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# 常微分方程教学大纲

1、 C. H. Edwards and D. E. Penny: Differential Equations and Linear Algebra, 3rd edition, Prentice Hall – Pearson, 2010.
2、林武忠、汪志鸣、张九超编著,常微分方程（第一版）, 科学出版社, 2003年9月。
3、王树禾编著《微分方程模型和混沌》,中国科学技术大学出版社，1999。
4、丁同仁，李承治主编《常微分方程教程》，高等教育出版社，1991。
5、王高雄等主编：《常微分方程》，第二版，高等教育出版社，1983。
6、叶彦谦主编：《常微分方程讲义》，第二版，人民教育出版社，1984。

Chapter 1 First order differential equations
1.2 First order linear differential equations
1.3 The Van Meegeren art forgeries(自学)
1.4 Separable equations
1.5 Population models
1.6 The spread of technological innovations(自学)
1.7 An atomic waste disposal problem(自学)
1.8 The dynamics of tumor growth mixing problems and orthogonal trajectories
1.9 Exact equations and why we cannot solve very many differential equations
1.10 The existence/uniqueness theorem (Picard iteration)
?Supplementary materials: Decay, Half Life, Air Resistance Problem, Newton’s Cooling Law, Pursuit problem
Chapter 2 Second order linear differential equations
2.1 Algebraic properties of solutions
2.2 Linear equations with constant coefficients
2.3 The nonhomogeneous equation
2.4 The method of variation of parameters
2.5 The method of judicious guessing
2.6 Mechanical vibrations: The Tacoma Bridge disaster
2.7 A model for the detection of diabetes (自学)
2.8 Series solutions: 2.81 Singular points Euler equations;2.82 Regular singular points the method of Frobenius;2.83 Equal roots and roots differing by an integer
2.9 The method of Laplace transforms
2.10 Some useful properties of Laplace transforms
2.11 Differential equations with discontinuous right hand sides
2.12 The Dirac delta function
2.13 The convolution integral Consider the initial value problem
2.15 Higher order equations
Supplementary materials Difference equations
Chapter 3 Systems of differential equations
3.1 Algebraic properties of solutions of linear system
3.2 Vector spaces (已学过内容，略)
3.3 Dimension of a vector space(已学过内容，略)
3.4 Applications of linear algebra to differential equations(已学过内容，略)
3.5 The theory of determinants(已学过内容，略)
3.6 Solutions of simultaneous linear equations(已学过内容，略)
3.7 Linear transformations(已学过内容，略)
3.8 The eigenvalue/eigenvector methods
3.9 Complex roots
3.10 Equal roots
3.11 Fundamental matrix solutions
3.12 The nonhomogeneous equation variation of parameters

Chapter 4 Qualitative theory of differential equations
4.2 Stability of linear systems
4.3 Stability of equilibrium solutions
4.4 The phase plane
4.6 Qualitative properties of orbits
4.7 Phase portraits of linear systems
4.8 Long time behavior of solutions the Poincare Bendixson Theorem
4.10 Predator-prey problems
4.11 The principle of competitive exclusion in population biology
4.12 The Threshold Theorem of epidemiology
4.13 A model for the spread of gonorrhea

 章次 一 二 三 四 复习、练习 学时 16 16 12 20 8