Numerical analysis

Team DDU......Page 1
Table of Contents......Page 7
Command Window......Page 13
Roots of Polynomials......Page 15
Polynomial Construction from Known Roots......Page 16
Evaluation of a Polynomial at Specified Values......Page 17
Rational Polynomials......Page 19
Using MATLAB to Make Plots......Page 21
Multiplication, Division and Exponentiation......Page 30
Script and Function Files......Page 37
Display Formats......Page 41
Summary......Page 42
Exercises......Page 47
Solutions to Exercises......Page 48
Newton\'s Method for Root Approximation......Page 51
Approximations with Spreadsheets......Page 57
The Bisection Method for Root Approximation......Page 69
Summary......Page 77
Exercises......Page 78
Solutions to Exercises......Page 79
Alternating Voltages and Currents......Page 85
Characteristics of Sinusoids......Page 86
Phasors......Page 94
Addition and Subtraction of Phasors......Page 95
Division of Phasors......Page 96
Exponential and Polar Forms of Phasors......Page 97
Summary......Page 102
Exercises......Page 105
Solutions to Exercises......Page 106
Matrix Definition......Page 111
Matrix Operations......Page 112
Special Forms of Matrices......Page 115
Determinants......Page 119
Minors and Cofactors......Page 122
Cramer\'s Rule......Page 126
Gaussian Elimination Method......Page 128
The Adjoint of a Matrix......Page 129
Singular and Non-Singular Matrices......Page 130
The Inverse of a Matrix......Page 131
Solution of Simultaneous Equations with Matrices......Page 133
Summary......Page 139
Exercises......Page 143
Solutions to Exercises......Page 145
Simple Differential Equations......Page 151
Classification......Page 152
Solutions of Ordinary Differential Equations (ODE)......Page 155
Solution of the Homogeneous ODE......Page 158
Using the Method of Undetermined Coefficients for the Forced Response......Page 160
Using the Method of Variation of Parameters for the Forced Response......Page 169
Expressing Differential Equations in State Equation Form......Page 173
Solution of Single State Equations......Page 177
The State Transition Matrix......Page 178
Computation of the State Transition Matrix......Page 180
Eigenvectors......Page 187
Summary......Page 191
Exercises......Page 196
Solutions to Exercises......Page 197
Wave Analysis......Page 205
Evaluation of the Coefficients......Page 206
Symmetry......Page 211
Waveforms in Trigonometric Form of Fourier Series......Page 216
Alternate Forms of the Trigonometric Fourier Series......Page 229
The Exponential Form of the Fourier Series......Page 232
Line Spectra......Page 237
Numerical Evaluation of Fourier Coefficients......Page 240
Power Series Expansion of Functions......Page 241
Taylor and Maclaurin Series......Page 244
Summary......Page 251
Exercises......Page 254
Solutions to Exercises......Page 256
Divided Differences......Page 265
Factorial Polynomials......Page 270
Antidifferences......Page 275
Newton\'s Divided Difference Interpolation Method......Page 279
Lagrange\'s Interpolation Method......Page 282
Gregory-Newton Forward Interpolation Method......Page 283
Gregory-Newton Backward Interpolation Method......Page 284
Interpolation with MATLAB......Page 287
Summary......Page 301
Exercises......Page 306
Solutions to Exercises......Page 307
Curve Fitting......Page 315
Linear Regression......Page 316
Parabolic Regression......Page 321
Regression with Power Series Approximations......Page 328
Summary......Page 338
Exercises......Page 340
Solutions to Exercises......Page 342
Taylor Series Method......Page 351
Runge-Kutta Method......Page 355
Adams\' Method......Page 363
Milne\'s Method......Page 366
Summary......Page 367
Exercises......Page 370
Solutions to Exercises......Page 371
The Trapezoidal Rule......Page 377
Simpson\'s Rule......Page 382
Summary......Page 389
Exercises......Page 391
Solution to Exercises......Page 392
Definition, Solutions, and Applications......Page 399
Fibonacci Numbers......Page 405
Summary......Page 408
Exercises......Page 411
Solutions to Exercises......Page 412
Partial Fraction Expansion......Page 415
Alternate Method of Partial Fraction Expansion......Page 427
Summary......Page 432
Exercises......Page 435
Solutions to Exercises......Page 436
The Gamma Function......Page 443
The Gamma Distribution......Page 457
The Beta Function......Page 459
The Beta Distribution......Page 462
Summary......Page 463
Exercises......Page 466
Solutions to Exercises......Page 467
Orthogonal Functions......Page 471
Orthogonal Trajectories......Page 472
Orthogonal Vectors......Page 474
The Gram-Schmidt Orthogonalization Procedure......Page 477
The LU Factorization......Page 479
The Cholesky Factorization......Page 485
The QR Factorization......Page 487
Singular Value Decomposition......Page 490
Summary......Page 491
Exercises......Page 493
Solutions to Exercises......Page 495
The Bessel Function......Page 501
Legendre Functions......Page 510
Laguerre Polynomials......Page 520
Chebyshev Polynomials......Page 521
Summary......Page 526
Exercises......Page 532
Solutions to Exercises......Page 533
Linear Programming......Page 539
Dynamic Programming......Page 542
Network Analysis......Page 552
Summary......Page 557
Exercises......Page 558
Solutions to Exercises......Page 560
Index......Page 567