| Professor: | Dr. Douglas Anderson |
| Ivers 234G | |
| 299-4453 | |
| andersod@cord.edu |
Office Hours: MTWRF 2:00-4:00, or by appointment.
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, 5th edition, by Zill and Cullen, ISBN 0-534-38002-6. 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 student free of charge.
Prerequisites: Math 122 (Calculus II) and Math 210 (Linear Algebra).
Quizzes/Projects: Exercises will be assigned each day for your practice in mastering the material; these problems will be odd numbered so that you can check your answers in the book. Every Tuesday, Wednesday, and Thursday there will be a quiz at the beginning of the period (or homework collected) over the essential material from the day before. On Fridays, after the exams, there will be a project assigned for you to work on over the weekend. Projects should be neat and organized; you will not only be graded on correct answers but also on the neatness and organization of your presentation, a clear explanation of the steps used to derive your answers, and the use of correct grammar and complete sentences. You must abide by the college's expectations regarding academic integrity.
Exams: Attendance is required for all exams. 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 and it must be made up in a timely manner (to be discussed with me individually). There is an exam scheduled for every Friday of the four-week period. These will all be unit exams covering the sections listed; there will be no final exam.
| Quizzes/HW Projects (3) Exam 1 Exam 2 Exam 3 Exam 4 |
150 |
Every Tues, Wed, Thurs |
| Date | Scheduled Section | Suggested Exercises |
| June 5 | 1.1 Intro to ODEs | (11) 11,12,15,17,18,23,25,26,40,46 |
| 2.2 Separable Variables | (57) 4,7,13,16,25,30,32,37,38 | |
| Mathematica Lab | Computer Lab | |
| 6 | 2.3 Linear Equations | (69) 3,4,11,14,17,18,33,34,50 |
| 2.4 Exact Equations | (78) 1,4*,6,8*,11,21,24*,42(b) | |
| 7 | 2.6 Euler's Method | (91) 1,2,7,8,14; (416) 12 |
| 3.1 Linear Models | (103) 1,2,7,8,13,14,19,20,38 | |
| 8 | Bifurcation Diagrams | |
| 3.3 Modeling with Systems | ||
| 9 | Exam 1 | 1.1~3.3 |
| Project 1 | Handout (due Monday, June 12) | |
| June 12 | 4.1 Linear Equations: Theory | (151) 5,6,9,10*,23,24,26*,28 |
| 4.2 Reduction of Order | Read and prepare | |
| 13 | 4.3 Constant Coefficients | (164) 7,13,17,19,37,39,49 |
| 4.4 Undetermined Coefficients | (176) 1,2,4,5,8,9,12,17,27,34 | |
| 14 | 4.6 Variation of Parameters | (192) 1,4,8,12,19,20 |
| 5.1.1 Free Motion | (229) 1,2,9,10,17-20,22 | |
| 15 | 5.1.3 Sinusoidal Forcing | (233) 29,30,35(read),36 |
| 5.1.3 Undamped Forcing | Beats and Resonance Handout | |
| 16 | Exam 2 | 4.1~5.1 |
| Project 2 | Mathematica Notebook (due Monday, June 19) | |
| June 19 | 8.1 Systems | (373) 12,14,17,18 |
| 8.2.1 Real Eigenvalues | (389) 1,2,4,18 | |
| 20 | 8.2.2 Repeated Eigenvalues | (391) 20,21*,32 |
| 8.2.3 Complex Eigenvalues | (392) 37*,38,47* | |
| 21 | 10.1 Autonomous Systems | (446) 3,4,6,9-14,24 |
| 10.2 System Stabililty | (456) 9-18,20 | |
| 22 | 10.3 Linearization | (467) 11,12,15,18 |
| 10.4 Systems Models | (479) 16,20 | |
| 23 | Exam 3 | 8.1~10.4 |
| Project 3 | Handout (due Monday, June 26) | |
| June 26 | 4.7 Cauchy-Euler Equation | (199) Case(ii),1,2,3,12,14*,19,20 |
| 4.9 Nonlinear Equations | (211) 3,4,10,14,18 | |
| 27 | 5.2 Boundary-Value Problems | (243) 15,21,25 |
| 7.1 Laplace Transform | (312) 3,4,7,8,12,18,34 | |
| 28 | 7.2 Inverse Transform | (322) 1,3,6,8,35,36,38 |
| 7.3 Translation Theorems | (333) 3,9,13,16,27,28,41,46,47,49-54,66,67 | |
| 29 | 7.4 Additional Properties | (347) 1,3,9,13,17,19,31,43 |
| 7.5 Dirac Delta Function | (354) 1,3,5,7 | |
| 30 | Exam 4 | 4.7~7.5 |