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差分与微分方程大中专理科数理化

大中专理科数理化新华书店全新正版书籍

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作者作者

出版社化学工业出版社

ISBN9787122358202

出版时间2020-02

版次1

装帧平装

开本16开

页数204页

字数261千字

定价49元

货号xhwx_1202140681

上书时间2021-12-23

浩子书屋

八年老店

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商品详情

品相描述：全新: 正版特价新书

商品描述: 目录：

chapter 1 basic difference equations models

1.1 difference equations of finan mathematics

1.1.1 pound interest and loan repayments

1.1.2 some money related models

1.2 difference equations of population theory

1.2.1 single equations for unstructured population models

1.2.2 structured populations and linear systems of difference equations

1.2.3 markov chain

chapter 2 basic differential equations models

2.1 equations related to finan mathematics

2.2 continuous population models

2.3 equations of motion: second order equations

2.4 modelling interacting quantities systems of differential equations

chapter 3 solution and applications of difference equations

3.1 linear first-order difference equations

3.2 difference calculus and general theory of linear difference equations

3.2.1 difference calculus

3.2.2 general theory of linear difference equations

3.3 linear homogeneous equations with constant coefficients

3.4 linear nonhomogeneous equations

3.5 limiting behavior of solution

3.6 autonomous（time-invariant）systems

3.7 exercises

chapter 4 concepts and solutions of differential equations

4.1 concepts

4.2 estence and uniqueness of solutions

4.3 first-order linear differential equations

4.4 exact equation and separation of variables

4.5 integrating factors

4.6 initial-value and two-point boundary-value

4.7 exercises

chapter 5 second and higher order differential equations

5.1 algebraic properties of solutions

5.2 linear equations with constant coefficients

5.3 the non-homogeneous equation

5.4 higher order differential equations

5.5 the euler equation

5.6 exercises

chapter 6 systems of differential equations

6.1 estence and uniqueness theorem

6.1.1 marks and definitions

6.1.2 estence and uniqueness of solutions

6.2 general theory of linear differential systems

6.2.1 linear homogeneous systems

6.2.2 linear inhomogeneous systems

6.3 linear differential systems with constant coefficients

6.3.1 definition and properties of matrix exponent expa

6.3.2 calculation of fundamental solution matrix

6.4 exercises

chapter 7 qualitative and stability theories

7.1 two-dimensional autonomous system and phase plane

7.2 plane singularity

7.2.1 trajectory distribution of two-dimensional linear systems

7.2.2 distribution of orbits of two-dimensional nonlinear systems in the neiorhood of singularities

7.3 limit cycle

7.4 lyapunov stability

7.4.1 stability

7.4.2 first appromation theory

7.5 exercises

appendix

a.1 solution of difference equations

a.1.1 first order linear constant coefficient difference equation

a.1.2 higher order linear constant coefficient difference equation

a.1.3 linear constant coefficient difference equations

a.2 solutions of ordinary differential equations

a.2.1 symbolic solutions

a.2.2 numerical solutions

a.3 exercises

references

内容简介：

本书详细介绍了差分方程和常微分方程的基本解和基本理论，其内容符合相关专业教学大纲的要求，共由七章组成，包括常见的差分和微分方程实际模型，差分方程的求解，一阶及高阶微分方程求解，微分方程组的基本理论及线微分方程组的解，定理论初步。本书并没有以基本概念和理论作为开端，而是从实际模型出发，更加注重理论知识的应用。本书可供高等学校数学、物理、工程及相关专业的学生、教师及研究人员参使用。