Scientific Computing - An Introduction using Maple and MATLAB

1. Front Matter

   Pages I-XVIII

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2. Why Study Scientific Computing?

   • Walter Gander, Martin J. Gander, Felix Kwok

   Pages 1-8

3. Finite Precision Arithmetic

   • Walter Gander, Martin J. Gander, Felix Kwok

   Pages 9-60

4. Linear Systems of Equations

   • Walter Gander, Martin J. Gander, Felix Kwok

   Pages 61-112

5. Interpolation

   • Walter Gander, Martin J. Gander, Felix Kwok

   Pages 113-179

6. Nonlinear Equations

   • Walter Gander, Martin J. Gander, Felix Kwok

   Pages 181-259

7. Least Squares Problems

   • Walter Gander, Martin J. Gander, Felix Kwok

   Pages 261-385

8. Eigenvalue Problems

   • Walter Gander, Martin J. Gander, Felix Kwok

   Pages 387-486

9. Differentiation

   • Walter Gander, Martin J. Gander, Felix Kwok

   Pages 487-515

10. Quadrature

    • Walter Gander, Martin J. Gander, Felix Kwok

    Pages 517-582

11. Numerical Ordinary Differential Equations

    • Walter Gander, Martin J. Gander, Felix Kwok

    Pages 583-671

12. Iterative Methods for Linear Systems

    • Walter Gander, Martin J. Gander, Felix Kwok

    Pages 673-815

13. Optimization

    • Walter Gander, Martin J. Gander, Felix Kwok

    Pages 817-886

14. Back Matter

    Pages 887-914

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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”.

• numerical mathematics
• scientific computing

From the book reviews:

“This is an elaborate book on fundamental numerical methods including numerical ordinary differential equations and optimization. … All chapters are organized in the same nice way by beginning with an introductary example and ending with a large number of exercises. The presentation of the material is reader orientated such that e.g. a student can learn directly from the book. Many details are given and special attention lies on various numerical calculations which enlight the performance of the respective algorithms.” (Rolf Dieter Grigorieff, zbMATH, Vol. 1296, 2014)

• Departement Informatik, ETH Zürich, Zürich, Switzerland

  Walter Gander

• Section de Mathématiques, Université de Genève, Genève, Switzerland

  Martin J. Gander, Felix Kwok