}",
+      journal        = "Phys.Rev.",
+      volume         = "D70",
+      pages          = "104003",
+      doi            = "10.1103/PhysRevD.70.104003, 10.1103/PhysRevD.74.029902",
+      year           = "2004",
+      note           = "A Seq. to gr-qc/0310034",
+      eprint         = "gr-qc/0405090",
+      archivePrefix  = "arXiv",
+      primaryClass   = "gr-qc",
+}
+@article{Peters:1964zz,
+      author         = "Peters, P.C.",
+      title          = "{Gravitational Radiation and the Motion of Two Point
+                        Masses}",
+      journal        = "Phys.Rev.",
+      volume         = "136",
+      pages          = "B1224-B1232",
+      doi            = "10.1103/PhysRev.136.B1224",
+      year           = "1964",
+}
+@article{Peters:1963ux,
+      author         = "Peters, P.C. and Mathews, J.",
+      title          = "{Gravitational radiation from point masses in a Keplerian
+                        orbit}",
+      journal        = "Phys.Rev.",
+      volume         = "131",
+      pages          = "435-439",
+      doi            = "10.1103/PhysRev.131.435",
+      year           = "1963",
+}
+@Article{Kesden:2010yp,
+     author    = "Kesden, Michael and Sperhake, Ulrich and Berti, Emanuele",
+     title     = "{Final spins from the merger of precessing binary black
+                  holes}",
+     journal   = "Phys. Rev.",
+     volume    = "D81",
+     year      = "2010",
+     pages     = "084054",
+     eprint    = "1002.2643",
+     archivePrefix = "arXiv",
+     primaryClass  =  "astro-ph.GA",
+     doi       = "10.1103/PhysRevD.81.084054",
+     SLACcitation  = "%%CITATION = 1002.2643;%%"
+}
+@Article{Schnittman:2004vq,
+     author    = "Schnittman, Jeremy D.",
+     title     = "{Spin-Orbit Resonance and the Evolution of Compact Binary
+                  Systems}",
+     journal   = "Phys. Rev.",
+     volume    = "D70",
+     year      = "2004",
+     pages     = "124020",
+     eprint    = "astro-ph/0409174",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.70.124020",
+     SLACcitation  = "%%CITATION = ASTRO-PH/0409174;%%"
+}
+
+
+@Article{Favata:2010ic,
+     author    = "Favata, Marc",
+     title     = "{Conservative corrections to the innermost stable circular
+                  orbit (ISCO) of a Kerr black hole: a new gauge-invariant
+                  post-Newtonian ISCO condition, and the ISCO shift due to
+                  test-particle spin and the gravitational self-force}",
+     journal   = "Phys. Rev.",
+     volume    = "D83",
+     year      = "2011",
+     pages     = "024028",
+     eprint    = "1010.2553",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1103/PhysRevD.83.024028",
+     SLACcitation  = "%%CITATION = 1010.2553;%%"
+}
+
+@Article{Ajith:2007qp,
+     author    = "Ajith, Parameswaran and others",
+     title     = "Phenomenological template family for black-hole coalescence
+                  waveforms",
+     journal   = "Class. Quant. Grav.",
+     volume    = "24",
+     year      = "2007",
+     pages     = "S689--S699",
+     eprint    = "",
+     SLACcitation  = "%%CITATION = ARXIV:0704.3764;%%"
+}
+%     eprint    = "arXiv:0704.3764 [gr-qc]",
+
+@Article{Racine:2008kj,
+     author    = "Racine, Etienne and Buonanno, Alessandra and Kidder,
+                  Lawrence E.",
+     title     = "{Recoil velocity at 2PN order for spinning black hole
+                  binaries}",
+     journal   = "Phys. Rev.",
+     volume    = "D80",
+     year      = "2009",
+     pages     = "044010",
+     eprint    = "0812.4413",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1103/PhysRevD.80.044010",
+     SLACcitation  = "%%CITATION = 0812.4413;%%"
+}
+@Article{Mikoczi:2005dn,
+     author    = "Mikoczi, Balazs and Vasuth, Matyas and Gergely, Laszlo A.",
+     title     = "{Self-interaction spin effects in inspiralling compact
+                  binaries}",
+     journal   = "Phys. Rev.",
+     volume    = "D71",
+     year      = "2005",
+     pages     = "124043",
+     eprint    = "astro-ph/0504538",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.71.124043",
+     SLACcitation  = "%%CITATION = ASTRO-PH/0504538;%%"
+}
+
+@Article{Damour:2001bu,
+     author    = "Damour, Thibault and Jaranowski, Piotr and Schaefer,
+                  Gerhard",
+     title     = "{Dimensional regularization of the gravitational
+                  interaction of point masses}",
+     journal   = "Phys. Lett.",
+     volume    = "B513",
+     year      = "2001",
+     pages     = "147-155",
+     eprint    = "gr-qc/0105038",
+     archivePrefix = "arXiv",
+     doi       = "10.1016/S0370-2693(01)00642-6",
+     SLACcitation  = "%%CITATION = GR-QC/0105038;%%"
+}
+@Article{Blanchet:2000ub,
+     author    = "Blanchet, Luc and Faye, Guillaume",
+     title     = "{General relativistic dynamics of compact binaries at the
+                  third  post-Newtonian order}",
+     journal   = "Phys. Rev.",
+     volume    = "D63",
+     year      = "2001",
+     pages     = "062005",
+     eprint    = "gr-qc/0007051",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.63.062005",
+     SLACcitation  = "%%CITATION = GR-QC/0007051;%%"
+}
+
+@Article{deAndrade:2000gf,
+     author    = "de Andrade, Vanessa C. and Blanchet, Luc and Faye,
+                  Guillaume",
+     title     = "{Third post-Newtonian dynamics of compact binaries:
+                  Noetherian  conserved quantities and equivalence between
+                  the harmonic coordinate  and ADM-Hamiltonian formalisms}",
+     journal   = "Class. Quant. Grav.",
+     volume    = "18",
+     year      = "2001",
+     pages     = "753-778",
+     eprint    = "gr-qc/0011063",
+     archivePrefix = "arXiv",
+     doi       = "10.1088/0264-9381/18/5/301",
+     SLACcitation  = "%%CITATION = GR-QC/0011063;%%"
+}
+
+
+@Article{Jaranowski:1999ye,
+     author    = "Jaranowski, Piotr and Schaefer, Gerhard",
+     title     = "{The binary black-hole problem at the third post-Newtonian
+                  approximation in the orbital motion: Static part}",
+     journal   = "Phys. Rev.",
+     volume    = "D60",
+     year      = "1999",
+     pages     = "124003",
+     eprint    = "gr-qc/9906092",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.60.124003",
+     SLACcitation  = "%%CITATION = GR-QC/9906092;%%"
+}
+
+
+@Article{Poisson:1997ha,
+     author    = "Poisson, Eric",
+     title     = "{Gravitational waves from inspiraling compact binaries:
+                  The quadrupole-moment term}",
+     journal   = "Phys. Rev.",
+     volume    = "D57",
+     year      = "1998",
+     pages     = "5287-5290",
+     eprint    = "gr-qc/9709032",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.57.5287",
+     SLACcitation  = "%%CITATION = GR-QC/9709032;%%"
+}
+
+@Article{Kidder:1995zr,
+     author    = "Kidder, Lawrence E.",
+     title     = "{Coalescing binary systems of compact objects to
+                  postNewtonian 5/2 order. 5. Spin effects}",
+     journal   = "Phys. Rev.",
+     volume    = "D52",
+     year      = "1995",
+     pages     = "821-847",
+     eprint    = "gr-qc/9506022",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.52.821",
+     SLACcitation  = "%%CITATION = GR-QC/9506022;%%"
+}
+
+
+@Article{Faye:2006gx,
+     author    = "Faye, Guillaume and Blanchet, Luc and Buonanno, Alessandra
+                  ",
+     title     = "{Higher-order spin effects in the dynamics of compact
+                  binaries. I:  Equations of motion}",
+     journal   = "Phys. Rev.",
+     volume    = "D74",
+     year      = "2006",
+     pages     = "104033",
+     eprint    = "gr-qc/0605139",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.74.104033",
+     SLACcitation  = "%%CITATION = GR-QC/0605139;%%"
+}
+
+
+@Article{Blanchet:2004ek,
+     author    = "Blanchet, Luc and Damour, Thibault and Esposito-Farese,
+                  Gilles and Iyer, Bala R.",
