Differential and Difference Equations(差分与微分方程)(本科教材)
本书特色
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This book introduces the basic solutions and theories of difference and ordinary differential equations in detail,which meets the requirements of the relevant professional syllabus and is composed of 7 chapters,including the common practical models of difference and differential equations,the solutions of difference equations, the solutions of first order and higher order differential equations,the basic theory of differential equations and the solutions of linear differential equations,qualitative theory.This book starts with not the basic concepts and theories,but the practical model and pays more attention to the application of theoretical knowledge.
This book can be used as a reference for students,teachers and researchers of mathematics,physics,engineering and related majors in colleges and universities.
This book introduces the basic solutions and theories of difference and ordinary differential equations in detail,which meets the requirements of the relevant professional syllabus and is composed of 7 chapters,including the common practical models of difference and differential equations,the solutions of difference equations, the solutions of first order and higher order differential equations,the basic theory of differential equations and the solutions of linear differential equations,qualitative theory.This book starts with not the basic concepts and theories,but the practical model and pays more attention to the application of theoretical knowledge.
This book can be used as a reference for students,teachers and researchers of mathematics,physics,engineering and related majors in colleges and universities.
本书详细介绍了差分方程和常微分方程的基本解法和基本理论，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性微分方程组的解法，定性理论初步。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、教师及研究人员参考使用。
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目录
Chapter 1Basic difference equations models0011.1Difference equations of financial mathematics0011.1.1Compound interest and loan repayments0011.1.2Some Money Related Models0021.2Difference equations of population theory0041.2.1Single equations for unstructured population models0041.2.2Structured populations and linear systems of difference equations0061.2.3Markov chain008Chapter 2Basic differential equations models0102.1Equations related to financial mathematics0102.2Continuous population models0112.3Equations of motion: second order equations0152.4Modelling interacting quantities systems of differential equations018Chapter 3Solution and applications of difference equations0213.1Linear first-order difference equations0213.2Difference calculus and general theory of linear difference equations0243.2.1Difference calculus0253.2.2General theory of linear difference equations0273.3Linear Homogeneous equations with constant coefficients0333.4Linear Nonhomogeneous equations0373.5Limiting behavior of solution0413.6Autonomous（Time-Invariant）Systems0433.7Exercises043Chapter 4Concepts and solutions of differential equations0474.1Concepts0474.2Existence and uniqueness of solutions0524.3First-order linear differential equations0564.4Exact equation and separation of variables0624.5Integrating factors0684.6Initial-value and two-point boundary-value0714.7Exercises074Chapter 5Second and higher order differential equations0775.1Algebraic properties of solutions0775.2Linear equations with constant coefficients0855.3The non-homogeneous equation0925.4Higher order differential equations0965.5The Euler equation1035.6Exercises105Chapter 6Systems of differential equations1066.1Existence and uniqueness theorem1066.1.1Marks and definitions1066.1.2Existence and uniqueness of solutions1126.2General theory of linear differential systems1176.2.1Linear homogeneous systems1176.2.2Linear inhomogeneous systems1236.3Linear differential systems with constant coefficients1266.3.1Definition and properties of matrix exponent expA1266.3.2Calculation of fundamental solution matrix1296.4Exercises141Chapter 7Qualitative and stability theories1477.1Two-dimensional autonomous system and phase plane1477.2Plane singularity1557.2.1Trajectory distribution of two-dimensional linear systems1567.2.2Distribution of orbits of two-dimensional nonlinear systems in the neighborhood of singularities1657.3Limit cycle1677.4Lyapunov stability1697.4.1Stability1697.4.2First approximation theory1737.5Exercises178Appendix182A.1Solution of difference equations182A.1.1First order linear constant coefficient difference equation182A.1.2Higher order linear constant coefficient difference equation184A.1.3Linear constant coefficient difference equations185A.2Solutions of ordinary differential equations186A.2.1Symbolic solutions186A.2.2Numerical solutions189A.3Exercises195References196
封面
书名:Differential and Difference Equations(差分与微分方程)(本科教材)
作者:李艳秋，郑冬梅，江舜君
页数:196页
定价:¥49.0
出版社:化学工业出版社
出版日期:2020-02-01
ISBN:9787122358202
PDF电子书大小:85MB 高清扫描完整版