| Professor: | Dr. Doug Anderson |
| Ivers 234G | |
| 299-4453 (office), 299-4151 (math department) | |
| e-mail: andersod@cord.edu |
Office Hours: Tuesday and Thursday 1-4 pm; other times by discovery.
Goals: This course aims to introduce elementary qualitative and analytic methods for analyzing ordinary differential equations (odes). These methods include separation of variables, integrating factors, characteristic equations, series solutions, and the Laplace transform for first and higher-order odes and mathematical models such as spring/mass systems (harmonic oscillators) and logistic growth.
Text/Mathematica: Differential Equations with Boundary Value Problems, 6th edition, by Zill and Cullen, ISBN 0-534-41887-2. We will also be using Mathematica, a computer algebra system. Mathematica 5.1.1 is available on the campus network, and can be downloaded onto the personal computer of any Concordia College student free of charge.
Prerequisite: Math 122 (Calculus II) or equivalent; Math 210 (Linear Algebra) is strongly encouraged.
Projects/Homework: Homework problems are recommended after each class period for your practice in mastering the
material. Note that all of the suggested problems are odd, so that you may check your own answers.
There will be five projects due during the semester. Project write-ups should be neat and organized.
You will not only be graded on correct answers but also on the neatness and organization of your results,
the explanation of your reasoning and the steps used to derive your answers, and the use of correct grammar
and complete sentences. All students must abide by the college's expectations regarding academic integrity
and quality. You may work in groups on the projects, but no more than four students will be allowed in any one
group. The composition of the groups may change from project to project. Keep in mind that under normal
circumstances everyone in the group will receive the same score on the project, although exceptions may be made for
obvious freeloaders. No late projects will be accepted.
Exams: There will be four in-class exams. Attendance is required for all of them on the dates listed.
If you should miss an exam for an emergency
you will be allowed to make it up only if you have notified me before the exam,
which must be made up in a timely manner (to be discussed with me individually).
|
Projects (5) Exam 1 Exam 2 Exam 3 Exam 4 Final Exam |
150 |
as scheduled |
|
A A- B+ B B- C+ |
601-650 |
C C- D+ D D- F |
471-496 |
| Date | Section | Exercises |
| Sep 2 | 1.1 Intro to ODEs | (10) 11,13,15,17,21,23,25,27,37,45 |
| 4 | Mathematica Lab | Sunday 6pm-8pm, Ivers 222 |
| 5 | 2.1 Slope Fields | (46) 1,3,5,7,9,11,13,19,21,25,29 |
| 7 | 2.2 Separable Variables | (54) 3,5,7,13,15,25,29a,32,37,39 |
| 9 | 2.3 Linear Equations | (65) 3,5,11,13,17,25,33,47 |
| 12 | Fall Symposium | No Class |
| 14 | 2.4 Exact Equations | (73) 1,5,7,11,15,21,27,29 |
| 16 | 2.5 Substitutions [PROJECT DUE: Harvesting] | (78) 5,7,9,13,15,23,27,35 |
| 19 | 2.6 Euler's Method | (84) 1,3,7,9,11; (372) 1,9 |
| 21 | Review | (85) 1-8,10-15,17-20,22,23 |
| 23 | Exam 1 | |
| 26 | 3.1 Linear Models | (98) 1,5,7,11,13,17,19,21,41 |
| 28 | 3.3 Systems of Equations | (118) 7,9,11,17 |
| 30 | 4.1 Linear Equations: Theory | (137) 3,5,7,9,13,19,21,23,27 |
| Oct 3 | 4.3 Constant Coefficients | (147) 7,13,17,19,37,39,49 |
| 5 | 4.4 Undetermined Coefficients | (158) 1,3,5,7,9,13,17,27,33 |
| 7 | 4.6 Variation of Parameters [PROJECT DUE: Swimming] | (172) 1,5,7,15,19,21 |
| 10 | 4.7 Cauchy-Euler Equation | (178) 1,3,5,13,15,19,21,27 |
| 12 | Review | (99) 14; (120) 2,4,7; (189) 1-4,7,9-11,17,18,20,21,24,36 |
| 14 | Exam 2 | |
| 17 | 5.1.1 Free Motion | (207) 1,5,9,11,17,19,21,25 |
| 19 | 5.1.3 Sinusoidal Forcing | (209) 29,31,35 |
| 21 | Fall Break | No Class |
| 24 | 5.1.3 Undamped Forcing | (210) 39,41 |
| 26 | 5.2 Boundary-Value Problems | (217) 15,17,25 |
| 28 | 5.3 Nonlinear Pendulum [PROJECT DUE: SIR Model] | (227) 3,9,11 |
| 31 | 6.1 Ordinary Points | (248) 17,23,25,31 |
| Nov 2 | 6.2 Singular Points | (257) 1,3,5,7,9,23 |
| 4 | Legendre Polynomials | Handout |
| 7 | Review | (230) 1-12,14-18,23; (271) 4,7,8,11,13 |
| 9 | Exam 3 | |
| 11 | 7.1 Laplace Transform | (283) 3,5,7,9,11,17,33 |
| 14 | 7.2 Inverse Transform | (292) 1,3,5,7,9,35,37,41 |
| 16 | 7.3 Translation Theorems [PROJECT DUE: Bungee] | (301) 3,9,13,17,27,29,41,43,47,49-53,65,67 |
| 18 | 7.4 Additional Properties | (312) 1,3,11,13,17,19,31,43 |
| 21 | 7.5 Dirac Delta Function | (318) 1,3,5,7 |
| 23 | 11.1 Orthogonal Functions | (434) 11,15,17,21 |
| 25 | Thanksgiving | No Class |
| 28 | 11.2 Fourier Series | (439) 5,17 |
| 30 | Review | (324) 1-3,6,7-21,33,35,37,38; (462) 1,6,13 |
| Dec 2 | Exam 4 | |
| 5 | 11.3 Cosine & Sine Series | (446) 11,13,37 |
| 7 | 11.4 Sturm-Liouville Problems [PROJECT DUE: Mayfair] | (454) 1,3,7 |
| 9 | Review | (462) 1-8,10 |
| 12 | Review | Exams 1-4 |
| 14 | Final Exam 8:30-10:30 |