+     title     = "{Gravitational radiation from inspiralling compact binaries
+                  completed at  the third post-Newtonian order}",
+     journal   = "Phys. Rev. Lett.",
+     volume    = "93",
+     year      = "2004",
+     pages     = "091101",
+     eprint    = "gr-qc/0406012",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevLett.93.091101",
+     SLACcitation  = "%%CITATION = GR-QC/0406012;%%"
+}
+
+@Article{Poisson:1995ef,
+     author    = "Poisson, Eric and Will, Clifford M.",
+     title     = "{Gravitational waves from inspiraling compact binaries:
+                  Parameter estimation using second postNewtonian wave
+                  forms}",
+     journal   = "Phys. Rev.",
+     volume    = "D52",
+     year      = "1995",
+     pages     = "848-855",
+     eprint    = "gr-qc/9502040",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.52.848",
+     SLACcitation  = "%%CITATION = GR-QC/9502040;%%"
+}
+
+
+@Article{Boyle:2009dg,
+     author    = "Boyle, Michael and Brown, Duncan A. and Pekowsky, Larne",
+     title     = "{Comparison of high-accuracy numerical simulations of
+                  black-hole binaries with stationary phase post-Newtonian
+                  template waveforms for Initial and Advanced LIGO}",
+     journal   = "Class. Quant. Grav.",
+     volume    = "26",
+     year      = "2009",
+     pages     = "114006",
+     eprint    = "0901.1628",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1088/0264-9381/26/11/114006",
+     SLACcitation  = "%%CITATION = 0901.1628;%%"
+}
+@Article{Lattimer:2006xb,
+     author    = "Lattimer, James M. and Prakash, Maddapa",
+     title     = "{Neutron Star Observations: Prognosis for Equation of State
+                  Constraints}",
+     journal   = "Phys. Rept.",
+     volume    = "442",
+     year      = "2007",
+     pages     = "109-165",
+     eprint    = "astro-ph/0612440",
+     archivePrefix = "arXiv",
+     doi       = "10.1016/j.physrep.2007.02.003",
+     SLACcitation  = "%%CITATION = ASTRO-PH/0612440;%%"
+}
+
+@ARTICLE{1994ApJ...424..823C,
+   author = {{Cook}, G.~B. and {Shapiro}, S.~L. and {Teukolsky}, S.~A.},
+    title = "{Rapidly rotating neutron stars in general relativity: Realistic equations of state}",
+  journal = {\apj},
+ keywords = {EQUATIONS OF STATE, PULSARS, RELATIVITY, STELLAR EVOLUTION, STELLAR MODELS, STELLAR ROTATION, ANGULAR MOMENTUM, BLACK HOLES (ASTRONOMY), COMPUTATIONAL GRIDS, COMPUTERIZED SIMULATION, EQUILIBRIUM METHODS, NUMERICAL ANALYSIS, STABILITY, STELLAR MASS},
+     year = 1994,
+    month = apr,
+   volume = 424,
+    pages = {823-845},
+      doi = {10.1086/173934},
+   adsurl = {http://adsabs.harvard.edu/abs/1994ApJ...424..823C},
+  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
+}
+
+@UNPUBLISHED{Ajith:2011xx,
+     author    = "Ajith, P.",
+     title     = "Comparison of post-Newtonian templates for gravitational waveforms from spinning binaries",
+     year      = "2011",
+     note      = "{In preparation.}"
+}
+
+@article{0264-9381-27-8-084006,
+  author={Gregory M Harry and the LIGO Scientific Collaboration},
+  title={Advanced LIGO: the next generation of gravitational wave detectors},
+  journal={Classical and Quantum Gravity},
+  volume={27},
+  number={8},
+  pages={084006},
+  url={http://stacks.iop.org/0264-9381/27/i=8/a=084006},
+  year={2010},
+  abstract={The Advanced LIGO gravitational wave detectors are next generation instruments which will replace the existing initial LIGO detectors. They are currently being constructed and installed. Advanced LIGO strain sensitivity is designed to be about a factor 10 better than initial LIGO over a broad band and usable to 10 Hz, in contrast to 40 Hz for initial LIGO. This is expected to allow for detections and significant astrophysics in most categories of gravitational waves. To achieve this sensitivity, all hardware subsystems are being replaced with improvements. Designs and expected performance are presented for the seismic isolation, suspensions, optics and laser subsystems. Possible enhancements to Advanced LIGO, either to resolve problems that may arise and/or to allow for improved performance, are now being researched. Some of these enhancements are discussed along with some potential technology being considered for detectors beyond Advanced LIGO.}
+}
+
+@Article{Galley:2010rc,
+     author    = "Galley, Chad R. and Herrmann, Frank and Silberholz, John
+                  and Tiglio, Manuel and Guerberoff, Gustavo",
+     title     = "{Statistical constraints on binary black hole inspiral
+                  dynamics}",
+     journal   = "Class. Quant. Grav.",
+     volume    = "27",
+     year      = "2010",
+     pages     = "245007",
+     eprint    = "1005.5560",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1088/0264-9381/27/24/245007",
+     SLACcitation  = "%%CITATION = 1005.5560;%%"
+}
+@Article{Buonanno:2006ui,
+     author    = "Buonanno, Alessandra and Cook, Gregory B. and Pretorius,
+                  Frans",
+     title     = "{Inspiral, merger and ring-down of equal-mass black-hole
+                  binaries}",
+     journal   = "Phys. Rev.",
+     volume    = "D75",
+     year      = "2007",
+     pages     = "124018",
+     eprint    = "gr-qc/0610122",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.75.124018",
+     SLACcitation  = "%%CITATION = GR-QC/0610122;%%"
+}
+
+@Article{PhysRevLett.99.181101,
+  title = {Consistency of Post-Newtonian Waveforms with Numerical Relativity},
+  author = {Baker, John G. and van~Meter, James R. and McWilliams, Sean T. and Centrella, Joan  and Kelly, Bernard J.},
+  journal = {Phys. Rev. Lett.},
+  volume = {99},
+  number = {18},
+  pages = {181101},
+  numpages = {4},
+  year = {2007},
+  month = {Oct},
+  doi = {10.1103/PhysRevLett.99.181101},
+  publisher = {American Physical Society}
+}
+
+@Article{Hannam:2007ik,
+     author    = "Hannam, Mark and Husa, Sascha and Sperhake, Ulrich and
+                  Bruegmann, Bernd and Gonzalez, Jose A.",
+     title     = "{Where post-Newtonian and numerical-relativity waveforms
+                  meet}",
+     journal   = "Phys. Rev.",
+     volume    = "D77",
+     year      = "2008",
+     pages     = "044020",
+     eprint    = "0706.1305",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1103/PhysRevD.77.044020",
+     SLACcitation  = "%%CITATION = 0706.1305;%%"
+}
+
+@Article{Gopakumar:2007vh,
+     author    = "Gopakumar, Achamveedu and Hannam, Mark and Husa, Sascha and
+                  Bruegmann, Bernd",
+     title     = "{Comparison between numerical relativity and a new class of
+                  post-Newtonian gravitational-wave phase evolutions: the
+                  non-spinning equal-mass case}",
+     journal   = "Phys. Rev.",
+     volume    = "D78",
+     year      = "2008",
+     pages     = "064026",
+     eprint    = "0712.3737",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1103/PhysRevD.78.064026",
+     SLACcitation  = "%%CITATION = 0712.3737;%%"
+}
+
+@Article{Boyle:2007ft,
+     author    = "Boyle, Michael and others",
+     title     = "{High-accuracy comparison of numerical relativity
+                  simulations with post-Newtonian expansions}",
+     journal   = "Phys. Rev.",
+     volume    = "D76",
+     year      = "2007",
+     pages     = "124038",
+     eprint    = "0710.0158",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1103/PhysRevD.76.124038",
+     SLACcitation  = "%%CITATION = 0710.0158;%%"
+}
+
+@Article{Hannam:2010ec,
+     author    = "Hannam, Mark and Husa, Sascha and Ohme, Frank and Muller,
+                  Doreen and Bruegmann, Bernd",
+     title     = "{Simulations of black-hole binaries with unequal masses or
+                  nonprecessing spins: Accuracy, physical properties, and
+                  comparison with post-Newtonian results}",
+     journal   = "Phys. Rev.",
