Book draft (2012)—feedback welcome

(This page is a stable link to this manuscript.)

The Third Branch of Physics: Essays on Scientific Computing

Norbert Schörghofer

Frontmatter

1. Analytic and Numeric Solutions
2. Roundoff and Number Representation
   • Number representation
   • IEEE standardization
   • Roundoff sensitivity basic
3. Themes of Numerical Analysis
   • Root finding: fast and unreliable
   • Error propagation and numerical instabilities
4. Programming Tools
   • Choosing a programming language
   • General-purpose mathematical software packages
   • Data visualization
5. Physics Sampler
   • Chaotic standard map
   • Celestial mechanics
6. Discrete Approximations of the Continuum
   • Differentiation: The art of finite-differencing
   • Verifying the convergence of a method
   • Numerical integration: Illusions about what lies between
7. From Programs to Data Analysis
   • Canned routines
   • Programming
   • Common beginner's mistakes
   • Data handling
   • Modern curve fitting
8. Performance Basics
   • Speed and limiting factors of computations
   • Data files
   • Parallel computing
9. Deep inside Computers
   • A programmer's view of computer hardware
   • Code optimization
   • Specialized hardware
10. Counting Operations
    • Introduction
    • Slow and fast methods for the determinant of a matrix
    • Non-intuitive operation counts in linear algebra
11. Random Numbers and Stochastic Methods
    • Generation of probabilistic distributions
    • Monte Carlo integration: accuracy through randomness
    • The Ising model
12. Algorithms, Data Structures, and Complexity
    • An example algorithm and data structures
    • Computational complexity; intractable problems
    • Complexity for finite precision
13. Symbolic Computation
    • Computer algebra systems
    • Diagrammatic techniques
14. A Crash Course on Partial Differential Equations
    • Initial value problems by finite differences
    • Numerical stability revisited
    • Methods for PDEs
15. Reformulated Boundary-Value Problems
    • Three formulations of electrostatics
    • Schrödinger equation
    • Outline of density functional method

Updates

Jul 2012: Many revisions and a few additions

Jan 2012: Some more changes and additions

Sep 2011: Finally got around to make changes and additions; among the additions is information about GPUs

Stable Links