1? 1 mathematical model and its classification 1

1? 2 A mathematical modeling example 2

1? 2? 1 assumption 2 of the model

1? 2? 2 Establishment and solution of the model 3

1? 2? 3 for solutions and further questions

Discussion 4

1? 2? 4 Overview of modeling process 5

1? 3 Basic methods and steps of mathematical modeling 5

1? 3? Basic methods of mathematical modeling in 1 5

1? 3? 2 General steps of mathematical modeling 5

1? 4 Mathematical Modeling Thesis Writing 7

2 interpolation and fitting 9

2? 1 Basic concepts of interpolation and fitting 9

2? 1? 1 interpolation and interpolation function 9

2? 1? 2 least square fitting 1 1

2? 1? 3 temperature prediction problem 12

2? 2. Distance between vehicles 12

2? 3 Numerical calculation of land area 15

3 differential equation modeling method 17

3? 1 ideas and methods of differential equation modeling

3? 2 optimal fishing strategy problem 22

3? 3 advertising mode 25

4 Difference Modeling 28

4? 1 linear difference equation 28

4? 2 Equilibrium point and stability of linear difference equations

Qualitative 29

4? 2? 1 sum of equilibrium points of first-order linear equations

Stability 29

4? 2? 2 the equilibrium point of second order linear difference equation

And stability 29

4? 2? 3 First order nonlinear difference equation 30

4? 3 difference equation model of financial problems 30 pages

4? 4 endowment insurance mode 3 1

4? 5 weight loss plan 32

5 computer simulation

5? 1 Overview of computer simulation modeling 35

5? 2 Monte Carlo method 35

5? 3 Monte Carlo method to calculate the land area 37

5? 4 trajectory problem of three people chasing 38

5? 4? 1 question 38

5? 4? 2 problem analysis and model building 38

5? 4? 3 Programming and Drawing Trajectory 39

5? 5 hound attack question 40

5? 5? 1 model building 40

5? 5? 2 numerical solution of hunting dog attack problem 40

6 Analytic Hierarchy Process 42

6? 1 Basic principles of analytic hierarchy process 42

6? 2 General steps of analytic hierarchy process 44

6? 3 urban air quality analysis 46

6? Application of AHP in solving some optimization problems

Application in question 52

7 Statistical description and analysis of data 55

7? 1 sum of probability distributions of random variables

Digital feature 55

7? 1? 1 statistics 55

7? 1? Matlab is used to calculate statistical data.

Command 56

7? 1? 3 Common probability distributions and numbers

Function 56

7? 2 newsboy's choice 57

7? 2? 1 problem analysis 57

7? 2? 2 assumptions of the model 58

7? 2? 3 the establishment and solution of the model 58

7? 2? 4 result analysis 59

7? 2? 5 Atlas implementation 59

7? 3 parameter estimation 60

7? 4 Hypothesis test 6 1

7? 4? 1 parameter hypothesis test 6 1

7? 4? 2 Hypothesis test of population distribution

7? 5 Difference analysis 65

7? 5? 1 ANOVA of single factor test 65

7? 5? 2 Two-factor test difference analysis 66

7? 5? 3 Analysis of variance of multivariate test 67

7? 6 cluster analysis 68

7? 6? 1 Calculation method of distance and correlation coefficient

Mathematical definition of 69

7? 6? 2 cluster analysis with Matlab 70

7? How to adjust 7 1

7? 7? Suppose 1 model 7 1

7? 7? 2 model establishment and solution 7 1

7? 7? 3 Further discussion of the solution 73

8 regression analysis method 75

8? 1 unary linear regression analysis 76

8? 1? Establishment of 1 unary linear regression model

And its Matlab implementation 76

8? 1? 2 Height and leg length 77

8? 2 Multiple linear regression analysis 78

8? 2? 1 Modeling of Multiple Linear Regression Model

Steps and its Matlab realization 78

8? 2? 2 The annual salary of a certain kind of research scholar 78

8? 2? 3 stepwise regression modeling 82

8? 2? 4 Polynomial Regression 83

8? 3 nonlinear regression analysis 86

8? 3? 1 nonlinear least squares fitting 86

8? 3? 2 nonlinear regression model 86

9 optimization model 9 1

9? 1 general form of mathematical programming 9 1

9? 2 Examples of Mathematical Programming Problems 92

9? 2? 1 blanking problem 92

9? 2? 2 packaging problem 94

9? 2? 3 site selection problem 95

9? 2? 4 distribution problem 96

9? 2? 5 production planning problems 98

9? 2? 6 Tactical decision model 99

9? 2? 7 investment decision-making issues 100

9? 2? 8 maritime issues 10 1

9? 3 dynamic programming and its application 102

9? 3? Introduction to 1 dynamic programming model 102

9? 3? 2 the optimality principle of dynamic programming and

Basic equation of dynamic programming 102

9? 3? 3 application example of dynamic programming 103

9? 4 Multi-wire cutting problem is optimal.

Mathematical model of design scheme 1 12

9? 5 ordering and transportation of steel pipes 1 17

9? 6 parachute selection 123

10 deterministic time series prediction method 128

10? 1 moving average method 128

10? 1? 1 simple moving average method 128

10? 1? 2 weighted moving average method 130

10? 2 average trend ranking method 130

10? 3 the impact of the SARS epidemic on the number of tourists

Impact 132

10? 3? 1 problem initiation 132

10? 3? 2 model analysis and assumptions 132

10? 3? 3 model establishment and solution 133

1 1 random time series prediction method 136

1 1? 1 basic concepts 136

1 1? 2 the construction of random time series prediction model

Method 137

1 1? 3 Shanghai Composite Index Band Prediction Empirical

Study 14 1

1 1? 3? 1 data smoothing and modeling

Select 14 1

1 1? 3? 2 model prediction 142

Appendix A Mathematical Modeling Training Question 144

Appendix BMatlab Instructions for Use 163

Overview of B 1Matlab 163

B2Matlab numerical calculation function 164

B3Matlab graphic function 170

B4 programming 175

Application of B5Matlab 180

Reference 197