+     volume    = "D82",
+     year      = "2010",
+     pages     = "124008",
+     eprint    = "1007.4789",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1103/PhysRevD.82.124008",
+     SLACcitation  = "%%CITATION = 1007.4789;%%"
+}
+
+@Article{Campanelli:2008nk,
+     author    = "Campanelli, Manuela and Lousto, Carlos O. and Nakano,
+                  Hiroyuki and Zlochower, Yosef",
+     title     = "{Comparison of Numerical and Post-Newtonian Waveforms for
+                  Generic Precessing Black-Hole Binaries}",
+     journal   = "Phys. Rev.",
+     volume    = "D79",
+     year      = "2009",
+     pages     = "084010",
+     eprint    = "0808.0713",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1103/PhysRevD.79.084010",
+     SLACcitation  = "%%CITATION = 0808.0713;%%"
+}
+
+@Article{PhysRevD.47.2198,
+  title = {Observing binary inspiral in gravitational radiation: One interferometer},
+  author = {Finn, Lee Samuel and Chernoff, David F.},
+  journal = {Phys. Rev. D},
+  volume = {47},
+  number = {6},
+  pages = {2198--2219},
+  numpages = {21},
+  year = {1993},
+  month = {Mar},
+  doi = {10.1103/PhysRevD.47.2198},
+  publisher = {American Physical Society}
+}
+
+@Article{PhysRevD.64.124013,
+  title = {Coalescence of two spinning black holes: An effective one-body approach},
+  author = {Damour, Thibault },
+  journal = {Phys. Rev. D},
+  volume = {64},
+  number = {12},
+  pages = {124013},
+  numpages = {22},
+  year = {2001},
+  month = {Nov},
+  doi = {10.1103/PhysRevD.64.124013},
+  publisher = {American Physical Society}
+}
+
+@Article{Ajith:2009bn,
+  title = {Inspiral-Merger-Ringdown Waveforms for Black-Hole Binaries with Nonprecessing Spins},
+  author = {Ajith, P.  and Hannam, M.  and Husa, S.  and Chen, Y.  and Br\"ugmann, B.  and Dorband, N.  and M\"uller, D.  and Ohme, F.  and Pollney, D.  and Reisswig, C.  and Santamar\'\i{}a, L.  and Seiler, J. },
+  journal = {Phys. Rev. Lett.},
+  volume = {106},
+  number = {24},
+  pages = {241101},
+  numpages = {4},
+  year = {2011},
+  month = {Jun},
+  doi = {10.1103/PhysRevLett.106.241101},
+  publisher = {American Physical Society},
+  eprint    = {0909.2867},
+  archivePrefix = {arXiv"},
+  primaryClass  =  {gr-qc},
+  SLACcitation  = {%%CITATION = 0909.2867;%%}
+}
+
+@Article{Robinson:2008un,
+     author    = "Robinson, C. A. K. and Sathyaprakash, B. S. and Sengupta,
+                  Anand S.",
+     title     = "{A geometric algorithm for efficient coincident detection
+                  of gravitational waves}",
+     journal   = "Phys. Rev.",
+     volume    = "D78",
+     year      = "2008",
+     pages     = "062002",
+     eprint    = "0804.4816",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1103/PhysRevD.78.062002",
+     SLACcitation  = "%%CITATION = 0804.4816;%%"
+}
+@Article{Apostolatos:1995pj,
+     author    = "Apostolatos, T. A.",
+     title     = "Search templates for gravitational waves from precessing,
+                  inspiraling binaries",
+     journal   = "Phys. Rev. D",
+     volume    = "52",
+     year      = "1995",
+     pages     = "605-620",
+     SLACcitation  = "%%CITATION = PHRVA,D52,605;%%"
+}
+
+@misc{Lundgren,
+      author    = "Brown, D. and Lundgren, A. and Pekowsky, L. and O'Shaughnessy, R.",
+      note = "{In preparation.}"
+}
+
+@Article{Buonanno:2009zt,
+     author    = "Buonanno, Alessandra and Iyer, Bala and Ochsner, Evan and
+                  Pan, Yi and Sathyaprakash, B. S.",
+     title     = "{Comparison of post-Newtonian templates for compact binary
+                  inspiral signals in gravitational-wave detectors}",
+     journal   = "Phys. Rev. D",
+     volume    = "80",
+     year      = "2009",
+     pages     = "084043",
+     eprint    = "0907.0700",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1103/PhysRevD.80.084043",
+     SLACcitation  = "%%CITATION = 0907.0700;%%"
+}
+@Article{Ajith:2007xh,
+     author    = "Ajith, P.",
+     title     = "{Gravitational-wave data analysis using binary black-hole
+                  waveforms}",
+     journal   = "Class. Quant. Grav.",
+     volume    = "25",
+     year      = "2008",
+     pages     = "114033",
+     eprint    = "",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1088/0264-9381/25/11/114033",
+     SLACcitation  = "%%CITATION = 0712.0343;%%"
+}
+
+
+@ARTICLE{1996Natur.381..584K,
+   author = {{Kaspi}, V.~M. and {Bailes}, M. and {Manchester}, R.~N. and 
+	{Stappers}, B.~W. and {Bell}, J.~F.},
+    title = "{Evidence from a processing pulsar orbit for a neutron-star birth kick}",
+  journal = {\nat},
+     year = 1996,
+    month = jun,
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+    pages = {584-586},
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+   adsurl = {http://adsabs.harvard.edu/abs/1996Natur.381..584K},
+  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
+}
+
+@Article{O'Leary:2007qa,
+     author    = "O'Leary, Ryan and O'Shaughnessy, Richard W. and Rasio,
+                  Frederic",
+     title     = "{Dynamical Interactions and the Black Hole Merger Rate of
+                  the Universe}",
+     journal   = "Phys. Rev. D",
+     volume    = "76",
+     year      = "2007",
+     pages     = "061504",
+     eprint    = "astro-ph/0701887",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.76.061504",
+     SLACcitation  = "%%CITATION = ASTRO-PH/0701887;%%"
+}
+
+@article{lrr-2006-6,
+  title    = {The Evolution of Compact Binary Star Systems},
+  author   = {Konstantin A. Postnov, Lev R. Yungelson},
+  journal  = {Living Reviews in Relativity},
+  year     = {2006},
+  number   = {6},
+  volume   = {9},
+  keywords = {astrophysics, binary systems, gravitational wave sources, supernovae, neutron stars, black holes, white dwarfs, AM CVn stars},
+  url      = {http://www.livingreviews.org/lrr-2006-6}
+}
+%
+% Note: Encoded in UTF-8! To use with TeX, adapt the encoding 
+% (with tools 'recode' or 'iconv') or use the ucs package 
+% (http://ctan.tug.org/tex-archive/macros/latex/contrib/unicode/)
+%
+  
+@Article{Allen:2004gu,
+     author    = "Allen, Bruce",
+     title     = "{A chi**2 time-frequency discriminator for gravitational
+                  wave detection}",
+     journal   = "Phys. Rev.",
+     volume    = "D71",
+     year      = "2005",
+     pages     = "062001",
+     eprint    = "gr-qc/0405045",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.71.062001",
+     SLACcitation  = "%%CITATION = GR-QC/0405045;%%"
+}
+
+@Article{VanDenBroeck:2006ar,
+     author    = "Van Den Broeck, Chris and Sengupta, Anand S.",
+     title     = "{Binary black hole spectroscopy}",
+     journal   = "Class. Quant. Grav.",
+     volume    = "24",
+     year      = "2007",
+     pages     = "1089-1114",
+     eprint    = "gr-qc/0610126",
+     archivePrefix = "arXiv",
+     doi       = "10.1088/0264-9381/24/5/005",
+     SLACcitation  = "%%CITATION = GR-QC/0610126;%%"
+}
+@Article{Ajith:2009fz,
+     author    = "Ajith, P. and Bose, Sukanta",
+     title     = "{Estimating the parameters of non-spinning binary black
+                  holes using ground-based gravitational-wave detectors:
+                  Statistical errors}",
+     journal   = "Phys. Rev. D",
+     volume    = "79",
+     pages     = "084032",
+     year      = "2009",
+     eprint    = "",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     SLACcitation  = "%%CITATION = 0901.4936;%%"
+}
+
+@book{NRecipes,
+     author = "Press, W. H. and Teukolsky, S. A. and Vetterling, W. T. and Flannery, B. P.",
+     title = "Numerical Recipes 3rd Edition: The Art of Scientific Computing",
+     year = "2007",
+     publisher = "Cambridge University Press",
+}
+
+@Article{amoeba,
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+
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+     author    = "McKechan, D. J. A. and Robinson, C. and Sathyaprakash, B.
