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Table of Contents
PART A. ORDINARY DIFFERENTIAL EQUATIONS (ODEs) 1
Chapter 1. First-Order ODEs 1
Chapter 2. Second-Order Linear ODEs 13
Chapter 3. Higher Order Linear ODEs 36
Chapter 4. Systems of ODEs. Phase Plane. Qualitative Methods 45
Chapter 5. Series Solutions of ODEs. Special Functions 65
Chapter 6. Laplace Transforms 79
PART B. LINEAR ALGEBRA. VECTOR CALCULUS 107
Chapter 7. Linear Algebra: Matrices, Vectors, Determinants. Linear Systems 107
Chapter 8. Linear Algebra: Matrix Eigenvalue Problems 129
Chapter 9. Vector Differential Calculus. Grad, Div, Curl 145
Chapter 10. Vector Integral Calculus. Integral Theorems 169
PART C. FOURIER ANALYSIS. PARTIAL DIFFERENTIAL EQUATIONS (PDEs) 201
Chapter 11. Fourier Analysis 201
Chapter 12. Partial Differential Equations (PDEs) 232