Scientific Computing and Differential Equations: An Introduction to Numerical Methods

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 environmentContains an introduction to numerical methods for both ordinary and partial differential equationsConcentrates on ordinary differential equations, especially boundary-value problemsContains most of the main topics for a first course in numerical methods, and can serve as a text for this courseUses 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

The World of Scientific Computing. Letting It Fly. Initial Value Problems. Pinning It Down: Boundary Value Problems. More on Linear Systems of Equations. Life Is Really Nonlinear. Is There More Than Finite Differences? N Important Numbers. Space and Time. The Curse of Dimensionality. Appendixes: Analysis of Differential Equations. Linear Algebra. Bibliography. Index.