+                  S.",
+     title     = "{A tapering window for time-domain templates and simulated
+                  signals in the detection of gravitational waves from
+                  coalescing compact binaries}",
+     journal   = "Class. Quant. Grav.",
+     volume    = "27",
+     year      = "2010",
+     pages     = "084020",
+     eprint    = "1003.2939",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1088/0264-9381/27/8/084020",
+     SLACcitation  = "%%CITATION = 1003.2939;%%"
+}
+
+@misc{LAL,
+      title = "{LSC} {A}lgorithms {L}ibrary",
+      url = "https://www.lsc-group.phys.uwm.edu/daswg/projects/lalsuite.html"
+}
+
+@misc{FFTW,
+      url = "http://www.fftw.org/"
+}
+
+@Article{Goldstein:2011ju,
+     author    = "Goldstein, Adam and others",
+     title     = "{A New Derivation of GRB Jet Opening Angles from the Prompt
+                  Gamma-Ray Emission}",
+     year      = "2011",
+     eprint    = "1101.2458",
+     archivePrefix = "arXiv",
+     primaryClass  =  "astro-ph.HE",
+     SLACcitation  = "%%CITATION = 1101.2458;%%"
+}
+
+@misc{AdLigoUrl,
+     url = "https://www.advancedligo.mit.edu/"
+}
+
+@misc{AdvLIGOPSD,
+     title         = {Advanced LIGO anticipated sensitivity curves}, 
+     note = {{L}IGO Document T0900288-v3},
+     url = {https://dcc.ligo.org/cgi-bin/DocDB/ShowDocument?docid=2974}
+}
+
+@Article{DIS01,
+     author    = "Damour, Thibault and others
+                  ",
+     title     = "A comparison of search templates for gravitational waves
+                  from binary  inspiral",
+     journal   = "Phys. Rev. D",
+     volume    = "63",
+     year      = "2001",
+     pages     = "044023",
+     eprint    = "",
+     SLACcitation  = "%%CITATION = GR-QC 0010009;%%"
+}
+
+@article{DIS98,
+     author        = {Damour, T. and Iyer, B R and Sathyaprakash, B S},
+     title         = {Improved filters for gravitational waves from inspiraling compact binaries},
+     journal       = {Phys. Rev. D},
+     volume        = {57},
+     pages         = {885--907},
+     year          = {1998},
+     keywords      = {Binary systems, Gravitational wave detectors},
+     onlinetitle   = {Improved filters for gravitational waves from inspiralling compact binaries},
+     onlineyear    = {1997},
+     fileformat    = {Online Los Alamos Preprint},
+     onlineaddress = {http://xxx.lanl.gov/abs/gr-qc/9708034},
+     cited         = {18 August 1997},
+     ReferencedIn  = {2002-3blanchet}
+}
+
+@Article{DJS2000,
+  title     = {Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation},
+  author    = {Damour, Thibault  and Jaranowski, Piotr  and Sch\"afer, Gerhard },
+  journal   = {Phys. Rev. D},
+  volume    = {62},
+  number    = {4},
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+  numpages  = {17},
+  year      = {2000},
+  month     = {Jul},
+  doi       = {10.1103/PhysRevD.62.044024},
+  publisher = {American Physical Society}
+}
+
+
+@Article{PhysRevD.54.2438,
+  title = {Influence of spin-spin coupling on inspiraling compact binaries with $M1=M2$ and $S1=S2$},
+  author = {Apostolatos, Theocharis A.},
+  journal = {Phys. Rev. D},
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+  number = {4},
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+  numpages = {3},
+  year = {1996},
+  month = {Aug},
+  doi = {10.1103/PhysRevD.54.2438},
+  publisher = {American Physical Society}
+}
+
+@Article{Baker05a,
+        author = {John G. Baker and others},
+        title =        {Gravitational wave extraction from an inspiraling
+                  configuration of merging black holes},
+        journal   = "Phys. Rev. Lett.",
+        volume    = "96",
+        year      = "2006",
+        pages     = "111102",
+        eprint    = {},
+}
+
+@Article{Blanchet:LivRev,
+  title    = {Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries},
+  author   = {Luc Blanchet},
+  journal  = {Living Rev. Relativity},
+  year     = {2006},
+  number   = {4},
+  volume   = {9},
+  eprint   = {gr-qc/0202016},
+  keywords = {gravitational radiation, post-Newtonian approximation, multipolar expansion, inspiralling compact binary},
+  url      = {http://www.livingreviews.org/lrr-2006-4}
+}
+
+@Article{PhysRevD.49.6274,
+  title = {Spin-induced orbital precession and its modulation of the gravitational waveforms from merging binaries},
+  author = {Apostolatos, Theocharis A. and others},
+  journal = {Phys. Rev. D},
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+  numpages = {23},
+  year = {1994},
+  month = {Jun},
+  doi = {10.1103/PhysRevD.49.6274},
+  publisher = {American Physical Society}
+}
+
+@ARTICLE{Kalogera:2004pr,
+   author = {{Kalogera}, V.},
+    title = "{Binary compact object inspiral: Detection expectations}",
+  journal = {Pramana},
+ keywords = {Compact objects, inspiral, event rates, precession.},
+     year = 2004,
+    month = oct,
+   volume = 63,
+    pages = {673-+},
+   adsurl = {http://adsabs.harvard.edu/abs/2004Prama..63..673K},
+  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
+}
+
+@ARTICLE{2005AJ....129.1993M,
+   author = {{Manchester}, R.~N. and {Hobbs}, G.~B. and {Teoh}, A. and {Hobbs}, M.
+	},
+    title = "{The Australia Telescope National Facility Pulsar Catalogue}",
+  journal = {Astronomical Journal},
+   eprint = {arXiv:astro-ph/0412641},
+ keywords = {Catalogs, Stars: Pulsars: General},
+     year = 2005,
+    month = apr,
+   volume = 129,
+    pages = {1993-2006},
+      doi = {10.1086/428488},
+   adsurl = {http://adsabs.harvard.edu/abs/2005AJ....129.1993M},
+  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
+}
+
+@Article{Sturani:2010ju,
+     author    = "Sturani, R. and others",
+     title     = "{Phenomenological gravitational waveforms from spinning
+                  coalescing binaries}",
+     year      = "2010",
+     eprint    = "1012.5172",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     SLACcitation  = "%%CITATION = 1012.5172;%%"
+}
+
+@Article{Santamaria:2010yb,
+     author    = "Santamaria, L. and others",
+     title     = "{Matching post-Newtonian and numerical relativity
+                  waveforms: systematic errors and a new phenomenological
+                  model for non-precessing black hole binaries}",
+     journal   = "Phys. Rev.",
+     volume    = "D82",
+     year      = "2010",
+     pages     = "064016",
+     eprint    = "1005.3306",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1103/PhysRevD.82.064016",
+     SLACcitation  = "%%CITATION = 1005.3306;%%"
+}
+
+@phdthesis{FaziThesis,
+ author = {Diego Fazi},
+ title = {Development of a physical-template search for gravitational waves from spinning compact-object binaries with LIGO},
+ year = {2009},
+ school = {University of Bologna}
+}
+
+@Article{Harry:2010fr,
+     author    = "Harry, Ian W. and Fairhurst, Stephen",
+     title     = "{A targeted coherent search for gravitational waves from
+                  compact binary coalescences}",
+     journal   = "Phys. Rev.",
+     volume    = "D83",
+     year      = "2011",
+     pages     = "084002",
+     eprint    = "1012.4939",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1103/PhysRevD.83.084002",
+     SLACcitation  = "%%CITATION = 1012.4939;%%"
+}
+
+@Article{Jones:2010iv,
+     author    = "Jones, Gareth",
+     title     = "{Searching for gravitational waves emitted by binaries with
+                  spinning components}",
+     year      = "2010",
