Chapter 1 First-Order Ordinary Differential Equations 1-1 Introduction to Differential Equations 1-2 Separable First-Order ODEs 1-3 Exact ODEs and Integration Factor 1-4 Linear ODEs 1-5 Solving First-order ODEs with the Grouping Method 1-6 Application of First-Order ODEs
Chapter 2 High-Order Linear Ordinary Differential Equation 2-1 Basic Theories 2-2 Solving Higher-Order ODE with the Reduction of Order Method 2-3 Homogeneous Solutions of Higher-Order ODEs 2-4 Finding Particular Solution Using the Method of Undetermined Coefficients 2-5 Finding Particular Solution Using the Method of Variation of Parameters 2-6 Finding Particular Solution Using the Method of Inverse Differential Operators 2-7 Equidimensional Linear ODEs 2-8 The Applications of Higher-Order ODEs in Engineering
Chapter 3 Laplace Transform 3-1 The Definition of Laplace Transform 3-2 Basic Characteristic and Theorems 3-3 Laplace Transform of Special Functions 3-4 Laplace Inverse Transform 3-5 The Application of Laplace Transform
Chapter 4 Power Series Solution of Ordinary Differential Equations 4-1 Expansion at a Regular Point for Solving ODE 4-2 Regular Singular Point Expansion for Solving ODE (Selected Reading)
Chapter 5 Vector Operations and Vector Spaces 5-1 The Basic Operations of Vector 5-2 Vector Geometry 5-3 Vector Spaces Rn
Chapter 6 Matrix Operations and Linear Algebra 6-1 Matrix Definition and Basic Operations 6-2 Matrix Row (Column) Operations and Determinant 6-3 Solution to Systems of Linear Equations 6-4 Eigenvalues and Eigenvectors 6-5 Matrix Diagonalization 6-6 Matrix Functions
Chapter 7 Linear differential equation system 7-1 The Solution of a System of First-Order Simultaneous Linear Differential Equations 7-2 The Solution of a Homogeneous System of Simultaneous Differential Equations 7-3 Diagonalization of Matrix for Solving Non-Homogeneous System of Simultaneous Differential Equations
Chapter 8 Vector Function Analysis 8-1 Vector Functions and Differentiation 8-2 Directional Derivative 8-3 Line Integral 8-4 Multiple Integral 8-5 Surface Integral 8-6 Green’s Theorem 8-7 Gauss's Divergence Theorem 8-8 Stokes’ Theorem
Chapter 9 Orthogonal Functions and Fourier Analysis 9-1 Orthogonal Functions 9-2 Fourier Series 9-3 Complex Fourier Series and Fourier Integral 9-4 Fourier Transform
Chapter 10 Partial Differential Equation 10-1 Introduction to Partial Differential Equation (PDE) 10-2 Solving Second-Order PDE Using the Method of Separation of Variables 10-3 Solving Non-Homogeneous Partial Differential Equation 10-4 Solving PDE Using Integral Transformations 10-5 Partial Differential Equations in Non-Cartesian Coordinate System
Chapter 11 Complex Analysis 11-1 Basic Concepts of Complex Number 11-2 Complex Functions 11-3 Differentiation of Complex Functions 11-4 Integration of Complex Functions 11-5 Taylor Series Expansion and Laurent Series Expansion 11-6 Residue Theorem 11-7 Definite Integral of Real Variable Functions
