Approximation Techniques for Engineers, 2nd Edition

This second edition includes eleven new sections based on the approximation of matrix functions, deflating the solution space and improving the accuracy of approximate solutions, iterative solution of initial value problems of systems of ordinary differential equations, and the method of trial functions for boundary value problems. The topics of the two new chapters are integral equations and mathematical optimization. The book provides alternative solutions to software tools amenable to hand computations to validate the results obtained by “black box” solvers. It also offers an insight into the mathematics behind many CAD, CAE tools of the industry. The book aims to provide a working knowledge of the various approximation techniques for engineering practice.

Table of Contents

Part I Data Approximations
Chapter 1 Classical Interpolation Methods
Chapter 2 Approximation With Splines
Chapter 3 Least Squares Approximation
Chapter 4 Approximation Of Functions
Chapter 5 Numerical Differentiation
Chapter 6 Numerical Integration

Part II Approximate Solutions
Chapter 7 Nonlinear Equations In One Variable
Chapter 8 Systems Of Nonlinear Equations
Chapter 9 Iterative Solution Of Linear Systems
Chapter 10 Approximate Solution Of Eigenvalue Problems
Chapter 11 Initial Value Problems
Chapter 12 Boundary Value Problems
Chapter 13 Integral Equations
Chapter 14 Mathematical Optimization