+     eprint    = "1002.1876",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     SLACcitation  = "%%CITATION = 1002.1876;%%"
+}
+
+@Article{Pan:2003qt,
+     author    = "Pan, Yi and Buonanno, Alessandra and Chen, Yanbei and
+                  Vallisneri, Michele",
+     title     = "{A physical template family for gravitational waves from
+                  precessing  binaries of spinning compact objects:
+                  Application to single-spin  binaries}",
+     journal   = "Phys. Rev.",
+     volume    = "D69",
+     year      = "2004",
+     pages     = "104017",
+     eprint    = "gr-qc/0310034",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.69.104017",
+     SLACcitation  = "%%CITATION = GR-QC/0310034;%%"
+}
+
+@Article{VanDenBroeck:2009gd,
+     author    = "Van Den Broeck, Chris and others",
+     title     = "{Template banks to search for compact binaries with
+                  spinning components in gravitational wave data}",
+     journal   = "Phys. Rev. D",
+     volume    = "80",
+     year      = "2009",
+     pages     = "024009",
+     eprint    = "0904.1715",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1103/PhysRevD.80.024009",
+     SLACcitation  = "%%CITATION = 0904.1715;%%"
+}
+
+@Article{PhysRevD.78.042002,
+  title = {Search of S3 LIGO data for gravitational wave signals from spinning black hole and neutron star binary inspirals},
+  collaboration = {LIGO Scientific Collaboration},
+  author = {Abbott, B.  and others},
+  journal = {Phys. Rev. D},
+  volume = {78},
+  number = {4},
+  pages = {042002},
+  numpages = {19},
+  year = {2008},
+  month = {Aug},
+  doi = {10.1103/PhysRevD.78.042002},
+  publisher = {American Physical Society}
+}
+
+
+@Article{PhysRevD.67.042003,
+  title = {Searching for gravitational waves from the inspiral of precessing binary systems: Problems with current waveforms},
+  author = {Grandcl\'ement, Philippe  and Kalogera, Vassiliki  and Vecchio, Alberto },
+  journal = {Phys. Rev. D},
+  volume = {67},
+  number = {4},
+  pages = {042003},
+  numpages = {6},
+  year = {2003},
+  month = {Feb},
+  doi = {10.1103/PhysRevD.67.042003},
+  publisher = {American Physical Society}
+}
+
+@Article{Sathyaprakash:1991mt,
+     author    = "Sathyaprakash, B. S. and Dhurandhar, S. V.",
+     title     = "{Choice of filters for the detection of gravitational waves
+                  from coalescing binaries}",
+     journal   = "Phys. Rev.",
+     volume    = "D44",
+     year      = "1991",
+     pages     = "3819-3834",
+     doi       = "10.1103/PhysRevD.44.3819",
+     SLACcitation  = "%%CITATION = PHRVA,D44,3819;%%"
+}
+
+@Article{Sathyaprakash:1994,
+  title = {Filtering post-Newtonian gravitational waves from coalescing binaries},
+  author = {Sathyaprakash, B. S.},
+  journal = {Phys. Rev. D},
+  volume = {50},
+  number = {12},
+  pages = {R7111--R7115},
+  numpages = {4},
+  year = {1994},
+  month = {Dec},
+  doi = {10.1103/PhysRevD.50.R7111},
+  publisher = {American Physical Society}
+}
+
+@Article{Owen:1995tm,
+     author    = "Owen, Benjamin J.",
+     title     = "Search templates for gravitational waves from inspiraling
+                  binaries: Choice of template spacing",
+     journal   = "Phys. Rev. D",
+     volume    = "53",
+     year      = "1996",
+     pages     = "6749-6761",
+     eprint    = "gr-qc/9511032",
+     SLACcitation  = "%%CITATION = GR-QC/9511032;%%"
+}
+
+
+@Article{Damour:2009kr,
+     author    = "Damour, Thibault and Nagar, Alessandro",
+     title     = "{An improved analytical description of inspiralling and
+                  coalescing black-hole binaries}",
+     journal   = "Phys. Rev. D",
+     volume    = "79",
+     year      = "2009",
+     pages     = "081503",
+     eprint    = "0902.0136",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     doi       = "10.1103/PhysRevD.79.081503",
+     SLACcitation  = "%%CITATION = 0902.0136;%%"
+}
+
+@Article{Volonteri:2004cf,
+     author    = "Volonteri, Marta and Madau, Piero and Quataert, Eliot and
+                  Rees, Martin J.",
+     title     = "{The distribution and cosmic evolution of massive black
+                  hole spins}",
+     journal   = "Astrophys. J.",
+     volume    = "620",
+     year      = "2005",
+     pages     = "69-77",
+     eprint    = "astro-ph/0410342",
+     archivePrefix = "arXiv",
+     doi       = "10.1086/426858",
+     SLACcitation  = "%%CITATION = ASTRO-PH/0410342;%%"
+}
+
+@Article{McClintock:2011zq,
+     author    = "McClintock, Jeffrey E. and others",
+     title     = "{Measuring the Spins of Accreting Black Holes}",
+     journal   = "Class. Quant. Grav.",
+     volume    = "28",
+     year      = "2011",
+     pages     = "114009",
+     eprint    = "1101.0811",
+     archivePrefix = "arXiv",
+     primaryClass  =  "astro-ph.HE",
+     doi       = "10.1088/0264-9381/28/11/114009",
+     SLACcitation  = "%%CITATION = 1101.0811;%%"
+}
+
+@Article{BCV2,
+     author    = "Buonanno, Alessandra and Chen, Yanbei and Vallisneri,
+                  Michele",
+     title     = "Detecting gravitational waves from precessing binaries of
+                  spinning compact objects: Adiabatic limit",
+     journal   = "Phys. Rev. D",
+     volume    = "67",
+     year      = "2003",
+     pages     = "104025",
+     eprint    = "gr-qc/0211087",
+     SLACcitation  = "%%CITATION = GR-QC/0211087;%%"
+}
+
+@book{Helstrom,
+ author = {Carl W. Helstrom},
+ title = {Elements of signal detection and estimation},
+ year = {1995},
+ isbn = {0-13-808940-X},
+ publisher = {Prentice-Hall, Inc.},
+ address = {Upper Saddle River, NJ, USA},
+ }
+
+@incollection{schutz-91,
+  address   = {Cambridge, U.K.; New York, U.S.A.},
+  author    = {Schutz, B.F.},
+  booktitle = {The Detection of Gravitational Waves},
+  editor    = {Blair, D.G.},
+  format    = {print},
+  keywords  = {Gravitational wave data analysis, Signal detection},
+  pages     = {406--452},
+  publisher = {Cambridge University Press},
+  title     = {Data processing, analysis and storage for interferometric antennas},
+  year      = {1991}
+}
+
+@Article{Blanchet:2011zv,
+     author    = "Blanchet, Luc and Buonanno, Alessandra and Faye, Guillaume
+                  ",
+     title     = "{Tail-induced spin-orbit effect in the gravitational
+                  radiation of compact binaries}",
+     year      = "2011",
+     eprint    = "1104.5659",
+     archivePrefix = "arXiv",
+     primaryClass  =  "gr-qc",
+     SLACcitation  = "%%CITATION = 1104.5659;%%"
+}
+
+@Article{Ajith:2007kx,
+  author =	 "Ajith, P. and others",
+  title =	 "{A template bank for gravitational waveforms from
+                  coalescing binary black holes: I. non-spinning
+                  binaries}",
+  journal =	 "Phys. Rev.",
+  volume =	 "D77",
+  year =	 2008,
+  pages =	 104017,
+  eprint =	 "0710.2335",
+  archivePrefix ="arXiv",
+  primaryClass = "gr-qc",
+  doi =		 "10.1103/PhysRevD.77.104017",
+  SLACcitation = "%%CITATION = 0710.2335;%%"
+}
+
+@Article{Alvi:2001,
+  title =	 {Energy and angular momentum flow into a black hole
+                  in a binary},
+  author =	 {Kashif Alvi},
+  journal =	 prd,
+  volume =	 64,
+  number =	 10,
+  pages =	 104020,
+  numpages =	 9,
+  year =	 2001,
+  month =	 {Oct},
+  url =		 {http://link.aps.org/doi/10.1103/PhysRevD.64.104020}
+}
+
+@Article{Arun:2004hn,
+     author    = "Arun, K. G. and Iyer, Bala R. and Sathyaprakash, B.
