Scientific Programming
Numeric, Symbolic, and Graphical Computing with Maxima
1st Edition
Published on 19. December 2018
562 pages
978-1-5275-2384-5 (ISBN)
Description
This book offers an introduction to computer programming, numerical analysis, and other mathematical ideas that extend the basic topics learned in calculus. It illustrates how mathematicians and scientists write computer programs, covering the general building blocks of programming languages and a description of how these concepts fit together to allow computers to produce the results they do. Topics explored here include binary arithmetic, algorithms for rendering graphics, the smooth interpolation of discrete data, and the numerical approximation of non-elementary integrals. The book uses an open-source computer algebra system called Maxima. Using Maxima, first-time programmers can perform familiar tasks, such as graphing functions or solving equations, and learn the basic structures of programming before moving on to other popular programming languages. The epilogue provides some simple examples of how this process works in practice. The book will particularly appeal to students who have finished their calculus sequence.
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Content
- Intro
- Table of Contents
- Foreword
- Chapter 1
- 1.1. Getting Started with Maxima
- 1.2. Symbolic Computation
- 1.3. User-Defined Functions
- 1.4. Repetition and Iteration
- 1.5. Leibniz's Series
- 1.6. Archimedes' Sequence
- 1.7. Computational Error
- Chapter 2
- 2.1. Fibonacci's Rabbits
- 2.2. The Babylonian Algorithm
- 2.3. Detecting Prime Numbers
- 2.4. Lists and Other Data Structures
- 2.5. Gaussian Elimination
- 2.6. Partial Pivoting
- 2.7. Binary Codes
- 2.8. Floating-Point Numbers
- Chapter 3
- 3.1. Celestial Mechanics
- 3.2. An Epitaph for Archimedes
- 3.3. Rabbits Revisited
- 3.4. Projectiles in Motion
- 3.5. Fourier Likes It Hot
- 3.6. Plotting Curves by Sampling
- 3.7. Plotting Lines with Pixels
- Chapter 4
- 4.1. Lagrange's Formula
- 4.2. Piecewise Linear Interpolation
- 4.3. Cubic Splines
- 4.4. Smooth Splines
- 4.5. Approximation with Splines
- 4.6. Interpolating Curves
- 4.7. Interpolating Surfaces
- Chapter 5
- 5.1. Riemann Sums
- 5.2. Trapezoids and Parabolas
- 5.3. Smooth Splines Revisited
- 5.4. Gaussian Quadrature
- 5.5. Monte Carlo Simulation
- Epilogue
- References
- Index
