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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.
Preface.
Author.
Matrices, Determinants, and Systems of Equations.
Introduction to Complex Variables.
Fourier Series and Fourier Transforms.
Ordinary Differential Equations Part I: Review of First- and Second-Order Equations.
Ordinary Differential Equations Part II: Power Series Solutions.
Ordinary Differential Equations Part III: Sturm–Liouville Equation.
Partial Differential Equations.
Laplace Transforms.
Putting It All Together—Examples from the Literature.
Appendix A Series Expansions.
Appendix B Delta Function.
Appendix C Gamma Function.
Bibliography.
Index