+S. and
+                  Sundararajan, Pranesh A.",
+     title     = "{Parameter estimation of inspiralling compact
+binaries
+                  using 3.5  post-Newtonian gravitational wave
+phasing: The
+                  non-spinning case}",
+     journal   = "Phys. Rev.",
+     volume    = "D71",
+     year      = "2005",
+     pages     = "084008",
+     eprint    = "gr-qc/0411146",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.71.084008",
+     SLACcitation  = "%%CITATION = GR-QC/0411146;%%"
+}
+
+
+@Article{Arun:2009,
+  title =	 {Higher-order spin effects in the amplitude and phase
+                  of gravitational waveforms emitted by inspiraling
+                  compact binaries: {R}eady-to-use gravitational
+                  waveforms},
+  volume =	 79,
+  url =		 {http://link.aps.org/doi/10.1103/PhysRevD.79.104023},
+  doi =		 {10.1103/PhysRevD.79.104023},
+  number =	 10,
+  journal =	 prd,
+  author =	 {K. G. Arun and Alessandra Buonanno and Guillaume
+                  Faye and Evan Ochsner},
+  month =	 may,
+  year =	 2009,
+  pages =	 104023,
+}
+
+@Article{Aylott:2009tn,
+  author =	 "Aylott, Benjamin and others",
+  title =	 "{Status of NINJA: the Numerical INJection Analysis
+                  project}",
+  journal =	 "Class. Quant. Grav.",
+  volume =	 26,
+  year =	 2009,
+  pages =	 114008,
+  eprint =	 "0905.4227",
+  archivePrefix ="arXiv",
+  primaryClass = "gr-qc",
+  doi =		 "10.1088/0264-9381/26/11/114008",
+  SLACcitation = "%%CITATION = 0905.4227;%%"
+}
+
+@Article{Aylott:2009ya,
+  author =	 "Aylott, Benjamin and others",
+  title =	 "{Testing gravitational-wave searches with numerical
+                  relativity waveforms: Results from the first
+                  Numerical INJection Analysis (NINJA) project}",
+  journal =	 "Class. Quant. Grav.",
+  volume =	 26,
+  year =	 2009,
+  pages =	 165008,
+  eprint =	 "0901.4399",
+  archivePrefix ="arXiv",
+  primaryClass = "gr-qc",
+  doi =		 "10.1088/0264-9381/26/16/165008",
+  SLACcitation = "%%CITATION = 0901.4399;%%"
+}
+
+@Article{Baker:2005vv,
+  author =	 "Baker, John G. and Centrella, Joan and Choi, Dae-Il
+                  and Koppitz, Michael and van Meter, James",
+  title =	 "{Gravitational wave extraction from an inspiraling
+                  configuration of merging black holes}",
+  journal =	 "Phys. Rev. Lett.",
+  volume =	 96,
+  year =	 2006,
+  pages =	 111102,
+  eprint =	 "gr-qc/0511103",
+  archivePrefix ="arXiv",
+  doi =		 "10.1103/PhysRevLett.96.111102",
+  SLACcitation = "%%CITATION = GR-QC/0511103;%%"
+}
+
+@Article{Blanchet:1996,
+  title =	 {Gravitational waveforms from inspiralling compact
+                  binaries to {second-post-Newtonian} order},
+  volume =	 13,
+  url =		 {http://stacks.iop.org/0264-9381/13/i=4/a=002},
+  number =	 4,
+  journal =	 cqg,
+  author =	 {Luc Blanchet and Bala R Iyer and Clifford M Will and
+                  Alan G Wiseman},
+  year =	 1996,
+  pages =	 575
+}
+
+@Article{Blanchet:2001,
+  title =	 {General relativistic dynamics of compact binaries at
+                  the third post-{N}ewtonian order},
+  volume =	 63,
+  url =		 {http://link.aps.org/doi/10.1103/PhysRevD.63.062005},
+  doi =		 {10.1103/PhysRevD.63.062005},
+  number =	 6,
+  journal =	 prd,
+  author =	 {Luc Blanchet and Guillaume Faye},
+  month =	 feb,
+  year =	 2001,
+  pages =	 062005
+}
+
+@Article{Blanchet:2002,
+  title =	 {Gravitational-wave inspiral of compact binary
+                  systems to $7/2$ post-{N}ewtonian order},
+  author =	 {Blanchet, Luc and Faye, Guillaume and Iyer, Bala
+                  R. and Joguet, Benoit},
+  journal =	 prd,
+  volume =	 65,
+  number =	 6,
+  pages =	 061501,
+  numpages =	 5,
+  year =	 2002,
+  month =	 {Feb},
+  url =		 {http://link.aps.org/doi/10.1103/PhysRevD.65.061501},
+  doi =		 {10.1103/PhysRevD.65.061501},
+  publisher =	 {American Physical Society}
+}
+
+@Article{Blanchet:2004,
+  title =	 {Gravitational Radiation from Inspiralling Compact
+                  Binaries Completed at the Third Post-{N}ewtonian
+                  Order},
+  volume =	 93,
+  url =
+                  {http://link.aps.org/doi/10.1103/PhysRevLett.93.091101},
+  doi =		 {10.1103/PhysRevLett.93.091101},
+  number =	 9,
+  journal =	 prl,
+  author =	 {Luc Blanchet and Thibault Damour and Gilles
+                  {Esposito-Far\`ese} and Bala R. Iyer},
+  year =	 2004,
+  pages =	 091101
+}
+
+@Article{Blanchet:2005a,
+  title =	 {Erratum: {G}ravitational-wave inspiral of compact
+                  binary systems to $7/2$ post-{N}ewtonian order
+                  [{Phys. Rev. D 65, 061501(R) (2002)}]},
+  author =	 {Blanchet, Luc and Faye, Guillaume and Iyer, Bala
+                  R. and Joguet, Benoit },
+  journal =	 prd,
+  volume =	 71,
+  number =	 12,
+  pages =	 129902,
+  numpages =	 2,
+  year =	 2005,
+  month =	 {Jun},
+  doi =		 {10.1103/PhysRevD.71.129902},
+  url =		 {http://link.aps.org/doi/10.1103/PhysRevD.71.129902},
+  publisher =	 {American Physical Society}
+}
+
+@Article{Blanchet:2005b,
+  title =	 {Erratum: {G}ravitational waves from inspiraling
+                  compact binaries: {E}nergy flux to third
+                  post-{N}ewtonian order [{Phys. Rev. D 65, 064005
+                  (2002)}]},
+  author =	 {Blanchet, Luc and Iyer, Bala R. and Joguet, Benoit },
+  journal =	 {Phys. Rev. D},
+  volume =	 71,
+  number =	 12,
+  pages =	 129903,
+  numpages =	 1,
+  year =	 2005,
+  month =	 {Jun},
+  url =		 {http://link.aps.org/doi/10.1103/PhysRevD.71.129903},
+  doi =		 {10.1103/PhysRevD.71.129903},
+  publisher =	 {American Physical Society}
+}
+
+@Article{Blanchet:2006gy,
+  title =	 {Higher-order spin effects in the dynamics of compact
+                  binaries. {II.} {R}adiation field},
+  volume =	 74,
+  url =		 {http://link.aps.org/doi/10.1103/PhysRevD.74.104034},
+  doi =		 {10.1103/PhysRevD.74.104034},
+  number =	 10,
+  journal =	 prd,
+  author =	 {Luc Blanchet and Alessandra Buonanno and Guillaume
+                  Faye},
+  month =	 nov,
+  year =	 2006,
+  note =	 {Note the two associated errata; the arXiv version
+                  has been corrected},
+  eprint =	 "gr-qc/0605140v4",
+  archivePrefix ="arXiv",
+  pages =	 104034
+}
+
+@Article{Blanchet:2007,
+  title =	 {Erratum: Higher-order spin effects in the dynamics
+                  of compact binaries. {II.} {R}adiation field
+                  {[Phys. Rev. D} 74, 104034 (2006)]},
+  volume =	 75,
+  shorttitle =	 {Erratum},
+  url =		 {http://link.aps.org/doi/10.1103/PhysRevD.75.049903},
+  doi =		 {10.1103/PhysRevD.75.049903},
+  number =	 4,
+  journal =	 prd,
+  author =	 {Luc Blanchet and Alessandra Buonanno and Guillaume
+                  Faye},
+  month =	 feb,
+  year =	 2007,
+  pages =	 049903
+}
+
+@Article{Blanchet:2008,
+  title =	 {The third post-{N}ewtonian gravitational wave
+                  polarizations and associated spherical harmonic
+                  modes for inspiralling compact binaries in
+                  quasi-circular orbits},
+  volume =	 25,
+  issn =	 {0264-9381},
+  url =		 {http://stacks.iop.org/0264-9381/25/i=16/a=165003},
+  number =	 16,
+  journal =	 cqg,
+  author =	 {Luc Blanchet and Guillaume Faye and Bala R. Iyer and
+                  Siddhartha Sinha},
+  year =	 2008,
+  pages =	 165003
+}
+
+@Article{Blanchet:2010,
+  title =	 {Erratum: {H}igher-order spin effects in the dynamics
+                  of compact binaries. {II.} {R}adiation field
+                  {[Phys. Rev. D} 74, 104034 (2006)]},
+  volume =	 81,
+  shorttitle =	 {Erratum},
+  url =		 {http://link.aps.org/doi/10.1103/PhysRevD.81.089901},
+  doi =		 {10.1103/PhysRevD.81.089901},
+  number =	 8,
+  journal =	 prd,
+  author =	 {Luc Blanchet and Alessandra Buonanno and Guillaume
+                  Faye},
+  month =	 apr,
+  year =	 2010,
+  pages =	 089901
+}
+
+@Article{Brown:2007jx,
+  author =	 "Brown, D. and others",
+  title =	 "{Data formats for numerical relativity waves}",
+  year =	 2007,
+  eprint =	 "0709.0093",
+  archivePrefix ="arXiv",
+  primaryClass = "gr-qc",
+  SLACcitation = "%%CITATION = 0709.0093;%%"
+}
+
+@Article{Buonanno:2007pf,
+  author =	 "Buonanno, Alessandra and others",
+  title =	 "{Toward faithful templates for non-spinning binary
+                  black holes using the effective-one-body approach}",
+  journal =	 "Phys. Rev.",
+  volume =	 "D76",
+  year =	 2007,
+  pages =	 104049,
+  eprint =	 "0706.3732",
+  archivePrefix ="arXiv",
+  primaryClass = "gr-qc",
+  doi =		 "10.1103/PhysRevD.76.104049",
+  SLACcitation = "%%CITATION = 0706.3732;%%"
+}
+
+@Article{Campanelli:2005dd,
+  author =	 "Campanelli, Manuela and Lousto, C. O. and
+                  Marronetti, P.  and Zlochower, Y.",
+  title =	 "{Accurate Evolutions of Orbiting Black-Hole Binaries
+                  Without Excision}",
+  journal =	 "Phys. Rev. Lett.",
+  volume =	 96,
+  year =	 2006,
+  pages =	 111101,
+  eprint =	 "gr-qc/0511048",
+  archivePrefix ="arXiv",
+  doi =		 "10.1103/PhysRevLett.96.111101",
+  SLACcitation = "%%CITATION = GR-QC/0511048;%%"
+}
+
+@Article{Damour:2000zb,
+     author    = "Damour, Thibault and Iyer, Bala R. and
+Sathyaprakash, B. S.
