MAP 2302: Elementary Differential Equations
University of Florida, Fall 2011
Instructor information:
Vince VatterOffice: Little Hall 412
Office hours: Mondays 1:55–2:45, Wednesdays 3:00–3:55, and by appointment
Office phone: (352) 392-0281 extension 245
Email: vatter at ufl dot edu
Text:
Fundamentals of Differential Equations and Boundary Value Problems, 6th edition, by Nagle, Saff, and Snider.Course Objectives:
First-order ordinary differential equations, theory of linear ordinary differential equations, solution of linear ordinary differential equations with constant coefficients, the Laplace transform and its application to solving linear ordinary differential equations. The actual selection of topics will be much like previous installments.Grading:
We will have four in-class midterm exans and a comprehensive final exam. The dates of the in-class midterm exams are:
- Monday, September 12,
- Monday, October 3,
- Friday, October 28, and
- Monday, November 21.
The final grades will be curved, but will be no tougher than the 10-point scale: 90%–100% will be some form of A, 80–90% will be at least some form of B, etc. After each midterm, you will receive a projected grade.
If you have a disagreement with the grading of one of your solutions, I ask that you submit a written request for reconsideration within one month.
Tentative Schedule:
| Lecture | Date | Topics | Section(s) |
|---|---|---|---|
| 1 | M 8/22 | Introduction | 1.3 & 2.2 |
| 2 | W 8/24 | Separable equations Suggested exercises: 1–21 odds |
2.2 |
| 3 | F 8/26 | Linear equations Suggested exercises: 1–15 odds |
2.3 |
| 4 | M 8/29 | Explicit & implicit solutions Suggested exercises: 1, 3, 5, 7, 15 (Section 1.2) |
1.2 |
| 5 | W 8/31 | Existence & uniqueness for first order IVPs Suggested exercises: 23, 25, 27, 29, 31 (Section 1.2), 1, 5, 17 (Section 1.3) |
1.2 & 1.3 |
| 6 | F 9/2 | Exact equations Suggested exercises: 1–15 odds, 21, 23 |
2.4 |
| M 9/5 | Class canceled for Labor Day | ||
| 7 | W 9/7 | Transformations & Bernoulli equations Suggested exercises: 1–11 odds, 17, 19, 21–25 odds |
2.6 |
| F 9/9 | Review for Midterm #1 Review problems: pdf or tex Review solutions: pdf or tex |
||
| M 9/12 |
Midterm #1:
pdf or
tex Solutions to Midterm #1: pdf |
||
| 8 | W 9/14 |
Second-order linear homogeneous differential equations I Suggested exercises: See Friday 9/16 |
4.2 & 4.3 |
| 9 | F 9/16 |
Second-order linear homogeneous differential equations II Suggested exercises: 1–19 odds (Section 4.2) and 9–27 odds (Section 4.3) |
4.2 & 4.3 |
| 10 | M 9/19 |
The method of undetermined coefficients I Suggested exercises: 9, 11, 13, 15 (Section 4.4) and 3, 5, 7, 17, 19 (Section 4.5) |
4.4 & 4.5 |
| 11 | W 9/21 |
The method of undetermined coefficients II Suggested exercises: 17, 19, 21 (Section 4.4) and 23–29 odds (Section 4.5) |
4.4 & 4.5 |
| F 9/23 | Group review of the method of undetermined coefficients: pdf or tex | ||
| 12 | M 9/26 |
Variation of parameters I Suggested exercises: 1– 17 odds |
4.6 |
| 13 | W 9/28 | Variation of parameters II | 4.6 |
| F 9/30 |
Review for Midterm #2 Review problems: pdf or tex Official formula sheet: pdf Review solutions: pdf or tex |
||
| M 10/3 |
Midterm #2:
pdf or
tex Solutions to Midterm #2: pdf |
||
| 14 | W 10/5 |
The Laplace transform I Suggested exercises: none! |
7.2 & 7.3 |
| 15 | F 10/7 |
The Laplace transform II Suggested exercises: 1–11 odds (Section 7.2) and 1–21 odds (Section 7.3) |
7.2 & 7.3 |
| 16 | M 10/10 |
The inverse Laplace transform Suggested exercises: 1–29 odds |
7.4 |
| 17 | W 10/12 |
Solving IVPs with the Laplace transform Suggested exercises: 15–23 odds |
7.5 |
| F 10/14 |
Group review: pdf or tex Solutions: pdf or tex |
7.6 | |
| 18 | M 10/17 |
Piecewise and periodic functions I Suggested exercises: 1–17 odds, 29, 31 (piecewise functions) |
7.6 |
| 19 | W 10/19 |
Piecewise and periodic functions II Suggested exercises: 21–31 odds, 41 (periodic functions) |
7.6 |
| F 10/21 |
Group review: pdf or tex Solutions: pdf or tex |
||
| 20 | M 10/24 |
Impulses and the Dirac Delta Suggested exercises: 1–19 odds |
7.8 |
| W 10/26 |
Review for Midterm #3 Review problems: pdf or tex Official formula sheet: pdf Review solutions: pdf or tex |
||
| F 10/28 |
Midterm #3: pdf or tex (special guest proctor!) Solutions to Midterm #3: pdf |
||
| 21 | M 10/31 |
Review of power series Suggested exercises: none, but please do practice with Taylor series |
8.2, or lecture notes |
| 22 | W 11/2 |
Power series solutions to ODEs Suggested exercises: 11–27 odds. |
8.3 |
| F 11/4 | Class canceled for Homecoming | ||
| 23 | M 11/7 |
More of the same Suggested exercises: 13, 15, 21, 23, 29 |
8.4 |
| 24 | W 11/9 |
Cauchy-Euler equations Suggested exercises: 1–10 odds (Section 8.5) |
8.5, or lecture notes |
| F 11/11 | Class canceled for Veterans Day | ||
| 25 | M 11/14 |
Ordinary vs. singular points & Method of Frobenius Suggested exercises: 1–9 odds (Section 8.3) and 1, 3, 5, 11, 17, 19, 21, 25 (Section 8.6). |
8.6 (with bits of 8.3) |
| 26 | W 11/16 | Springs (special guest lecturer!) | 4.1 |
| F 11/18 |
Review for Midterm #4 Review problems: pdf or tex Review answers: text file |
||
| M 11/21 |
Midterm #4:
pdf or
tex
(special guest proctor!) Solutions to Midterm #4: pdf |
||
| 27 | W 11/23 | Highly optional discussion of Midterm #4 | |
| F 11/25 | Class canceled for Thanksgiving | ||
| 28 | M 11/28 |
The mass-spring analogy Suggested exercises: 11, 15 |
4.8 (pgs. 206–209 only) |
| 29 | W 11/30 |
Free mechanical vibrations I Suggested exercises: 1–13 odds |
4.9 |
| 30 | F 12/2 | Free mechanical vibrations II | 4.9 |
| M 12/5 |
Review for final exam I Review problems: pdf or tex Review solutions: pdf or tex |
||
| W 12/7 | Review for final exam II | ||
Final exam: You may take the final exam on either Wednesday 12/14 or Friday 12/16, but you may only take the exam once! The two different days will be given two different exams. The classrooms and times are as follows:
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