An introduction to the numerical solution of differential equations. : D. Quinney, Research Studies Press/Wiley, 1985, 283 pages, £15, ISBN 0-86380-033-5/0-471-90849-5.
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 68 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0378-4754
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✦ Synopsis
This book can be used for a first course on numerical methods for solving ordinary and partial differential equations. The classical methods are presented in an informal way and the proofs of theorems are only given when they directly illustrate the applications. The book contains many worked numerical examples showing when the methods work and when they don't. Some exercices are also given. Contents: 1. Recurrence relations and iterative methods; 2. Ordinary differential equations, initial value problems; 3. Ordinary differential equations, boundary value problems; 4. Parabolic partial differential equations; 5. Hyperbolic partial differential equations; 6. Elliptic partial differential equations. (CB) G. Strang: Introduction to Applied Mathematics. Wellesley-Cambridge Press, 1986, 758 pages, $36, ISBN 0-9614088-O-4.
Applied mathematics deals with the numerical solution of equations (differential, partial differential and integral) arising from various sciences and thus it is of central importance for many people. Applied mathematics is changing and growing quite rapidly and it needed a modern and alive approach. It is the aim of this book to provide such a treatment and to be a text for applied mathematics, advanced calculus and engineering mathematics. It gives the essential classical methods and tools but it also reaches beyond the usual courses to introduce more recent ideas such as the Kalman filter, finite elements, strange attractors, solitons, combinatorial optimization. Karmarkar's method for linear programming and fast Fourier transforms.
The book is extremely well written and presented. It presents numerous interesting exercices with some solutions. Direct orders to the author at MIT are the simplest.
Contents: 1. Symmetric linear systems; 2. Equilibrium equations; 3. Equilibrium in the continuous case; 4. Analytical methods; 5. Numerical methods; 6. Initial-value problems; 7. Network flows and combinatorics; 8. Optimization.