+                  ",
+     title     = "{A comparison of search templates for gravitational
+waves
+                  from binary  inspiral}",
+     journal   = "Phys. Rev.",
+     volume    = "D63",
+     year      = "2001",
+     pages     = "044023",
+     eprint    = "gr-qc/0010009",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.63.044023",
+     SLACcitation  = "%%CITATION = GR-QC/0010009;%%"
+}
+
+@Article{Damour:2002kr,
+     author    = "Damour, Thibault and Iyer, Bala R. and
+Sathyaprakash, B. S.
+                  ",
+     title     = "{A comparison of search templates for gravitational
+waves
+                  from binary  inspiral: 3.5-PN update}",
+     journal   = "Phys. Rev.",
+     volume    = "D66",
+     year      = "2002",
+     pages     = "027502",
+     eprint    = "gr-qc/0207021",
+     archivePrefix = "arXiv",
+     doi       = "10.1103/PhysRevD.66.027502",
+     SLACcitation  = "%%CITATION = GR-QC/0207021;%%"
+}
+
+
+
+@Article{Duez:2009yz,
+  author =	 "Duez, Matthew D.",
+  title =	 "{Numerical relativity confronts compact neutron star
+                  binaries: a review and status report}",
+  year =	 2009,
+  eprint =	 "0912.3529",
+  archivePrefix ="arXiv",
+  primaryClass = "astro-ph.HE",
+  SLACcitation = "%%CITATION = 0912.3529;%%"
+}
+
+@Article{Faber:2009zz,
+  author =	 "Faber, Joshua",
+  title =	 "{Status of neutron star-black hole and binary
+                  neutron star simulations}",
+  journal =	 "Class. Quant. Grav.",
+  volume =	 26,
+  year =	 2009,
+  pages =	 114004,
+  doi =		 "10.1088/0264-9381/26/11/114004",
+  SLACcitation = "%%CITATION = CQGRD,26,114004;%%"
+}
+
+@Article{Hannam:2009hh,
+  author =	 "Hannam, Mark and others",
+  title =	 "{The Samurai Project: verifying the consistency of
+                  black- hole-binary waveforms for gravitational-wave
+                  detection}",
+  journal =	 "Phys. Rev.",
+  volume =	 "D79",
+  year =	 2009,
+  pages =	 084025,
+  eprint =	 "0901.2437",
+  archivePrefix ="arXiv",
+  primaryClass = "gr-qc",
+  doi =		 "10.1103/PhysRevD.79.084025",
+  SLACcitation = "%%CITATION = 0901.2437;%%"
+}
+
+@Article{Hannam:2009rd,
+  author =	 "Hannam, Mark",
+  title =	 "{Status of black-hole-binary simulations for
+                  gravitational- wave detection}",
+  journal =	 "Class. Quant. Grav.",
+  volume =	 26,
+  year =	 2009,
+  pages =	 114001,
+  eprint =	 "0901.2931",
+  archivePrefix ="arXiv",
+  primaryClass = "gr-qc",
+  doi =		 "10.1088/0264-9381/26/11/114001",
+  SLACcitation = "%%CITATION = 0901.2931;%%"
+}
+
+@Article{Hinder:2010vn,
+  author =	 "Hinder, Ian",
+  title =	 "{The Current Status of Binary Black Hole Simulations
+                  in Numerical Relativity}",
+  year =	 2010,
+  eprint =	 "1001.5161",
+  archivePrefix ="arXiv",
+  primaryClass = "gr-qc",
+  SLACcitation = "%%CITATION = 1001.5161;%%"
+}
+
+@Article{Husa:2007zz,
+  author =	 "Husa, Sascha",
+  title =	 "{Numerical modeling of black holes as sources of
+                  gravitational waves in a nutshell}",
+  journal =	 "Eur. Phys. J. ST",
+  volume =	 152,
+  year =	 2007,
+  pages =	 "183-207",
+  eprint =	 "0812.4395",
+  archivePrefix ="arXiv",
+  primaryClass = "gr-qc",
+  doi =		 "10.1140/epjst/e2007-00381-6",
+  SLACcitation = "%%CITATION = 0812.4395;%%"
+}
+
+@Article{Ott:2008wt,
+  author =	 "Ott, Christian D.",
+  title =	 "{The Gravitational Wave Signature of Core-Collapse
+                  Supernovae}",
+  journal =	 "Class. Quant. Grav.",
+  volume =	 26,
+  year =	 2009,
+  pages =	 063001,
+  eprint =	 "0809.0695",
+  archivePrefix ="arXiv",
+  primaryClass = "astro-ph",
+  doi =		 "10.1088/0264-9381/26/6/063001",
+  SLACcitation = "%%CITATION = 0809.0695;%%"
+}
+
+@Article{Pretorius:2005gq,
+  author =	 "Pretorius, Frans",
+  title =	 "{Evolution of Binary Black Hole Spacetimes}",
+  journal =	 "Phys. Rev. Lett.",
+  volume =	 95,
+  year =	 2005,
+  pages =	 121101,
+  eprint =	 "gr-qc/0507014",
+  archivePrefix ="arXiv",
+  doi =		 "10.1103/PhysRevLett.95.121101",
+  SLACcitation = "%%CITATION = GR-QC/0507014;%%"
+}
+
+@Article{Pretorius:2007nq,
+  author =	 "Pretorius, Frans",
+  title =	 "{Binary Black Hole Coalescence}",
+  year =	 2007,
+  eprint =	 "0710.1338",
+  archivePrefix ="arXiv",
+  primaryClass = "gr-qc",
+  SLACcitation = "%%CITATION = 0710.1338;%%"
+}
+
+@Article{Tagoshi:1997,
+  title =	 {{Post-Newtonian} Expansion of Gravitational Waves
+                  from a Particle in Circular Orbits around a Rotating
+                  Black Hole {:Effects} of Black Hole Absorption},
+  shorttitle =	 {{Post-Newtonian} Expansion of Gravitational Waves
+                  from a Particle in Circular Orbits around a Rotating
+                  Black Hole},
+  url =		 {http://arxiv.org/abs/gr-qc/9711072},
+  doi =		 {doi:10.1143/PTP.98.829},
+  journal =	 {gr-qc/9711072},
+  author =	 {Hideyuki Tagoshi and Shuhei Mano and Eiichi
+                  Takasugi},
+  month =	 nov,
+  year =	 1997,
+}
+
+@Article{WillWiseman:1996,
+  title =	 {Gravitational radiation from compact binary systems:
+                  Gravitational waveforms and energy loss to second
+                  {post-Newtonian} order},
+  volume =	 54,
+  url =		 {http://link.aps.org/doi/10.1103/PhysRevD.54.4813},
+  doi =		 {10.1103/PhysRevD.54.4813},
+  number =	 8,
+  journal =	 prd,
+  author =	 {Clifford M. Will and Alan G. Wiseman},
+  month =	 oct,
+  year =	 1996,
+  pages =	 4813
+}
+
+@TECHREPORT{lalspec,
+    author = "{Abbott et al.\ (LIGO Scientific Collaboration)}, B.~P.",
+    number = "T990030-v2",
+    month  = "April",
+    year   = "2010",
+}
+
+@article{Centrella:2010mx,
+      author         = "Centrella, Joan M. and Baker, John G. and Kelly, Bernard
+                        J. and van Meter, James R.",
+      title          = "{Black-hole binaries, gravitational waves, and numerical
+                        relativity}",
+      journal        = "Rev.Mod.Phys.",
+      volume         = "82",
+      year           = "19??",
+      note           = "* Temporary entry *",
+      eprint         = "1010.5260",
+      archivePrefix  = "arXiv",
+      primaryClass   = "gr-qc",
+}

Lab.tex

+\documentclass[prd,preprintnumbers,eqsecnum,floatfix,letterpaper,nofootinbib]{revtex4}
+\usepackage{color}
+\usepackage{url}
+\usepackage{calc}
+\usepackage{amsmath,amssymb,graphicx}
