Mathematics for Engineering, Technology and Computing Science

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