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| Hardcover ISBN: | 978-0-8218-2953-0 |
| Product Code: | GSM/57 |
| List Price: | $135.00 |
| MAA Member Price: | $121.50 |
| AMS Member Price: | $108.00 |
| Softcover ISBN: | 978-0-8218-3414-5 |
| Product Code: | GSM/57.S |
| List Price: | $89.00 |
| MAA Member Price: | $80.10 |
| AMS Member Price: | $71.20 |
| eBook ISBN: | 978-1-4704-2103-8 |
| Product Code: | GSM/57.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Hardcover ISBN: | 978-0-8218-2953-0 |
| eBook ISBN: | 978-1-4704-2103-8 |
| Product Code: | GSM/57.B |
| List Price: | $220.00 $177.50 |
| MAA Member Price: | $198.00 $159.75 |
| AMS Member Price: | $176.00 $142.00 |
| Softcover ISBN: | 978-0-8218-3414-5 |
| eBook ISBN: | 978-1-4704-2103-8 |
| Product Code: | GSM/57.S.B |
| List Price: | $174.00 $131.50 |
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| AMS Member Price: | $139.20 $105.20 |
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Book DetailsGraduate Studies in MathematicsVolume: 57; 2003; 453 ppMSC: Primary 65
This book succinctly covers the key topics of numerical methods. While it is basically a survey of the subject, it has enough depth for the student to walk away with the ability to implement the methods by writing computer programs or by applying them to problems in physics or engineering.
The author manages to cover the essentials while avoiding redundancies and using well-chosen examples and exercises. The exposition is supplemented by numerous figures. Work estimates and pseudo codes are provided for many algorithms, which can be easily converted to computer programs. Topics covered include interpolation, the fast Fourier transform, iterative methods for solving systems of linear and nonlinear equations, numerical methods for solving ODEs, numerical methods for matrix eigenvalue problems, approximation theory, and computer arithmetic.
In general, the author assumes only a knowledge of calculus and linear algebra. The book is suitable as a text for a first course in numerical methods for mathematics students or students in neighboring fields, such as engineering, physics, and computer science.
ReadershipAdvanced undergraduates, graduate students, and research mathematicians interested in numerical methods; students in neighboring fields such as engineering, physics, and computer science.
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Table of Contents
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Chapters
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Chapter 1. Interpolation by polynomials
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Chapter 2. Spline functions
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Chapter 3. The discrete Fourier transform and its applications
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Chapter 4. Solution of linear systems of equations
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Chapter 5. Nonlinear systems of equations
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Chapter 6. The numerical integration of functions
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Chapter 7. Explicit one-step methods for initial value problems in ordinary differential equations
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Chapter 8. Multistep methods for initial value problems of ordinary differential equations
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Chapter 9. Boundary value problems for ordinary differential equations
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Chapter 10. Jacobi, Gauss-Seidel and relaxation methods for the solution of linear systems of equations
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Chapter 11. The conjugate gradient and GMRES methods
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Chapter 12. Eigenvalue problems
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Chapter 13. Numerical methods for eigenvalue problems
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Chapter 14. Peano’s error representation
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Chapter 15. Approximation theory
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Chapter 16. Computer arithmetic
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Additional Material
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Reviews
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From a review of the German edition:
Appealing result of [the author's] endeavours ... The presentation is concise ... avoiding unnecessary redundancies, but nevertheless is self-contained ... even instructors are offered new views and insights ... the author offers many well-chosen exercises ... The book really is a valuable contribution to the literature on its subject.
Zentralblatt MATH
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
This book succinctly covers the key topics of numerical methods. While it is basically a survey of the subject, it has enough depth for the student to walk away with the ability to implement the methods by writing computer programs or by applying them to problems in physics or engineering.
The author manages to cover the essentials while avoiding redundancies and using well-chosen examples and exercises. The exposition is supplemented by numerous figures. Work estimates and pseudo codes are provided for many algorithms, which can be easily converted to computer programs. Topics covered include interpolation, the fast Fourier transform, iterative methods for solving systems of linear and nonlinear equations, numerical methods for solving ODEs, numerical methods for matrix eigenvalue problems, approximation theory, and computer arithmetic.
In general, the author assumes only a knowledge of calculus and linear algebra. The book is suitable as a text for a first course in numerical methods for mathematics students or students in neighboring fields, such as engineering, physics, and computer science.
Advanced undergraduates, graduate students, and research mathematicians interested in numerical methods; students in neighboring fields such as engineering, physics, and computer science.
-
Chapters
-
Chapter 1. Interpolation by polynomials
-
Chapter 2. Spline functions
-
Chapter 3. The discrete Fourier transform and its applications
-
Chapter 4. Solution of linear systems of equations
-
Chapter 5. Nonlinear systems of equations
-
Chapter 6. The numerical integration of functions
-
Chapter 7. Explicit one-step methods for initial value problems in ordinary differential equations
-
Chapter 8. Multistep methods for initial value problems of ordinary differential equations
-
Chapter 9. Boundary value problems for ordinary differential equations
-
Chapter 10. Jacobi, Gauss-Seidel and relaxation methods for the solution of linear systems of equations
-
Chapter 11. The conjugate gradient and GMRES methods
-
Chapter 12. Eigenvalue problems
-
Chapter 13. Numerical methods for eigenvalue problems
-
Chapter 14. Peano’s error representation
-
Chapter 15. Approximation theory
-
Chapter 16. Computer arithmetic
-
From a review of the German edition:
Appealing result of [the author's] endeavours ... The presentation is concise ... avoiding unnecessary redundancies, but nevertheless is self-contained ... even instructors are offered new views and insights ... the author offers many well-chosen exercises ... The book really is a valuable contribution to the literature on its subject.
Zentralblatt MATH
