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1 | (24) |
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1.1 ABOUT THE SOFTWARE MATLAB |
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1 | (1) |
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1.2 AN INTRODUCTION TO MATLAB |
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2 | (15) |
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1.2.1 Matrices and matrix computation |
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2 | (5) |
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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 | (1) |
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12 | (1) |
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1.2.8 Relations and loops |
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13 | (4) |
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17 | (8) |
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2 Number System and Errors |
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25 | (20) |
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2.1 FLOATING-POINT ARITHMETIC |
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25 | (5) |
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30 | (6) |
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36 | (2) |
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38 | (7) |
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45 | (66) |
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47 | (8) |
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3.2 THE METHOD OF FALSE POSITION |
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55 | (7) |
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3.3 FIXED-POINT ITERATION |
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62 | (8) |
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70 | (6) |
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76 | (11) |
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3.6 CONVERGENCE OF THE NEWTON AND SECANT METHODS |
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87 | (3) |
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3.7 MULTIPLE ROOTS AND THE MODIFIED NEWTON METHOD |
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90 | (7) |
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3.8 NEWTON'S METHOD FOR NONLINEAR SYSTEMS |
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97 | (6) |
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103 | (8) |
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4 System of Linear Equations |
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111 | (68) |
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4.1 MATRICES AND MATRIX OPERATIONS |
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112 | (4) |
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4.2 NAIVE GAUSSIAN ELIMINATION |
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116 | (8) |
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4.3 GAUSSIAN ELIMINATION WITH SCALED PARTIAL PIVOTING |
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124 | (15) |
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139 | (16) |
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4.4.1 Croft's and Choleski's methods |
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140 | (4) |
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4.4.2 Gaussian elimination method |
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144 | (11) |
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155 | (15) |
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4.5.1 Jacobi iterative method |
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156 | (3) |
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4.5.2 Gauss-Seidel iterative method |
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159 | (1) |
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160 | (10) |
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170 | (9) |
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179 | (32) |
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5.1 POLYNOMIAL INTERPOLATION THEORY |
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180 | (3) |
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5.2 NEWTON'S DIVIDED DIFFERENCE INTERPOLATINGPOLYNOMIAL |
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183 | (12) |
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5.3 THE ERROR OF THE INTERPOLATING POLYNOMIAL |
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195 | (6) |
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5.4 LAGRANGE INTERPOLATING POLYNOMIAL |
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201 | (6) |
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207 | (4) |
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6 Interpolation with Spline Functions |
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211 | (32) |
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6.1 PIECEWISE LINEAR INTERPOLATION |
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212 | (7) |
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219 | (5) |
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6.3 NATURAL CUBIC SPLINES |
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224 | (16) |
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240 | (3) |
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7 The Method of Least Squares |
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243 | (32) |
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244 | (7) |
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7.2 LEAST SQUARES POLYNOMIAL |
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251 | (9) |
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7.3 NONLINEAR LEAST SQUARES |
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260 | (9) |
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260 | (2) |
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262 | (7) |
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7.4 TRIGONOMETRIC LEAST SQUARES POLYNOMIAL |
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269 | (3) |
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272 | (3) |
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275 | (26) |
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8.1 ANALYSIS OF SINGLE-VARIABLE FUNCTIONS |
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276 | (2) |
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278 | (16) |
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8.2.1 Bracketing the minimum |
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278 | (1) |
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8.2.2 Golden section search |
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279 | (4) |
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283 | (3) |
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8.2.4 Parabolic Interpolation |
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286 | (8) |
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8.3 MINIMIZATION USING DERIVATIVES |
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294 | (4) |
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294 | (1) |
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295 | (3) |
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298 | (3) |
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9 Numerical Differentiation |
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301 | (20) |
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9.1 NUMERICAL DIFFERENTIATION |
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301 | (8) |
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309 | (7) |
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316 | (5) |
| 10 Numerical Integration |
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321 | (50) |
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322 | (11) |
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333 | (11) |
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344 | (9) |
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353 | (12) |
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365 | (6) |
| 11 Numerical Methods for Differential Equations |
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371 | (86) |
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372 | (8) |
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380 | (5) |
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11.3 HIGHER ORDER TAYLOR SERIES METHODS |
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385 | (5) |
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390 | (16) |
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406 | (1) |
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11.6 ADAMS-BASHFORTH METHODS |
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406 | (11) |
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11.7 PREDICTOR-CORRECTOR METHODS |
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417 | (1) |
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11.8 ADAMS-MOULTON METHODS |
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418 | (9) |
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427 | (4) |
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11.10 HIGHER ORDER EQUATIONS AND SYSTEMS OF DIFFERENTIAL EQUATIONS |
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431 | (7) |
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11.11 IMPLICIT METHODS AND STIFF SYSTEMS |
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438 | (3) |
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11.12 PHASE PLANE ANALYSIS: CHAOTIC DIFFERENTIAL EQUATIONS |
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441 | (6) |
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447 | (10) |
| 12 Boundary-Value Problems |
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457 | (28) |
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12.1 FINITE-DIFFERENCE METHODS |
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458 | (9) |
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467 | (13) |
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12.2.1 The nonlinear case |
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467 | (5) |
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472 | (8) |
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480 | (5) |
| 13 Eigenvalues and Eigenvectors |
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485 | (30) |
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485 | (5) |
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490 | (4) |
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13.3 THE QUADRATIC METHOD |
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494 | (11) |
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13.4 EIGENVALUES FOR BOUNDARY-VALUE PROBLEMS |
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505 | (3) |
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13.5 BIFURCATIONS IN DIFFERENTIAL EQUATIONS |
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508 | (5) |
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513 | (2) |
| 14 Partial Differential Equations |
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515 | (44) |
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516 | (13) |
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516 | (5) |
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521 | (8) |
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14.2 HYPERBOLIC EQUATIONS |
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529 | (7) |
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536 | (7) |
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14.4 INTRODUCTION TO FINITE-ELEMENT METHOD |
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543 | (14) |
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543 | (8) |
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14.4.2 The Finite Element Method |
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551 | (6) |
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557 | (2) |
| Bibliography and References |
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559 | (6) |
| Appendix |
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565 | (10) |
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565 | (4) |
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A.1 Limits and continuity |
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565 | (1) |
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566 | (1) |
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567 | (2) |
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B MATLAB Built-in Functions |
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569 | (4) |
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573 | (2) |
| Answers to Selected Exercises |
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575 | (28) |
| Index |
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603 | |