Math 240 - Differential Equations

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 Syllabus* Spring 2000 Midterm I* Spring 1999 Spring 2000 Midterm II* Spring 1999 Spring 2000 Final* Spring 1999 Spring 2000

*The files are in .pdf format. Download Acrobat Reader here. Postcript or .dvi files are available upon request no spam
 Week Topic Notes 1 Feb.7-11 Introduction to Differential Equations 2 Feb.14-18 First Order O.D.E. Separation of Variables 3 Feb.21-25 Integrating Factors. Homogeneous Equations 4 Feb.28-Mar.3 Applications of First Order O.D.E.     (**) 5 Mar.6-10 Linear Dependence. Wronskian     (**) 6 Mar.13-15 Reduction of Order 7 Mar.20-24 Method of Undetermined Coefficients Midterm I 8 Mar.27-31 Variation of Parameters 9 Apr.3-7 Applications of Second Order O.D.E. 10 Apr.10-14 Inverse Differential Operators* 11 Apr.17-21 Singularities of Differential Equations* 12 Apr.24-28 Series Solutions Midterm II 13 May 1-5 Series Solutions 14 May 8-12 The Laplace Transform 15 May 15-18 The Laplace Transform Finals week Final

* These topics are likely to be skipped

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Midterm I     (25%)   March 24, 2000, 1:40 pm     See   important remarks

Topics covered (tentative):
• The notion of differential equation; classes of equations
• Solutions: definition, existence, uniqueness
• First order equations: separation of variables, homogeneous equations, linear equations
• Integrating factors
• Special equations/methods: substitution, linear coefficients, Bernulli's equation
• Applications of first order equations     (see problematic topics)

Chapters:     1, 2, 4, 5(1-5).
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Midterm II     (25%)   April 28, 2000, 1:40 pm     See   important remarks

Topics covered (tentative):
• Higher order linear equations: existence and uniqueness of solutions; independence of solutions, Wronskian; structure of the general solution to a homogeneous/nonhomogeneous equation; operator notation
• Homogeneous linear equations with constant coefficients
• Nonhomogeneous equations: method of undetermined coefficients
• Nonhomogeneous equations: variation of parameters
• Reduction of order
• Applications of second order linear O.D.E. (pay special attention to harmonic oscillators, such as spring, oscillating circuit, simple pendulum). You can use formulas for damped and undamped vibration; however, in certain cases (say, forced vibration) considering the equation might still be necessary (see, e.g., Problem 1 in 1999 Final)
• Nonlinear equations: reduction of order (see 16.8, 16.9)

Chapters:     6, 7, 8, 9, 10, 16(8, 9).
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Final     (40%)   See your class schedule     See   important remarks

Topics covered (tentative):
• Power series solution to a linear differential equation at an ordinary point. Radius of convergence
• Power series solution at a regular singular point. The indicial equation
• The Laplace transform: definition, basic properties, transforms of particular functions
• The Gamma function
• The inverse transform: basic properties, techniques, table of transforms
• Application of the Laplace transform to solving linear O.D.E.'s (especially, with discontinuous right hand side part)
• The convolution theorem

Chapters:     14, 15(1-5), 17, 18(1-9, 12). (Of course, the material covered by the midterms is also included.)
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Quizzes     (10%)   Held weekly on Tuesday in class (10-15 mins at the end) except midterm weeks. Hopefully 10 quizzes will be given, with grading out of 8 best.

All questions regarding the quizzes are to be directed to the assistant. The assistant is instructed to  give no credit  to identical papers. The same applies to the exams.
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Remarks

During the exams please keep in mind the following:
• Calculators are  not  allowed
• Identical solutions (especially identically wrong ones) will  not  get credit. I reserve the right to decide what "identical" means. You still have the right to complain
• Do not argue about the distribution of the credits among different parts of a problem. I only accept complaints concerning my misunderstanding/misreadung your solution
• Show all your work. Correct answers without sufficient explanation might  not  get full credit
• Indicate clearly and unambiguously your final result. In proofs, state explicitly each claim
• Do not misread the questions or skip parts thereof. If you did, do not complain
• If you believe that a problem is misstated, do not try to solve it; explain your point of view instead
• Each problem has a reasonably short solution. If your calculation goes completely out of hands, something must be wrong