Engineering Mathematics�

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


 

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 ...