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.

chapter 2|28 pages

Introduction to Complex Variables

chapter 3|38 pages

Fourier Series and Fourier Transforms

chapter 4|76 pages

Ordinary Differential Equations Part I

Review of First- and Second-Order Equations

chapter 5|80 pages

Ordinary Differential Equations Part II

Power Series Solutions

chapter 6|36 pages

Ordinary Differential Equations Part III

Sturm–Liouville Equation

chapter 7|118 pages

Partial Differential Equations

chapter 8|64 pages

Laplace Transforms