Preface

Chapter 1: Preliminaries

1.1 PROGRAMMING 1
1.2 BASIC ELEMENTS OF MATLAB 3
1.3 BASIC ELEMENTS OF C++ 10
1.4 PROGRAMS AND FUNCTIONS 16
1.5 NUMERICAL ERRORS 26

Chapter 2: Ordinary Differential Equations I: Basic Methods

2.1 PROJECTILE MOTION 37
2.2 SIMPLE PENDULUM 46

Chapter 3: Ordinary Differential Equations II: Advanced Methods

3.1 ORBITS OF COMETS 67
3.2 RUNGE-KUTTA METHODS 74
3.3 ADAPTIVE METHODS 81
3.4 *CHAOS IN THE LORENZ MODEL 86

*(Optional Section)

Chapter 4: Solving Systems of Equations

4.1 LINEAR SYSTEMS OF EQUATIONS 107
4.2 MATRIX INVERSE 116
4.3 *NONLINEAR SYSTEMS OF EQUATIONS 122

Chapter 5: Analysis of Data

5.1 CURVE FITTING 141
5.2 SPECTRAL ANALYSIS 153
5.3 *NORMAL MODES 163

Chapter 6: Partial Differential Equations I: Foundations and Explicit Methods

6.1 INTRODUCTION TO PDEs 191
6.2 DIFFUSION EQUATION 195
6.3 *CRITICAL MASS 202

Chapter 7: Partial Differential Equations II: Advanced Explicit Methods

7.1 ADVECTION EQUATION 215
7.2 *PHYSICS OF TRAFFIC FLOW 225

Chapter 8: Partial Differential Equations III: Relaxation and Spectral Methods

8.1 RELAXATION METHODS 249
8.2 *SPECTRAL METHODS 258

Chapter 9: Partial Differential Equations IV: Stability and Implicit Methods

9.1 STABILITY ANALYSIS 279
9.2 IMPLICIT SCHEMES 287
9.3 *SPARSE MATRICES 294

Chapter 10: Special Functions and Quadrature

10.1 SPECIAL FUNCTIONS 309
10.2 BASIC NUMERICAL INTEGRATION 318
10.3 *GAUSSIAN QUADRATURE 325

Chapter 11: Stochastic Methods

11.1 KINETIC THEORY 341
11.2 RANDOM NUMBER GENERATORS 347
11.3 DIRECT SIMULATION MONTE CARLO 356
11.4 *NONEQUILIBRIUM STATES 365

Bibliography

Selected Solutions

Index