ENGINEERING MATHEMATICS

By X. NARIK

CONTENTS CHAPTER 1 LINEAR ALGEBRA AND MATRICES 1 1 INTRODUCTION 1 2 MOTIVATION 1 3 BASICS AND DEFINITIONS OF MATRICES 1 4 COMPUTATION BY ELEMENTARY OPERATIONS 1 5 THE SOLUTION OF LINEAR ALGEBRAIC SYSTEMS 1 6 BASICS OF LINEAR ALGEBRA 1 7 LINEAR TRANSFORMATIONS 1 8 EIGENVALUE AND EIGENVECTOR PROBLEMS 1 9 CAYLEY-HAMILTON THEOREM AND MINIMUM POLYNOMIAL OF A MATRIX 1 10 SYMMETRIC AND ORTHOGONAL MATRICES 1 11 SINGULAR VALUES, SINGULAR VECTORS, AND NORMS OF MATRICES 1 12 MATRIX FACTORIZATIONS EXERCISES CHAPTER 2 DIFFERENTIAL EQUATIONS – PART I 2 1 INTRODUCTION 2 2 CLASSIFICATION OF DIFFERENTIAL EQUATIONS 2 3 ORDINARY DIFFERENTIAL EQUATIONS IN ENGINEERING PROBLEMS 2 4 SOLUTION CONCEPTS 2 5 FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS 2 6 SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS 2 7 HIGH-ORDER ORDINARY DIFFERENTIAL EQUATIONS 2 8 THE SOLUTION OF A FIRST-ORDER SYSTEM OF DIFFERENTIAL EQUATIONS CHAPTER 3 DIFFERENTIAL EQUATIONS – PART II 3 1 INTRODUCTION 3 2 SECOND-ORDER VARIABLE-COEFFICIENTS ORDINARY DIFFERENTIAL EQUATIONS 3 3 SPECIAL SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS 3 4 NONLINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS 3 5 METHOD OF A PARAMETER 3 6 SOLUTION METHOD BASED ON JACOBI ELLIPTIC FUNCTIONS CHAPTER 4 LAPLACE TRANSFORMS 4 1 INTRODUCTION 4 2 DEFINITIONS AND THEOREMS 4 3 LAPLACE INVERSE 4 4 THE SOLUTION OF DIFFERENTIAL EQUATIONS USING LAPLACE TRANSFORMATION 4 5 LAPLACE TRANSFORM OF ESPECIAL FUNCTIONS 4 6 CONVOLUTION THEOREM 4 7 ADVANCED APPLICATIONS CHAPTER 5 NUMERICAL METHODS 5 1 INTRODUCTION 5 2 DEFINITIONS AND CONCEPTS 5 3 THE SOLUTION OF NONLINEAR ALGEBRAIC EQUATIONS 5 4 POLYNOMIAL APPROXIMATION AND INTERPOLATION 5 5 NUMERICAL DIFFERENTIATION 5 6 NUMERICAL INTEGRATION 5 7 NUMERICAL METHODS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS 5 8 NUMERICAL SOLUTION OF BOUNDARY VALUE PROBLEM ANSWERS TO SELECTED EXERCISES SECTIONS 1 1–1 5 SECTIONS 1 6–1 7 SECTIONS 1 8–1 9 SECTION 1 10–1 12 SECTION 2 1–2 4 SECTION 2 5 SECTION 2 6 SECTIONS 2 7–2 8 SECTION 3 2 SECTION 3 3 SECTION 4 2 SECTION 4 3–4 4 SECTION 5 3 SECTION 5 4 SECTION 5 5–5 6 SECTION 5 7–5 8 REFERENCES