Book draft (last updated 2015)

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

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*Lessons in Scientific Computing*

Also known as
**The Third Branch of Physics: Essays on Scientific Computing**
*Norbert Schörghofer*

Frontmatter

- Analytic and Numeric Solutions
- A Few Concepts of Numerical Analysis
- Root finding: fast and unreliable
- Error propagation and numerical instabilities

- Roundoff and Number Representation
- Number representation
- Wonders of the IEEE standard
- Roundoff sensitivity basic

- Programming Tools
- Choosing a programming language
- General-purpose mathematical software packages
- Data visualization

- Physics Sampler
- Chaotic standard map
- Celestial mechanics

- Discrete Approximations of the Continuum
- Verifying the convergence of a method
- Differentiation: The art of finite-differencing
- Numerical integration: Illusions about what lies between

- From Programs to Data Analysis
- Canned routines
- Programming
- Data handling
- Modern curve fitting

- Performance Basics
- Speed and limiting factors of computations
- Data files
- Parallel computing

- Deep inside Computers
- A programmer's view of computer hardware
- Code optimization
- Specialized hardware

- Counting Operations
- Introduction
- Slow and fast methods for the determinant of a matrix
- Non-intuitive operation counts in linear algebra

- Random Numbers and Stochastic Methods
- Generation of probabilistic distributions
- Monte Carlo integration: accuracy through randomness
- The Ising model

- Algorithms, Data Structures, and Complexity
- An example algorithm and data structures
- Computational complexity; intractable problems
- Complexity for finite precision

- Symbolic Computation
- Computer algebra systems
- Diagrammatic techniques

- A Crash Course on Partial Differential Equations
- Initial value problems by finite differences
- Numerical stability revisited
- Methods for PDEs

- Reformulated Boundary-Value Problems
- Three formulations of electrostatics
- Schrödinger equation
- Outline of density functional method

Appendix A: Answers to Brainteasers

Appendix B: Notes

#### 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

`www2.hawaii.edu/~norbert/compphysics.html`

`tinyurl.com/computationalphysics`

Email author at *norbert@hawaii.edu*