Also Available in Softcover GSM/57.S
Hardcover ISBN:  9780821829530 
Product Code:  GSM/57 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470421038 
Product Code:  GSM/57.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821829530 
eBook: ISBN:  9781470421038 
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 
Also Available in Softcover GSM/57.S
Hardcover ISBN:  9780821829530 
Product Code:  GSM/57 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470421038 
Product Code:  GSM/57.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821829530 
eBook ISBN:  9781470421038 
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 

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 wellchosen 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.

Table of Contents

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 onestep 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, GaussSeidel 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


Additional Material

Reviews

From a review of the German edition:
Appealing result of [the author's] endeavours ... The presentation is concise ... avoiding unnecessary redundancies, but nevertheless is selfcontained ... even instructors are offered new views and insights ... the author offers many wellchosen exercises ... The book really is a valuable contribution to the literature on its subject.
Zentralblatt MATH


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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 wellchosen 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 onestep 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, GaussSeidel 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 selfcontained ... even instructors are offered new views and insights ... the author offers many wellchosen exercises ... The book really is a valuable contribution to the literature on its subject.
Zentralblatt MATH