+\usepackage{amssymb,amsmath}
+\usepackage{tensor}
+\usepackage{bm}
+\usepackage{times}
+\usepackage[varg]{txfonts}
+\usepackage[colorlinks, pdfborder={0 0 0}]{hyperref}
+\definecolor{LinkColor}{rgb}{0.75, 0, 0}
+\definecolor{CiteColor}{rgb}{0, 0.5, 0.5}
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+\maxdeadcycles=1000
+\allowdisplaybreaks
+\newcommand{\comment}[1]{\textcolor{red}{\textit{#1}}}
+\newcommand{\checkthis}{\textcolor{magenta}{(CHECKTHIS)}}
+
+\newcommand{\bx}{\mathbf{x}}
+\newcommand{\boldeta}{\bm{\eta}}
+
+\begin{document}
+
+\newcommand{\be}{\begin{equation}}
+\newcommand{\ee}{\end{equation}}
+\newcommand{\ber}{\begin{eqnarray}}
+\newcommand{\eer}{\end{eqnarray}}
+\def\bea{\begin{eqnarray}}
+\def\eea{\end{eqnarray}}
+\newcommand{\etal}{\emph{et al.}}
+
+\newcommand{\Sl}{S_\ell}
+\newcommand{\Sigmal}{\Sigma_\ell}
+\newcommand{\Flux}{\mathcal{F}}
+\newcommand{\LNh}{\hat{\mathbf{L}}_N}
+\newcommand{\LN}{\mathbf{L}_N}
+\newcommand{\bS}{\mathbf{S}}
+\newcommand{\bJ}{\mathbf{J}}
+\newcommand{\e}{\mathrm{e}}
+\newcommand{\rmi}{\mathrm{i}}
+\newcommand{\flow}{f_\mathrm{low}}
+\newcommand{\fcut}{f_\mathrm{cut}}
+
+\newcommand{\bchi}{\bm{\chi}}
+\newcommand{\blambda}{\bm{\lambda}}
+\newcommand{\bLambda}{\bm{\Lambda}}
+\newcommand{\bchia}{\bm{\chi}_a}
+\newcommand{\bchis}{\bm{\chi}_s}
+\newcommand{\chis}{\chi_s}
+\newcommand{\chia}{\chi_a}
+\newcommand{\chiadL}{\bchia \cdot \LNh}
+\newcommand{\chisdL}{\bchis \cdot \LNh}
+\newcommand{\chisSqr}{\bchis^2}
+\newcommand{\chiaSqr}{\bchia^2}
+\newcommand{\chisDchia}{\bchis \cdot \bchia}
+\newcommand{\cA}{\mathcal{A}}
+\newcommand{\cB}{\mathcal{B}}
+\newcommand{\cC}{\mathcal{C}}
+\newcommand{\cP}{\mathcal{P}}
+
+
+\title{ICTS Graduate Course: Numerical Methods (PHY410.5)}
+\author{P.~Ajith}\email{ajith@icts.res.in}
+\author{Prayush Kumar}\email{prayush@icts.res.in}
+\affiliation{International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India.}
+\bigskip
+\date{\today}
+\maketitle
+
+\section{Numerical differentiation}
+\input{diff.tex}
+
+%\section{Lab 2}
+%\input{rest.tex}
+
+\bibliography{Lab}
+\end{document}

Makefile

+#
+# $Header: /numrelcvs/NumrelGWDA/docs/TemplBank/Makefile,v 1.4 2007/09/23 10:57:22 ajith Exp $
+#
+
+DOCS = Lab.pdf
+
+BYPROD = Lab.ps Lab.blg
+
+TEXS = Lab.tex 
+
+FIGS = 
+
+default: ${DOCS}
+
+#Lab.pdf: Lab.ps
+#	ps2pdf Lab.ps Lab.pdf
+
+#Lab.ps: Lab.dvi ${FIGS}
+#	dvips -t a4 -P pdf -o Lab.ps Lab.dvi
+
+Lab.pdf: Lab.tex ${FIGS} ${TEXS}
+#	latex Lab && latex Lab && latex Lab && bibtex Lab
+	pdflatex Lab  && bibtex Lab && bibtex Lab && pdflatex Lab && pdflatex Lab 
+
+Lab.ps: Lab.pdf ${FIGS}
+	pdftops Lab.pdf
+
+%.pdf: %.eps
+	epstopdf --outfile=$@ ${@:.pdf=.eps}
+
+clean:
+	rm -f *.aux *.log *.out *.dvi *~ ${DOCS} ${BYPROD}
+
+copy:
+	cp Lab.pdf /Users/pajith/Sites/ICTS/P._Ajiths_Homepage/Teaching_files
+publish: 
+	/Users/pajith/Sites/ICTS/P._Ajiths_Homepage/updateweb.sh

diff.tex

+\subsection{Finite differencing, convergence, error estimates}
+
+We derived the following finite-differencing approximants for the derivative of a function $f(x)$: 
+\begin{eqnarray}
+\mathit{Forward~differencing:} & f'(x) \simeq \frac{f(x+h)-f(x)}{h} + \mathcal{O}\,(h) \\
+\mathit{Backward~differencing:} & f'(x) \simeq \frac{f(x)-f(x-h)}{h} + \mathcal{O}\,(h) \\
+\mathit{Central~differencing:} & f'(x) \simeq \frac{f(x+h)-f(x-h)}{2h} + \mathcal{O}\,(h^2)
+\end{eqnarray}
+
+\subsubsection*{Problems:}
+\begin{enumerate}
+\item Write a Python function to compute derivatives using these three finite differencing methods. Compute the derivative of the function $f(x) = e^x \, \sin(x)$ over the range $x = [0, 2\pi]$. Plot the numerically computed derivative $f_{(h)}'(x)$ for three different values of $h$. 
+\item Plot the error $\Delta f_{h}'(x) := |f_{h}'(x) - f'(x)|$ for three different values of $h$, and estimate the order of convergence $n$ of each finite-difference approximation. Plot $n(x)$, where 
+\begin{equation}
+n(x) = \log_2 \frac{f'_{4h}(x) - f'_{2h}(x)}{f'_{2h}(x) - f'_{h}(x)}
+\label{eq:order_convg}
+\end{equation}
+\item Reduce the step size $h$ successively. At what value of $h$ does the round-off error dominate the error budget? 
+%\item Derive a central differencing approximant for the first derivative $f'(x)$ that is accurate to $\mathcal{O}(h^4)$. 
+\end{enumerate}
+
+\subsection{Richardson extrapolation}
+
+We have seen that, if the order of the error in the numerical estimate of a function $f(x)$ is known, Richardson extrapolation provides a powerful way of improving the accuracy of the estimate. If we have two numerical estimates $f_{h}(x)$ and $f_{2h}(x)$ each having an error of $\mathcal{O}\,h^k$, a better estimate is given by 
+\begin{equation}
+f(x) \simeq \frac{2 ~ 2^k\, f_{h}(x) - f_{2h}(x)}{2\,2^k -1 } + \mathcal{O}\,(h^{l}),
+\end{equation}
+where $l$ is the next-to-leading-order error term (for e.g., $l = k+2$ for central differencing, while $l = k+1$ for forward/backward differencing). 
+
+\subsubsection*{Problems:}
+\label{sec:BBH_nr_data_fd}
+\begin{enumerate}
+\item Gravitational-waves (GWs) have two independent polarization states -- called ``plus'' and ``cross'' states. GW signals from the coalescence of black-hole binaries, in the simplest case, are circularly polarized: 
+\begin{eqnarray}
+h_+(t) & = A(t) \, \cos \varphi(t), ~~~ h_\times(t) & = A(t) \, \sin \varphi(t). 
+\end{eqnarray}
+Download the data file~\cite{nrdata} containing $h_+(t)$ and $h_\times(t)$. (This is the reduced form of the data produced by a numerical-relativity simulation of black-hole binaries performed by the SXS collaboration and is publicly available at~\cite{SXScatalog}). Compute the phase evolution $\varphi(t)$, the frequency evolution $\omega(t) := d\varphi(t)/dt$ and the rate of change of frequency $\dot{\omega}(t) := d\omega(t)/dt$ using second-order central difference approximation. 
+\item Estimate the order of convergence of the numerical computation of $\omega(t)$ and $\dot{\omega}(t)$. 
+\item Perform an extrapolation of $\omega(t)$ and $\dot{\omega}(t)$ to the next order using estimates of two different time-resolutions.  
+\item Derive an explicit expression for $f'(x)$ with error $\mathcal{O}(h^4)$ using Richardson extrapolation. This is the fourth-order finite differencing approximant for the derivative, which we will use later. 
+
+\end{enumerate}