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1 | (20) |
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About the Software Matlab |
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1 | (1) |
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An Introduction to Matlab |
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2 | (11) |
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Matrices and matrix computation |
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2 | (4) |
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6 | (1) |
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7 | (1) |
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8 | (1) |
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9 | (1) |
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10 | (1) |
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11 | (2) |
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13 | (8) |
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21 | (16) |
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Floating-Point Arithmetic |
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21 | (5) |
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26 | (3) |
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29 | (1) |
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30 | (7) |
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37 | (42) |
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37 | (7) |
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The Method of False Position |
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44 | (4) |
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48 | (4) |
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52 | (6) |
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Convergence of the Newton and Secant Methods |
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58 | (2) |
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60 | (6) |
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Multiple Roots and the Modified Newton Method |
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66 | (6) |
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Newton's Method for Nonlinear Systems |
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72 | (7) |
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System of Linear Equations |
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79 | (52) |
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Matrices and Matrix Operations |
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79 | (4) |
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Naive Gaussian Elimination |
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83 | (9) |
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Gaussian Elimination with Scaled Partial Pivoting |
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92 | (10) |
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102 | (13) |
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Crout's and Choleski's methods |
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102 | (6) |
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Gaussian elimination method |
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108 | (7) |
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115 | (16) |
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115 | (4) |
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Gauss-Seidel iterative method |
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119 | (4) |
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123 | (8) |
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131 | (22) |
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Polynomial Interpolation Theory |
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132 | (2) |
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Newton's Divided Difference Interpolating Polynomial |
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134 | (10) |
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The Error of the Interpolating Polynomial |
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144 | (3) |
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Lagrange Interpolating Polynomial |
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147 | (6) |
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Interpolation with Spline Functions |
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153 | (22) |
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Piecewise Linear Interpolation |
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153 | (5) |
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158 | (3) |
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161 | (14) |
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The Method of Least Squares |
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175 | (28) |
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176 | (6) |
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182 | (8) |
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190 | (7) |
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191 | (2) |
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193 | (4) |
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Trigonometric Least Squares Polynomial |
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197 | (6) |
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Numerical Differentiation and Integration |
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203 | (44) |
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Numerical Differentiation |
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204 | (4) |
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208 | (6) |
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214 | (8) |
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222 | (8) |
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230 | (7) |
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237 | (10) |
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Numerical Methods for Ordinary Differential Equations |
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247 | (64) |
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247 | (7) |
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254 | (5) |
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Higher Order Taylor Series Methods |
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259 | (3) |
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262 | (10) |
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272 | (1) |
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273 | (9) |
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Predictor-Corrector Methods |
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282 | (1) |
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283 | (6) |
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289 | (3) |
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Higher Order Equations and Systems |
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292 | (7) |
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Implicit Methods and Stiff Systems |
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299 | (2) |
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Phase Plane Analysis: Chaotic Equations |
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301 | (10) |
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311 | (18) |
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Finite-Difference Methods |
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311 | (7) |
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318 | (11) |
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318 | (3) |
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321 | (8) |
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Eigenvalues and Eigenvectors |
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329 | (30) |
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329 | (5) |
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334 | (4) |
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338 | (11) |
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Eigenvalues for Boundary-Value Problems |
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349 | (3) |
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Bifurcations in Differential Equations |
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352 | (7) |
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Partial Differential Equations |
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359 | (30) |
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360 | (13) |
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360 | (6) |
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366 | (7) |
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373 | (7) |
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380 | (9) |
Bibliography and References |
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389 | (4) |
Appendix A Calculus Review |
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393 | (4) |
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A.0.1 Limits and continuity |
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393 | (1) |
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394 | (1) |
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394 | (3) |
Appendix B MATLAB Built-In Functions |
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397 | (4) |
Appendix C Text MATLAB Functions |
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401 | (2) |
Answers to Selected Exercises |
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403 | (24) |
Index |
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427 | |