Scientific Computing – An Introduction using Maple and MATLAB

Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple – Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.

Table of Contents

Chapter 1. Why Study Scientific Computing?
Chapter 2. Finite Precision Arithmetic
Chapter 3. Linear Systems of Equations
Chapter 4. Interpolation
Chapter 5. Nonlinear Equations
Chapter 6. Least Squares Problems
Chapter 7. Eigenvalue Problems
Chapter 8. Differentiation
Chapter 9. Quadrature
Chapter 10. Numerical Ordinary Differential Equations
Chapter 11. Iterative Methods for Linear Systems
Chapter 12. Optimization