MTWR 2:45-4:20pm, 520 Mathematics Building
July 6- August 14
Instructor: Chen-Yun Lin (408 Mathematics, cylin@math.columbia.edu)
Office Hours: After the class or by appointment.
Text: Elementary Differential Equations and Boundary Value Problems, William E. Boyce & Richard C. DiPrima, 9th Edition.
Policies: Students are required to hand in homework every week, take the quizzes, midterms and the final. Students are also expected to attend every class. Here are some suggested policies:
Calculators: Calculators are not required for this course. If you have a graphing calculator, you might find it helpful when you are working on your homework. However, you will not be allowed to use a calculator during the exams.
Homework: Homework will be assigned daily and will be due the following monday. Late work will not be accepted. Collaboration on homework is encouraged as long as the work you hand in is your own. Please make homework neat (with staple). Late homework will not be accepted.
Exams: There will be one midterm and the date of the midterm is shown below. The midterm will be an in-class one.
There will be no make-up exams without a note from a doctor or a
dean.
Quizzes: I reserve the right to give short pop quizzes. They will be 10-15 minutes long and cover material from the homeworks.
Grading: The tentative grading scheme is as follows:
This schedule is tentative and might change as the class progresses. Please check regularly for current homework information.
| DATE | TOPICS | HOMEWORK |
| 07/06 | Introduction (Chapter 1) |
Due 07/13
1.1: 1, 2 1.3: 1-6, 13, 14 |
| 07/07 | Linear Equations, Integrating Factors (2.1)
Separable Equations (2.2) |
Due 07/13
2.1: 15, 30, 38 2.2: 6, 11(a), 26, 36(b) |
| 07/08 | Difference between Linear and Nonlinear (2.4)
Autonomous Equations (2.5) |
Due 07/13
2.4: 17 2.5: 3, 12 |
| 07/09 | Exact Equations (2.6)
Existence and Uniqueness(2.8) |
Due 07/13
2.6: 7, 11, 25, 29 |
| 07/13 | Basic Homogeneous Second Order Equations with Constant Coefficients; The Wronskian. (3.1, 3.2) |
Due 07/20
3.1: 2, 12, 26 3.2: 4, 13, 24, 32 |
| 07/14 |
Complex Roots and Repeated Roots; Reduction of Order. (3.3, 3.4) |
Due 07/20
3.3: 10, 20, 39 3.4: 6, 14, 26, 41 |
| 07/15 | Non-homogeneous Equations: Undetermined Coefficients. (3.5) |
Due 07/20
3.5: 6, 8, 17 |
| 07/16 | Non-homogeneous: Variation of Parameters. (3.6) |
Due 07/20
3.6: 5, 10, 19 |
| 07/20 | Nonhomogeneous Equations of Higher Order. (4.3, 4.4) |
Due 07/27
4.3: 3, 11, 18 4.4: 1, 10 |
| 07/21 | Series Solution near a Ordinary Point. (5.1, 5.2) |
Due 07/27
5.2:2, 21 5.3:12, 22 |
| 07/22 | Regular Singular Points. (5.4, 5.5) |
Due 07/27
5.4: 6, 20, 33 5.5: 7, 14 |
| 07/23 | More Examples. (5.6) |
Due 07/27
5.6: 5, 15 |
| 07/27 | Review | |
| 08/28 | Midterm: Chapters 2, 3, 4, 5 | |
| 07/29 | Laplace Transform; Initial Value Problems. (6.1, 6.2) |
Due 08/03
6.1: 5, 7, 11, 19 6.2: 8, 14, 21, 26 |
| 07/30 | Step Functions; Discontinuous Forcing Functions. (6.3, 6.4) |
Due 08/03
6.3: 6, 11, 15, 23, 34, 37 6.4: 2, 4, 9 |
| 08/03 | Impulse Function; Convolution. (6.5, 6.6) |
Due 08/03
6.5: 3, 11, 12 6.6: 4, 7, 10, 13, 28 |
| 08/04 | Review of Linear Algebra. ( 7.2, 7.3) |
Due 08/03
7.2: 6, 13, 23, 26 7.3: 3, 7, 15, 25 |
| 08/05 | Basic Theory and Case of distinct real eigenvalues. (7.4, 7.5) |
Due 08/03
7.4: 2, 4, 6 7.5: 2, 7, 17, 23 |
| 08/06 | Complex Eigenvalues. (7.6) |
Due 08/03
7.6: 6, 8, 15, 22 |
| 08/10 | Fundamental Matrix and Repeated Eigenvalues (7.7, 7.8) |
Due 08/03
7.7: 6, 10, 12, 15 7.8: 1, 13, 18, 21 |
| 08/11 | Nonhomogeneous Linear Systems. (7.9) |
Due
7.9: 6, 12, 14 |
| 08/12 | Review | |
| 08/13 | Final Exam |
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