|
Section
|
Topic
|
Page
|
|
Chapter 1
|
Introduction
|
3
|
|
1.1
|
The Nature of Computational Science
|
3
|
|
1.1.1
|
How Computational Scientists Do It (visualization)
|
4
|
|
1.2
|
Aims of This Book
|
5
|
|
1.3
|
Using this Book with the Disk and Web
|
6
|
|
Chapter 2
|
Computing Software Basics
|
9
|
|
2.1
|
Problem 1: Making Computers Obey (unix
help)
|
9
|
|
2.2
|
Theory: Computer Languages
|
9
|
|
2.3
|
Implementation: Programming Concepts
|
11
|
|
2.4
|
Implementation: Fortran, area.f
|
12
|
|
2.5
|
Implementation: C, area.c
|
13
|
|
2.6
|
Implementation: Shells,
Editors, and Programs
|
13
|
|
2.7
|
Theory: Program Design
|
14
|
|
2.8
|
Method: Structured Programming
|
16
|
|
2.9
|
Method: Programming Hints
|
17
|
|
2.10
|
Problem 2: Limited Range of Numbers
|
20
|
|
2.11
|
Theory: Number Representation
|
20
|
|
2.12
|
Method: Fixed and Floating
|
21
|
|
2.13
|
Implementation: Over- and Underflows, over.f
(.c)
|
23
|
|
2.14
|
Model: Machine Precision
|
23
|
|
2.15
|
Implementation: Determining Your Precision, limit.f
(.c)
|
25
|
|
2.16
|
Problem 3: Complex Numbers and Inverse Functions
|
25
|
|
2.17
|
Theory: Complex Numbers
|
25
|
|
2.18
|
Implementation: Complex Numbers, complex.c
(.f
)
|
27
|
|
2.19
|
Exploration: Complex energies in Quantum Mechanics
|
28
|
|
2.20
|
Problem 4: Summing Series
|
29
|
|
2.21
|
Method: Numeric
|
29
|
|
2.22
|
Implementation: Pseudocode
|
29
|
|
2.23
|
Implementation: Good Algorithm, exp-good.f
(.c)
|
30
|
|
2.24
|
Implementation: Bad Algorithm, exp-bad.f
(.c)
|
30
|
|
2.25
|
Assessment
|
30
|
|
Chapter 3
|
Errors and Uncertainties in Computations
|
31
|
|
3.1
|
Problem: Living with Errors
|
31
|
|
3.2
|
Theory: Types of Errors
|
32
|
|
3.3
|
Model: Subtractive Cancellation
|
33
|
|
3.4
|
Assessment: Subtractive Cancellation Experiment
|
34
|
|
3.5
|
Model: Multiplicative Error
|
36
|
|
3.6
|
Problem 1: Errors in Spherical Bessel Functions
|
37
|
|
3.7
|
Method: Numeric Recursion Relations
|
38
|
|
3.8
|
Implementation: Recursion Relations, bessel.f
(.c)
|
40
|
|
3.9
|
Assessment
|
40
|
|
3.10
|
Problem 2: Error in Algorithms
|
40
|
|
3.11
|
Model: Errors in Algorithms
|
41
|
|
3.11.1
|
Total Error
|
41
|
|
3.12
|
Method: Optimizing with Known Error Behavior
|
42
|
|
3.13
|
Method: Empirical Error Analysis
|
43
|
|
3.14
|
Assessment: Experiment
|
44
|
|
Chapter 4
|
Integration
|
47
|
|
4.1
|
Problem: Integrating a Spectrum
|
47
|
|
4.2
|
Model: Quadrature, Summing Boxes
|
47
|
|
4.3
|
Method: Trapezoid Rule
|
50
|
|
4.4
|
Method: Simpson's Rule
|
51
|
|
4.5
|
Assessment: Integration Error, Analytic
|
52
|
|
4.6
|
Method: Gaussian Quadrature
|
55
|
|
4.6.1
|
Scaling with Integration Rules
|
56
|
|
4.7
|
Implementation: Integration, integ.f
(.c)
|
58
|
|
4.8
|
Assessment: Empirical Error Estimate
|
58
|
|
4.9
|
Assessment: Experimentation
|
59
|
|
4.10
|
Method: Romberg Extrapolation
|
59
|
|
4.10.1
|
Other Closed Newton-Cotes Formulas
|
60
|