HANDBOOK OF MATHEMATICS
CONTENTS CHAPTER 1 LINEAR ALGEBRA AND MATRICES 11 INTRODUCTION 12 MOTIVATION 13 BASICS AND DEFINITIONS OF MATRICES 14 COMPUTATION BY ELEMENTARY OPERATIONS 15 THE SOLUTION OF LINEAR ALGEBRAIC SYSTEMS 16 BASICS OF LINEAR ALGEBRA 17 LINEAR TRANSFORMATIONS 18 EIGENVALUE AND EIGENVECTOR PROBLEMS 19 CAYLEY-HAMILTON THEOREM AND MINIMUM POLYNOMIAL OF A MATRIX 110 SYMMETRIC AND ORTHOGONAL MATRICES 111 SINGULAR VALUES, SINGULAR VECTORS, AND NORMS OF MATRICES 112 MATRIX FACTORIZATIONS EXERCISES CHAPTER 2 DIFFERENTIAL EQUATIONS – PART I 21 INTRODUCTION 22 CLASSIFICATION OF DIFFERENTIAL EQUATIONS 23 ORDINARY DIFFERENTIAL EQUATIONS IN ENGINEERING PROBLEMS 24 SOLUTION CONCEPTS 25 FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS 26 SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS 27 HIGH-ORDER ORDINARY DIFFERENTIAL EQUATIONS 28 THE SOLUTION OF A FIRST-ORDER SYSTEM OF DIFFERENTIAL EQUATIONS CHAPTER 3 DIFFERENTIAL EQUATIONS – PART II 31 INTRODUCTION 32 SECOND-ORDER VARIABLE-COEFFICIENTS ORDINARY DIFFERENTIAL EQUATIONS 33 SPECIAL SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS 34 NONLINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS 35 METHOD OF A PARAMETER 36 SOLUTION METHOD BASED ON JACOBI ELLIPTIC FUNCTIONS CHAPTER 4 LAPLACE TRANSFORMS 41 INTRODUCTION 42 DEFINITIONS AND THEOREMS 43 LAPLACE INVERSE 44 THE SOLUTION OF DIFFERENTIAL EQUATIONS USING LAPLACE TRANSFORMATION 45 LAPLACE TRANSFORM OF ESPECIAL FUNCTIONS 46 CONVOLUTION THEOREM 47 ADVANCED APPLICATIONS CHAPTER 5 NUMERICAL METHODS 51 INTRODUCTION 52 DEFINITIONS AND CONCEPTS 53 THE SOLUTION OF NONLINEAR ALGEBRAIC EQUATIONS 54 POLYNOMIAL APPROXIMATION AND INTERPOLATION 55 NUMERICAL DIFFERENTIATION 56 NUMERICAL INTEGRATION 57 NUMERICAL METHODS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS 58 NUMERICAL SOLUTION OF BOUNDARY VALUE PROBLEM ANSWERS TO SELECTED EXERCISES SECTIONS 11–15 SECTIONS 16–17 SECTIONS 18–19 SECTION 110–112 SECTION 21–24 SECTION 25 SECTION 26 SECTIONS 27–28 SECTION 32 SECTION 33 SECTION 42 SECTION 43–44 SECTION 53 SECTION 54 SECTION 55–56 SECTION 57–58 REFERENCES