Scientific Computing and Differential Equations: An Introduction to Numerical Methods

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Elsevier, Jun 28, 2014 - Mathematics - 344 pages
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Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context.
This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also well-suited to serve as a textbook for numerical differential equations courses at the graduate level.
  • An introductory chapter gives an overview of scientific computing, indicating its important role in solving differential equations, and placing the subject in the larger environment
  • Contains an introduction to numerical methods for both ordinary and partial differential equations
  • Concentrates on ordinary differential equations, especially boundary-value problems
  • Contains most of the main topics for a first course in numerical methods, and can serve as a text for this course
  • Uses material for junior/senior level undergraduate courses in math and computer science plus material for numerical differential equations courses for engineering/science students at the graduate level

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Contents

Chapter 1 The World of Scientific Computing
1
Initial Value Problems
15
Boundary Value Problems
67
Chapter 4 More on Linear Systems of Equations
89
Chapter 5 Life Is Really Nonlinear
145
Chapter 6 Is There More Than Finite Differences?
179
Chapter 7 N Important Numbers
211
Chapter 8 Space and Time
247
Chapter 9 The Curse of Dimensionality
273
Analysis and Differential Equations
309
Linear Algebra
315
Bibliography
321
Author Index
329
Subject Index
333
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