Chapter 1: Introduction
1.1 Getting Started with Coding
1.2 Getting to Know the Linux Command Line
1.3 Bonjour Tout Le Monde
1.4 The Rest of the Book
Chapter 2: Getting Comfortable
2.1 Computers: What You Should Know
2.2 Some Important Mathematics
Exercises
Chapter 3: Interpolation and Data Fitting
3.1 Interpolation
3.2 Data Fitting
Exercises
Chapter 4: Searching for Roots
4.1 Finding Roots
4.2 Hybrid Methods
4.3 What’s The Point of Root Searching?
Exercises
Chapter 5: Numerical Quadrature
5.1 Simple Quadrature
5.2 Advanced Quadrature
Exercises
Chapter 6: Ordinary Differential Equations
6.1 Classification of Differential Equations
6.2 Solving First-Order ODEs
6.3 Solving Second-Order ODEs
Exercises
Chapter 7: Fourier Analysis
7.1 The Fourier Series
7.2 Fourier Transforms
7.3 The Discrete Fourier Transform
7.4 The Fast Fourier Transform
Exercises
Chapter 8: Monte Carlo Methods
8.1 Monte Carlo Integration
8.2 Monte Carlo Simulations
Exercises
Chapter 9: Partial Differential Equations
9.1 Classes, Boundary Values, and Initial Conditions
9.2 Finite Difference Methods
9.3 Richardson Extrapolation
9.4 Numerical Methods to Solve PDEs
9.5 Pointers to the Finite Element Method
Exercises
Chapter 10: Advanced Numerical Quadrature
10.1 General Quadrature
10.2 Orthogonal Polynomials
10.3 Gauss–Legendre Quadrature
10.4 Programming Gauss–Legendre
10.5 Gauss–Laguerre Quadrature
Exercises
Chapter 11: Advanced ODE Solver and Applications
11.1 Runge–Kutta–Fehlberg
11.2 Phase Space
11.3 Van Der Pol Oscillator
11.4 The “Simple” Pendulum
11.5 Halley’s Comet
11.6 To Infinity and Beyond
11.7 To The Infinitesimal and Below
Exercises
Chapter 12: High-Performance Computing
12.1 Indexing and Blocking
12.2 Parallel Programming
Exercises
Bibliography
Appendix: A Crash Course in C++ Programming
Index
