Advanced Engineering Mathematics with Mathematica

Edward B. Magrab

• Publisher: CRC Press
• Year: 2020
• Print ISBN: 9780367893255
• eBook ISBN: 9781000034523
• Topic: Mathematics
• Subtopic: Civil Engineering
• Index: Mathematics

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.

1 Matrices, Determinants, and Systems of Equations

1.1 Definitions

A matrix is a rectangular array of numbers (or symbols or expressions) consisting of m rows and n columns. Such an array is called a matrix of order (m × n) [or simply an (m × n) matrix], and is denoted as

$$A=\left(\begin{array}{cccc}{a}_{\text{11}}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ ⋮& & & \\ a_{m1}& a_{m2}& \cdots & a_{mn}\end{array}\right)$$

(1.1)

where the a_ij are the elements of the array. The first subscript denotes the row, and the second subscript denotes the column in which the element appears. When the number of rows equals the number of columns, that is, when m = n, the matrix is called a square matrix of order n.

Operations with matrices are subject to certain rules, which will be indicated as we progress. It should be realized that a matrix is not a single quantity; it is a representation of an array ...

Table of contents

• Cover
• Half-Title
• Title
• Copyright
• Dedication
• Contents
• Preface
• Author
• Chapter 1 Matrices, Determinants, and Systems of Equations
• Chapter 2 Introduction to Complex Variables
• Chapter 3 Fourier Series and Fourier Transforms
• Chapter 4 Ordinary Differential Equations Part I: Review of First- and Second-Order Equations
• Chapter 5 Ordinary Differential Equations Part II: Power Series Solutions
• Chapter 6 Ordinary Differential Equations Part III: Sturm–Liouville Equation
• Chapter 7 Partial Differential Equations
• Chapter 8 Laplace Transforms
• Chapter 9 Putting It All Together—Examples from the Literature
• Appendix A Series Expansions
• Appendix B Delta Function
• Appendix C Gamma Function
• Bibliography
• Index