Chapter 1 Solving Mathematical Problems with MATLAB
Introduction to 1. 1 MATLAB
Characteristics and composition of1.1.1MATLAB
1. 1.2 command window
1.2 numeric array
1.2. 1 Basic method of creating numeric arrays
1.2.2 accessing array elements
1.2.3 colon operator
1.2.4 array and matrix functions
1.2.5 array operation
1.2.6 matrix operation
1.3 mathematical function
1.3. 1 basic mathematical function
1.3.2 polynomial function
1.3.3 images, zeros and maxima of anonymous functions and univariate continuous functions.
1.4 data type
1.4. 1 numeric type
1.4.2 logical array
1.4.3 character array
1.4.4 cellular array
1.4.5 structure array
1.5 Drawing 2D graphics
1.5. 1 p 10t function
1.5.2 Edit graphics
1.5.3 Introduction to other drawing commands
1.6 MATLAB programming
1.6. 1 M file
1.6.2 control flow statement
1.7 data fitting
The principle of fitting 1.7. 1 proportional function
1.7.2 linear function fitting principle
1.7.3 polynomial fitting principle
MATLAB Realization of 1.7.4 Polynomial Fitting
MATLAB implementation of nonlinear fitting of 1.7.5
Exercise 1
Chapter 2 Overview of Mathematical Modeling
2. 1 Concept, method and significance of mathematical modeling
2. 1. 1 Concept and classification of mathematical model
2. 1.2 The whole process of mathematical modeling
2. 1.3 Mathematical Modeling Paper Writing
2. 1.4 Mathematical modeling method
2. 1.5 Significance of learning mathematical modeling
2.2 Vehicle braking distance
2.3 pig sales opportunities
Exercise 2
Chapter III Difference Equation Model
3. 1 Basic concept of difference equation model
3. 1. 1 dynamic model
3. 1.2 First order difference equation
3. 1.3 second-order difference equation
3. 1.4 Equilibrium Point and Asymptotic Stability
3.2 First-order linear difference equation with constant coefficients and its application
3.2. 1 first order linear homogeneous difference equation with constant coefficients
3.2.2 First-order linear non-homogeneous difference equation with constant coefficients
3.2.3 Natural evolution and artificial incubation of endangered species
3.2.4 Mortgage loan
3.3 Second-order linear homogeneous difference equation with constant coefficients and its application
3.3. 1 second order linear homogeneous difference equation with constant coefficients
3.3.2 Fibonacci sequence
3.3.3 Cobweb Model in Market Economy
3.3.4 Propagation of annual plants
3.4 Discrete Block Growth Model and Its Application
3.4. 1 discrete delay growth model
3.4.2 Growth of Yeast Culture
3.4.3 Population forecast
Exercise 3
Chapter four ordinary differential equation model
4. 1 first-order kinetic reaction model
4. 1. 1 first order kinetic reaction model and its properties
4. 1.2 C- 14 dating method
4. 1.3 Newton's cooling law
4. 1.4 Altitude and atmospheric pressure
4. Is1.5 original or fake?
4. 1.6 emission estimation
4. 1.7 drunk driving
4.2 Quantitative evolution of a single population
4.2. 1 natural growth equation
4.2.2 Growth retardation equation
4.3 Numerical solution and graphic analysis of ordinary differential equations
4.3. Euler method for numerical solution of1ordinary differential equation
4.3.2 Fast Realization of Numerical Solution of Ordinary Differential Equation
4.3.3 Graphical Analysis of Ordinary Differential Equations (Groups)
Exercise 4
Chapter V Numerical Approximation Model
5. 1 one-dimensional interpolation method
5. 1. 1 Introduction
5. 1.2 polynomial interpolation
5. 1.3 piecewise linear interpolation
5. 1.4 cubic spline interpolation
MATLAB implementation of 5. 1.5 cubic spline
5.2 numerical integration and numerical differentiation
5.2. 1 numerical integration
Numerical differentiation
Water tower flow estimation
Exercise 5
Chapter VI Statistical Regression Model
6. 1 descriptive statistics
6. 1. 1 data
6. 1.2 frequency table and histogram
6. 1.3 statistics
6. 1.4 distribution, quantile and statistical chart
6. Inference of1.5 Normal Distribution
6.2 univariate linear regression analysis
6.2. 1 the concept of regression model
6.2.2 The principle of univariate linear regression analysis
6.2.3 MATLAB Realization of Linear Regression Analysis
6.2.4 Linear Regression Analysis Cases
Exercise 6
Chapter VII Optimization Model
7. 1 inventory model
7. Necessary and Sufficient Conditions for Extreme Value of1.1Function
7. 1.2 deterministic static inventory model
7.2 linear programming
7.2. 1 Introduction to Linear Programming
7.2.2 MATLAB Realization of Linear Programming
7.2.3 Linear programming model of two-dimensional variables
Portfolio optimization
Exercise 7
Answers or hints to some exercises.
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