Introduction
Computational Physics and Computational Science
How to Use this Book
Computing Software Basics
Making Computers Obey
Computer Languages
Programming Warmup
Shells, Editors, and Programs
Limited Range and Precision of Numbers
Number Representation
IEEE Floating Point Numbers
Over/Underflows Exercise
Machine Precision
Determine Your Machine Precision
Structured Program Design
Summing Series
Numeric Summation
Good and Bad Pseudocode
Assessment
Errors and Uncertainties in Computations
Living with Errors
Types of Errors
Model for Disaster: Subtractive Cancellation
Subtractive Cancellation Exercises
Model for Roundoff Error Accumulation
Errors in Spherical Bessel Functions (Problem)
Numeric Recursion Relations (Method)
Implementation and Assessment: Recursion Relations
Experimental Error Determination
Errors in Algorithms
Minimizing the Error
Error Assessment
Object-Oriented Programming: Kinematics
Problem: Superposition of Motions
Theory: Object-Oriented Programming
Theory: Newton's Laws, Equation of Motion
OOP Method: Class Structure
Implementation: Uniform 1D Motion, unim1d.cpp
Assessment: Exploration, shms.cpp
Integration
Problem: Integrating a Spectrum
Quadrature as Box Counting (Math)
Algorithm: Trapezoid Rule
Algorithm: Simpson's Rule
Integration Error
Algorithm: Gaussian Quadrature
Empirical Error Estimate (Assessment)
Experimentation
Higher Order Rules
Differentiation
Problem 1: Numerical Limits
Method: Numeric
Forward Difference
Central Difference
Extrapolated Difference
Error Analysis
Error Analysis (Implementation and Assessment)
Second Derivatives
Trial and Error Searching
Quantum States in SquareWell
Trial-and-Error Root Finding via Bisection Algorithm
1 Bisection Algorithm Implementation
Newton-Raphson Algorithm
Matrix Computing and N-D Newton Raphson
Two Masses on a String
Classes of Matrix Problems
Data Fitting
Fitting Experimental Spectrum
Fitting Exponential Decay
Theory: Probability and Statistics
Least-Squares Fitting
Appendix: Calling LAPACK from C
Deterministic Randomness
Random Sequences
Monte Carlo Applications
A RandomWalk
Radioactive Decay
Implementation and Visualization
Integration by Stone Throwing
Integration by Rejection
High-Dimensional Integration
Integrating Rapidly Varying Functions
Thermodynamic Simulations: Ising Model
Statistical Mechanics
An Ising Chain (Model)
The Metropolis Algorithm
Computer Hardware Basics: Memory and CPU
High-Performance Computers
The Central Processing Unit
High-Performance Computing: Profiling and Tuning
Rules for Optimization
Programming for Data Cache
Differential Equation Applications
UNIT I. Free Nonlinear Oscillations
Nonlinear Oscillator
Math: Types of Differential Equations
Dynamical Form for ODEs
ODE Algorithms
Solution for Nonlinear Oscillations