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Differential and Difference Equations(差分與微分方程)(本科教材) 版權信息
- ISBN：9787122358202
- 條形碼：9787122358202 ; 978-7-122-35820-2
- 裝幀：平裝-膠訂
- 冊數：暫無
- 重量：暫無
- 所屬分類：>
Differential and Difference Equations(差分與微分方程)(本科教材) 本書特色
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.
本書詳細介紹了差分方程和常微分方程的基本解法和基本理論，其內容符合相關專業教學大綱的要求，共由七章組成，包括常見的差分和微分方程實際模型，差分方程的求解，一階及高階微分方程求解，微分方程組的基本理論及線性微分方程組的解法，定性理論初步。本書并沒有以基本概念和理論作為開端，而是從實際模型出發，更加注重理論知識的應用。
本書可供高等學校數學、物理、工程及相關專業的學生、教師及研究人員參考使用。
Differential and Difference Equations(差分與微分方程)(本科教材) 內容簡介
本書詳細介紹了差分方程和常微分方程的基本解法和基本理論，其內容符合相關專業教學大綱的要求，共由七章組成，包括常見的差分和微分方程實際模型，差分方程的求解，一階及高階微分方程求解，微分方程組的基本理論及線性微分方程組的解法，定性理論初步。本書并沒有以基本概念和理論作為開端，而是從實際模型出發，更加注重理論知識的應用。 本書可供高等學校數學、物理、工程及相關專業的學生、教師及研究人員參考使用。
Differential and Difference Equations(差分與微分方程)(本科教材) 目錄
Chapter 1Basic difference equations models001
1.1Difference equations of financial mathematics001
1.1.1Compound interest and loan repayments001
1.1.2Some Money Related Models002
1.2Difference equations of population theory004
1.2.1Single equations for unstructured population models004
1.2.2Structured populations and linear systems of difference equations006
1.2.3Markov chain008
Chapter 2Basic differential equations models010
2.1Equations related to financial mathematics010
2.2Continuous population models011
2.3Equations of motion: second order equations015
2.4Modelling interacting quantities systems of differential equations018
Chapter 3Solution and applications of difference equations021
3.1Linear first-order difference equations021
3.2Difference calculus and general theory of linear difference equations024
3.2.1Difference calculus025
3.2.2General theory of linear difference equations027
3.3Linear Homogeneous equations with constant coefficients033
3.4Linear Nonhomogeneous equations037
3.5Limiting behavior of solution041
3.6Autonomous（Time-Invariant）Systems043
3.7Exercises043
Chapter 4Concepts and solutions of differential equations047
4.1Concepts047
4.2Existence and uniqueness of solutions052
4.3First-order linear differential equations056
4.4Exact equation and separation of variables062
4.5Integrating factors068
4.6Initial-value and two-point boundary-value071
4.7Exercises074
Chapter 5Second and higher order differential equations077
5.1Algebraic properties of solutions077
5.2Linear equations with constant coefficients085
5.3The non-homogeneous equation092
5.4Higher order differential equations096
5.5The Euler equation103
5.6Exercises105
Chapter 6Systems of differential equations106
6.1Existence and uniqueness theorem106
6.1.1Marks and definitions106
6.1.2Existence and uniqueness of solutions112
6.2General theory of linear differential systems117
6.2.1Linear homogeneous systems117
6.2.2Linear inhomogeneous systems123
6.3Linear differential systems with constant coefficients126
6.3.1Definition and properties of matrix exponent expA126
6.3.2Calculation of fundamental solution matrix129
6.4Exercises141
Chapter 7Qualitative and stability theories147
7.1Two-dimensional autonomous system and phase plane147
7.2Plane singularity155
7.2.1Trajectory distribution of two-dimensional linear systems156
7.2.2Distribution of orbits of two-dimensional nonlinear systems in the neighborhood of singularities165
7.3Limit cycle167
7.4Lyapunov stability169
7.4.1Stability169
7.4.2First approximation theory173
7.5Exercises178
Appendix182
A.1Solution of difference equations182
A.1.1First order linear constant coefficient difference equation182
