Chapter 65438 +0 Basic Concepts

1. 1 Overview of differential equations

Basic concepts of 1.2 ordinary differential equations

1.2. 1 General expression of ordinary differential equation

1.2.2 Solutions of ordinary differential equations

1.3 exercise questions

Chapter II Basic Solutions of First Order Ordinary Differential Equations

2. 1 variable separation method

2. 1. 1 Variable Separable Equation

2. 1.2 can be transformed into an equation with separated variables.

2.2 Solutions of First Order Linear Ordinary Differential Equations

2.3 Appropriate equations and integration factors

2.3. 1 Inherent equation

2.3.2 Discrimination Theorem of Inherent Equation

Integration coefficient

2.4 the solution of the first order implicit equation

2.4. 1 can solve the equation of y (or x).

2.4.2 Equation without Y (or X)

2.5 Existence Theorem of Solutions of First Order Differential Equations

2.6 practice

Chapter III Higher Order Differential Equations

3. 1 general theory of linear differential equations

3. 1. 1 Introduction

3. 1.2 Properties and Structure of Solutions of Homogeneous Linear Equations

3. 1.3 nonhomogeneous linear equation and constant variation method

3.2 Solutions of Linear Equations with Constant Coefficients

3.2. 1 Complex-valued Functions and Complex-valued Solutions

3.2.2 Solutions of homogeneous linear equations with constant coefficients

3.2.3 Euler equation.

3.2.4 Solutions of Non-homogeneous Linear Equations with Constant Coefficients

3.3 practice

Chapter 4 linear differential equation system

4. 1 general theory of linear differential equations

4. 1. 1 vector function and matrix function

4. 1.2 Existence and Uniqueness of Solutions of Linear Equations

4. The general solution structure of1.3 homogeneous linear equations

4. The general solution structure of1.4 nonhomogeneous linear equations

4.2 Constant coefficient linear differential equation system

Matrix index definitions and attributes

4.2.2 Calculation of Basic Solution Matrix

4.3 practice

Chapter 5 Difference Equation

5. 1 difference and difference equation

5. 1. 1 difference concept

5. Concept of1.2 difference equation

5.2 Constant coefficient first-order linear difference equation

5.2. 1 General solution of first-order homogeneous linear difference equation with constant coefficients

5.2.2 General solution of first-order non-homogeneous linear difference equation with constant coefficients

5.3 Second Order Linear Difference Equation with Constant Coefficients

5.3. 1 General solution of second-order homogeneous linear difference equation with constant coefficients

5.3.2 General solution of second-order non-homogeneous linear difference equation with constant coefficients

5.4 practice

Chapter VI Introduction of Partial Differential Equations

6. A preliminary study of1first order partial differential equation

6. Basic concept of1.1

6. 1.2 The first integration of the first order ordinary differential equation

6. 1.3 Solutions of first-order homogeneous linear partial differential equations

6. 1.4 Solutions of first-order quasilinear nonhomogeneous partial differential equations

6.2 Preliminary Study on Second Order Partial Differential Equation

6.2. 1 Classification and canonical form of second-order linear partial differential equations

6.2.2 The definite solutions of heat conduction equation, wave equation and potential equation.

6.3 practice

The second part is the optimization method

Chapter 65438 +0 Linear Programming and Simplex Method

1. 1 linear programming problem and its mathematical model

Put forward the question of 1. 1. 1

1. 1.2 standard form of linear programming problem

1. 1.3 the concept of solutions to linear programming problems

Geometric significance of 1.2 linear programming problem

Graphical solution of binary linear programming problem 1.2. 1

1.2.2 Basic concepts

1.2.3 Fundamental Theorem

1.3 simplex method

1.3. 1 reference example

1.3.2 Determination of feasible solution of initial basis

1.3.3 Theorem for Determining Optimal Test and Solution

1.3.4 exchange basic iteration

1.3.5 Simplex Table

Further discussion on 1.4 simplex method

1.4. 1 artificial variable

1.4.2 degradation and cycle

1.5 exercise questions

The second chapter is dual theory and sensitivity analysis

2. 1 dual problem

2.2 dual theory

2.2. 1 dual problem representation

2.2.2 Basic properties of dual problems

2.3 Double problem-the economic explanation of shadow price

2.4 dual simplex method

2.5 Sensitivity analysis

2.5. 1 Analysis on the change of resource amount bi

2.5.2 Analysis of ci change in objective function

2.5.3 technical coefficient change analysis aij

2.5.4 Analysis of adding new variables

2.5.5 Analysis of Adding New Constraints

2.6 practice

Chapter III Nonlinear Programming

3. 1 Basic knowledge

3. 1. 1 Mathematical model of nonlinear programming problem

3. 1.2 convex programming

3. 1.3 optimality conditions

3. 1.4 Overview of nonlinear programming methods

3.2 Solutions to unconstrained nonlinear programming problems

3.2. 1 steepest descent method

Yoke gradient method

3.2.3 Pattern Vector Search Method

3.3 Solving constrained nonlinear programming problems

3.3. 1 feasible direction method

3.3.2 Extended objective function method

3.4 practice

Chapter 4 Multi-objective Planning

4. 1 Basic knowledge

4. 1. 1 Mathematical model of multi-objective programming problem

4. 1.2 efficient solution, weak efficient solution and optimal solution

4.2 Evaluation function method

4.2. 1 linear weighted sum method

4.2.2 Ideal point method

Multiplication and division

4.2.4 Efficiency function method

4.3 Hierarchical solution method

4.4 Progressive Tolerance and Restraint Law

4.5 Compromise and Constraint Methods

4.6 practice

Chapter V Dynamic Planning

5. 1 Introduction to Dynamic Planning

5. 1. 1 reference example

5. 1.2 The concept of dynamic programming

5.2 Basic solution of dynamic programming problem

5.3 practice

The third part is the preliminary study of stochastic process.

Chapter 1 Basic knowledge of stochastic process

1. 1 the concept of stochastic process

Distribution and numerical characteristics of 1.2 stochastic process

1.2. 1 family of distribution functions of stochastic processes

1.2.2 Numerical characteristics of stochastic processes

1.2.3 classification of stochastic processes

1.3 exercise questions

Chapter II Mean Square Calculus

2. Mean square limit of1random variable sequence

2.2 Mean Square Continuity of Stochastic Processes

2.3 Mean square derivative of stochastic process

2.4 Mean Square Integral of Stochastic Process

2.5 Mean Square Calculus of Normal Process

2.6 stochastic differential equation

2.7 practice

Chapter 3 Markov chain

3. 1 Markov chain

3.2 Chepmann-André Andrey Kolmogorov Equation

3.2. 1 Chapman Andre Andrey Kolmogorov equation

3.2.2 Initial probability distribution and absolute probability distribution

3.2.3 Finite dimensional probability distribution

3.3 Ergodicity of Markov Chains

3.4 practice

Chapter 4 Stationary Process

4. 1 strictly stationary process and its numerical characteristics

4.2 Wide Stationary Process

4.3 Properties of correlation function

4.4 practice

The fourth part exercises reference answers

The first part is the answer to the differential equation exercise.

The second part is the answer to the exercise of optimization method.

The third part is the preliminary practice answer of stochastic process.