Mathematics for Engineering, Technology and Computing Science

The Commonwealth and International Library: Electrical Engineering Division

1st Edition - January 1, 1970

Author: Hedley G. Martin

Editor: N. Hiller

eBook ISBN:

9 7 8 - 1 - 4 8 3 1 - 6 0 3 7 - 5

Mathematics for Engineering, Technology and Computing Science is a text on mathematics for courses in engineering, technology, and computing science. It covers linear algebra,… Read more

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Mathematics for Engineering, Technology and Computing Science is a text on mathematics for courses in engineering, technology, and computing science. It covers linear algebra, ordinary differential equations, and vector analysis, together with line and multiple integrals. This book consists of eight chapters and begins with a discussion on determinants and linear equations, with emphasis on how the value of a determinant is defined and how it may be obtained. Solution of linear equations and the dependence between linear equations are also considered. The next chapter introduces the reader to matrix algebra and linear equations; ordinary differential equations; ordinary linear differential equations of the second order; and solution in power series of differential equations. The Laplace transformation is also examined, along with line and multiple integrals. The last chapter is devoted to vector analysis and includes the basic ideas needed for an algebra of vectors as well as examples and problems of several applications. This monograph will be of interest to students of mathematics, computer science, and engineering courses.

Preface

1 Determinants and Linear Equations

1.1 Introduction

1.2 Notation and Definitions

1.3 Evaluation of Determinants

1.4 Properties of Determinants

1.5 Solution of Linear Equations

1.6 Mesh Current and Node Voltage Network Analysis

1.7 Homogeneous Systems of Equations

1.8 Dependence between Linear Equations

1.9 Consistency of Equations

1.10 Permutations

1.11 Operations On Determinants

2 Matrix Algebra and Linear Equations

2.1 Basic Notation and Definitions

2.2 Matrix Products

2.3 The Inverse of a Square Matrix

2.4 Submatrices and Rank

2.5 General Homogeneous Systems

2.6 General Inhomogeneous Systems

2.7 Network Analysis

2.8 Partitioned Matrices

2.9 Eigenvalues and Eigenvectors

2.10 Applications of Eigenvalues

3 Introduction to Ordinary Differential Equations

3.1 Introduction

3.2 Definitions

3.3 Solution of a Differential Equation

3.4 Direction Fields and Isoclines

3.5 Numerical Solution

3.6 General, Particular and Singular Solutions

3.7 Equations of the First Order and First Degree

4 Ordinary Linear Differential Equations of the Second Order

4.1 Definition of a Linear Equation

4.2 Solution of the Reduced Equation

4.3 The Complete Equation and the Nature of Its Solution

4.4 Derivation of Particular Integrals by Operator Methods

4.5 General Expressions for a Particular Integral

4.6 Applications to Electrical Circuits

4.7 Simultaneous Differential Equations

4.8 The Euler Linear Equation

5 Solution in Power Series of Differential Equations

5.1 Introduction

5.2 Outline of the Method

5.3 Power Series

5.4 Successive Differentiation

5.5 Ordinary Points

5.6 Regular Singular Points

5.7 Relation between Solutions

5.8 The Gamma Function

5.9 Bessel's Differential Equation

5.10 Bessel Functions of Low Order

6 The Laplace Transformation

6.1 Introduction

6.2 Definition of the Transformation

6.3 Transforms of Elementary Functions

6.4 The First Shift Theorem

6.5 Transforms of Derivatives and Integrals

6.6 Application to Ordinary Differential Equations

6.7 Techniques of Inversion

6.8 Differentiation and Integration of Transforms

6.9 The Unit Step Function

6.10 The Second Shift Theorem

6.11 Periodic Functions

6.12 The Unit Impulse Function

7 Line and Multiple Integrals

7.1 Introduction

7.2 Definition of a Line Integral

7.3 Evaluation of Line Integrals

7.4 Dependence on the Path of Integration

7.5 Definition of a Double Integral

7.6 Evaluation of Double Integrals

7.7 Reversal of Integration Order

7.8 Triple Integrals

7.9 Change of Variables In Multiple Integrals

7.10 Polar Coordinates

7.11 Surface Integrals

7.12 Integral Theorems

8 Vector Analysis

8.1 Introduction

8.2 Definitions

8.3 Addition of Vectors

8.4 Products of Vectors

8.5 Differentiation of Vectors

8.6 Elements of Vector Field Theory

8.7 Integrals of Vector Functions

8.8 Integral Theorems in Vector Form

Answers to Problems

Index