A.1.2Higher order linear constant coefficient difference equation184
A.1.3Linear constant coefficient difference equations185
A.2Solutions of ordinary differential equations186
A.2.1Symbolic solutions186
A.2.2Numerical solutions189
A.3Exercises195
References196
1.1Difference equations of financial mathematics001
1.1.1Compound interest and loan repayments001
1.1.2Some Money Related Models002
1.2Difference equations of population theory004
1.2.1Single equations for unstructured population models004
1.2.2Structured populations and linear systems of difference equations006
1.2.3Markov chain008
Chapter 2Basic differential equations models010
2.1Equations related to financial mathematics010
2.2Continuous population models011
2.3Equations of motion: second order equations015
2.4Modelling interacting quantities systems of differential equations018
Chapter 3Solution and applications of difference equations021
3.1Linear first-order difference equations021
3.2Difference calculus and general theory of linear difference equations024
3.2.1Difference calculus025
3.2.2General theory of linear difference equations027
3.3Linear Homogeneous equations with constant coefficients033
3.4Linear Nonhomogeneous equations037
3.5Limiting behavior of solution041
3.6Autonomous（Time-Invariant）Systems043
3.7Exercises043
Chapter 4Concepts and solutions of differential equations047
4.1Concepts047
4.2Existence and uniqueness of solutions052
4.3First-order linear differential equations056
4.4Exact equation and separation of variables062
4.5Integrating factors068
4.6Initial-value and two-point boundary-value071
4.7Exercises074
Chapter 5Second and higher order differential equations077
5.1Algebraic properties of solutions077
5.2Linear equations with constant coefficients085
5.3The non-homogeneous equation092
5.4Higher order differential equations096
5.5The Euler equation103
5.6Exercises105
Chapter 6Systems of differential equations106
6.1Existence and uniqueness theorem106
6.1.1Marks and definitions106
6.1.2Existence and uniqueness of solutions112
6.2General theory of linear differential systems117
6.2.1Linear homogeneous systems117
6.2.2Linear inhomogeneous systems123
6.3Linear differential systems with constant coefficients126
6.3.1Definition and properties of matrix exponent expA126
6.3.2Calculation of fundamental solution matrix129
6.4Exercises141
Chapter 7Qualitative and stability theories147
7.1Two-dimensional autonomous system and phase plane147
7.2Plane singularity155
7.2.1Trajectory distribution of two-dimensional linear systems156
7.2.2Distribution of orbits of two-dimensional nonlinear systems in the neighborhood of singularities165
7.3Limit cycle167
7.4Lyapunov stability169
7.4.1Stability169
7.4.2First approximation theory173
7.5Exercises178
Appendix182
A.1Solution of difference equations182
A.1.1First order linear constant coefficient difference equation182
A.1.2Higher order linear constant coefficient difference equation184
A.1.3Linear constant coefficient difference equations185
A.2Solutions of ordinary differential equations186
A.2.1Symbolic solutions186
A.2.2Numerical solutions189
A.3Exercises195
References196
展開全部
Differential and Difference Equations(差分與微分方程)(本科教材) 作者簡介
李艷秋，南京工業大學數理學院，副教授，本人自從事科研工作以來一直致力于微分方程和動力系統方面的研究，多年的研究已經取得了豐碩的成果：累計在國內外核心期刊發表論文20余篇，包括多篇SCI、EI高水平論文，教學方面，主要承擔高等數學，線性代數，概率論，概率統計，Method for Differential Equations，Differential and Difference Equations等主干課程的講授任務，并多次獲得院級授課競賽一等獎。參與本科生畢業設計及美國大學生數學建模競賽的指導工作，發表教學論文兩篇。
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