Virdol's teaching

ORDINARY DIFFERENTIAL EQUATIONS, E1210 - Fall 2009

Time and place: MW 1:10pm-2:25pm in Mathematics Building 203
Instructor: Cristian Virdol
Email: virdol@math.columbia.edu
Phone: (212) 854-9235
Office hours: MW 2:25pm-3:25pm in Mathematics Building 307A
Teaching Assistant: Alexander Boger. His office hours are: in Math 406.
Text: W. Boyce and R. DiPrima, Elementary Differential Equations and Boundary Value Problems, Ninth Edition or W. Boyce and R. DiPrima, Elementary Differential Equations, Ninth Edition. The books are available at Columbia bookstore.
Prerequisite: Calculus IIIA/IIS or the equivalent.
Midterms: There will be two midterms and a final exam. There are no makeup exams.
Calculators will not be permitted on exams.
The First Midterm will be during the lecture time on Monday, October 12 and will cover the sections: 1.1, 1.2, 1.3, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 3.1.
The Second midterm will be during the lecture time on Wednesday, November 18. It will cover the sections: 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 4.2, 4.3, 7.1, 7.2, 7.3, 7.5, 7.6, 7.7, 7.8.
The Final Exam will be on Monday, December 21, 1:10pm-4:00pm (in Math 203).
Grading: The final grade will be based on the the exams and homework with the following weights: final (40%), midterms (20% each) and homework (20%).

Schedule and Homework

It is practically impossible to learn mathematics without doing a lot of problems. Therefore, it is extremely important that you do the assigned problems carefully and promptly. Don't get behind! I will assign homework each Monday. It will be due next week on Monday in class. I expect that graded homework will be returned to you a week later. You may discuss homework problems with other students, the TA or me before they are turned in. In fact, the right kind of discussion can be quite valuable. I do expect two things, though: (i) you should try seriously to do the exercise yourself before discussing it with anyone, and (ii) you should write up the solution yourself after understanding it thoroughly, without following someone else's written version. Otherwise, the homework does you no good. Note that there are answers in the back of the book for many of the problems. They are useful in checking your work, of course, but this makes it particularly important that you show your work.

Note: No late homework will be accepted.

This schedule is tentative and may be modified as the semester goes on.

Date	Reading	Homework
Sept. 9	1.1: Some basic mathematical models, direction fields 1.2: Solutions of some differential equations	1.1: 12, 21 1.2: 1(a only) 13, 14 (due on Sept. 21)
Sept. 14	1.3: Classification of differential equations 2.2: Separable equations	1.3: 6, 18 2.2: 8, 17(a,c only), 19(a,c only) (due on Sept. 21)
Sept. 16	2.1: Linear equations, integrating factors 2.6: Exact equations	2.1: 14, 20, 30 2.6: 4, 7, 14, 22 (due on Sept. 28)
Sept. 21	2.4: Difference between linear and nonlinear equations	2.4: 4, 10, 14 (due on Sept. 28)
Sept. 23	2.3: Modeling	2.3: 3, 10, 13 (due on Oct. 5)
Sept. 28	2.5: Dynamics 3.1: Homogenous equations with constant coefficients	2.5: 3, 10, 13, 16 3.1: 7, 11, 18 (due on Oct. 5)
Sept. 30	4.2: Homogenous equations with constant coefficients	4.2: 13, 19, 30 (due on Oct. 19)
Oct. 5	3.1: Fundamental solutions 3.2: Linear independence and the Wronskian	3.1: 9, 13, 18, 24 3.2: 4, 10, 21 (due on Oct. 19)
Oct. 7	Review Practice Midterm
Oct. 12	First Midterm (1.1 - 3.1)
Oct. 13	Last day to drop a class for Barnard, Columbia College, General Studies, SIPA, GSAS, and Continuing Education
Oct. 14	3.3, 3.4: Complex roots, repeated roots	3.3: 10, 22 3.4: 13, 24 (due on Oct. 26)
Oct. 19	3.5, 4.3: Method of Undetermined Coefficients	3.5: 3, 4, 15 4.3: 3, 6, 16 (due on Oct. 26)
Oct. 21	3.6: Variations of parameters 3.7, 3.8: Mechanical Vibrations	3.6: 4, 15, 22 3.7: 3, 15, 24 3.8: 15, 18(a only) (due on Nov. 9)
Oct. 26	7.1: Introduction to Linear Systems (2 equations)	7.1: 3, 5 (due on Nov. 9)
Oct. 28	7.2, 7.3: Eigenvalues and eigenvectors of 2x2 matrices	7.2: 4, 14 7.3: 16, 19, 25 (due on Nov. 16)
Nov. 2	Academic Holiday
Nov. 4	7.5, 7.6: Linear systems with constant coefficients	7.5: 8, 11, 17 7.6: 5, 9 (due on Nov. 16)
Nov. 9	7.7: Linear systems with constant coefficients	7.7: 3, 6, 11, 12 (due on Nov. 16)
Nov. 11	7.8: Repeated eigenvalues 7.9: Nonhomogeneous linear systems	7.8: 1, 3, 8 7.9: 1, 3, 7 (due on Nov. 23)
Nov. 16	Review Practice Midterm
Nov. 18	Second Midterm (3.2-7.8)
Nov. 19	Last day to drop a class for schools not otherwise noted above; Last day to exercise Pass/Fail option
Nov. 23	9.1: Stability for linear systems 9.2: Autonomous systems and stability	9.1: 9(a,b,c only), 15 9.2: 1, 2 (due on Nov. 30)
Nov. 25	9.3: Almost linear systems 6.1: Laplace Transform	9.3: 6(a, b, c only), 14(a,b,c only) 6.1: 15, 16 (due on Dec. 7)
Nov. 30	6.2: Solutions of initial value problems	6.2: 8, 22 (due on Dec. 7)
Dec. 2	6.3: Step functions 6.4: Discontinuos forcing terms	6.3: 9, 15, 30 6.4: 4, 10 (due on Dec. 14)
Dec. 7	5.1, 5.2, 5,3: Power series methods
Dec. 9	5.1, 5.2, 5,3: Power series methods
Dec. 14	Review
Dec. 21	Final Exam: 1:10pm-4:00pm