Ordinary Differential Equations

ORDINARY DIFFERENTIAL EQUATIONS, E1210, section 001 - Fall 2007

Time and place: MW 9:10-10:25 in Hamilton 702
Instructor: Joel Bellaiche
Phone: (212)854-9235
Office hours: Friday 9-11am in Mathematics Building 525
Teaching Assistant: Shanshan Ding. TA's office hours: Thurdays 1pm-3pm in Columbia Math Help Room.
Text: W. Boyce and R. DiPrima, Elementary Differential Equations and Boundary Value Problems, Eight Edition or W. Boyce and R. DiPrima, Elementary Differential Equations, Eight Edition. The books are available at Columbia bookstore.
Prerequisite: Calculus I and II 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, Oct. 1 and will cover 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 Monday, November 12. It will cover sections: 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4.2, 4.3, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8.
The Final Exam will be on Wednesday, Dec 19, 9am-noon.
Grading: The final grade will be based on 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! Homework will be due each 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.

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Date	Reading	Graded Homework	Suggested Homework
Sep 5	1.1: Some basic mathematical models, direction fields 1.2: Solutions of some differential equations	1.1: 12, 13 1.2: 1(a only), 13, 14 (due on Sep 17)	1.1:1,2,3,22,23 1.2: 3,4,5
Sep 10	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 Sep 17)	1.3:1,2,3,7,8,9,15,16,17 2.2:1,2,3,4,5,6,7,29
Sep 12	2.2: Separable equations 2.1: Linear equations, integrating factors	2.1: 14, 20, 30 (due on Sep 24)
Sep 17	2.1 Linear equations. 2.4: Difference between linear and nonlinear equations	2.4: 4, 10, 14 (due on Sep 24)	2.1:1,2,3,4,7,8,10,14,15,31,32,33,38
Sep 19	2.3: Modeling	2.3: 3, 10, 13 (due on Oct 1)	2.3:6,7,12
Sep 24	2.5: Dynamics	2.5: 3, 10, 13, 16 2.6: 4,10, 18 (due on Oct 1)	2.4:22,23,24
Sep 26	2.5 Autonomous equations and stability. 2.6: Exact equations <&> Review		Practice Midterm ant its solution Midterm
Oct 1	First Midterm (1.1 - 2.6)
Oct 3	3.1: Second order homogenous equations with constant coefficients	3:1 10, 20 (due on Oct 15)	3.1:1,2,3,11,12,13,21,28
Oct 8	3.2: Fundamental solutions 3.3: Linear independence and the Wronskian	3.2: 13 3.3: 10, 21 (due on Oct 15)	3.2:1,2,3,4,14,17,21 3.3:1,2,3,15,16,17,18,27
Tuesday, Oct 9	Last day to drop a class for Barnard, Columbia College, General Studies, SIPA, GSAS, and Continuing Education
Oct 10	3.4, 3.5: Complex roots, repeated roots	3.4: 10, 22 3.5: 13, 24 (due on Oct 22)	Review:Complex numbers, complex exponential and Euler formula (for example in Stewart, App. G) 3.4:11,12,27,33,38; 3.5:1,2,3,4,11,12,14
Oct 15	3.5: Repeated roots; 3.8: Mechanical and electric vibrations	3.8: 6 (due on Oct 22) (due on Oct 22)	3.5:1,2,3,4,5,6,18,19
Oct 17	3.5: Repeated roots; 3.8: Mechanical and electric vibrations	3.8 : 3,15,24 (due on oct 29)	3.8;1,2,5,11,27
Oct. 22	3.6,3.7: Variations of parameters 3.9: Mechanical Vibrations	3.6: 7,9,10 3.7: 4, 15, 22 3.9: 15, 18 (a only) (due on Oct 29)	3.6:11,12 3.7 : 5,6,21 3.8: 26
Oct. 24	7.1: Introduction to Linear Systems (2 equations)	7.1: 3, 5 (due on Nov 7)	7.1:6
Oct 29	7.2, 7.3: Eigenvalues and eigenvectors of 2x2 matrices	7.2: 4, 14 7.3: 16, 19 (due on Nov 7)
Oct 31	7.4: Basic theory of system of first order linear equations		7.4:2,5,6,7
Nov 5	Academic holiday
Nov 12	Second Midterm (3.2-7.8)		Practice Midterm and solutions solution to the midterm
Nov 14	7.5, 7.6: Linear systems with constant coefficients	7.5: 8, 11 7.6: 3, 9 (due on Nov 26 )	7.5:9,10,15,19
Nov 19	7.6,7.7: Linear systems with constant coefficients.	7.7: 6, 11 (due on Nov 26)	7.6:28,29; 7.7:1,2,3,15,16
Nov 21	7.8: Repeated eigenvalues 7.9: Nonhomogeneous linear systems	7.8: 3, 8 7.9: 3, 7 (due on Dec 3)	7.8:15, 17
Nov 26	Last day to drop a class for schools not otherwise noted above; Last day to exercise Pass/Fail option
Nov 26	7.8	9.1: 9(a, b, c only) (due on Dec 3)	7.9:1,2,4,11
Nov 28	7.9 : non homogeneous linear system systems and stability	9.2: 1, 2 (due on Dec 14)
Dec 3	9.1, 9.2 : stablity	9.3: 6(a, b, c only), 14(a, b, c only) (due on Dec 14)	9.1:5,6,13
Dec 5	9.3: Almost Linear System		9.2:3,4
Dec 10	9.3: Almost Linear System. Review		9.3:1,2,4
	Practice Final
Dec 19	Final Exam: 9:00-noon