Advanced Engineering Mathematics with Mathematica® presents advanced analytical solution methods that are used to solve boundary-value problems in engineering and integrates these methods with Mathematica® procedures. It emphasizes the Sturm–Liouville system and the generation and application of orthogonal functions, which are used by the separation of variables method to solve partial differential equations. It introduces the relevant aspects of complex variables, matrices and determinants, Fourier series and transforms, solution techniques for ordinary differential equations, the Laplace transform, and procedures to make ordinary and partial differential equations used in engineering non-dimensional. To show the diverse applications of the material, numerous and widely varied solved boundary value problems are presented.
Table of Contents
1. Matrices, Determinants, and Systems of Equations
2. Introduction to Complex Variables
3. Fourier Series and Fourier Transforms
4. Ordinary Differential Equations Part I: Review of First- and Second-Order Equations
5. Ordinary Differential Equations Part II: Power Series Solutions
6. Ordinary Differential Equations Part III: Sturm–Liouville Equation
7. Partial Differential Equations
8. Laplace Transforms
9. Putting It All Together—Examples from the Literature
Edward B. Magrab is Emeritus Professor in the Department of Mechanical Engineering at the University of Maryland at College Park. He has extensive experience in analytical and experimental analysis of vibrations and acoustics, served as an engineering consultant to numerous companies, and authored or coauthored a number of books on vibrations, noise control, instrumentation, integrated product design, and Mathematica®. He is a Life Fellow of the American Society of Mechanical Engineers.