Differential Equations

Math 311, Section 5635, Fall 2006

MWF 1:20-2:30, Ivers 221

Professor: Dr. Doug Anderson
  Ivers 234D
  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 5.2 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

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
100
100
100
100
100

  as scheduled 
  September 22 
  October 13 
  November 8 
  December 1 
  December 14 (Thursday), 8:30


With a total of 650 points, the course grades will be as follows:

A- 
B+ 

B- 
C+

601-650
581-600
562-580
536-561
516-535
497-515

C
C-
D+
D
D-
F

471-496
451-470
432-450
406-431
386-405
0-385


Daily Schedule and Assignments:

Date Section Exercises
Sep 1 1.1 Intro to ODEs (10) 11,15,21,25,27,37,45,47,51,52,53
      
3 Mathematica Lab Sunday 6pm-8pm, Ivers 222
4 2.1 Slope Fields (46) 1,3,5,7,9,11,13,19,21,25,29
6 2.2 Separable Variables (54) 3,5,7,13,15,25,29a,32,37,39
8 2.3 Linear Equations (65) 3,5,11,13,17,25,33,47
      
11 Fall Symposium Memorial Auditorium
13 2.4 Exact Equations (73) 1,5,7,11,15,21,27,29
15 2.5 Substitutions [PROJECT DUE: Harvesting] (78) 5,7,9,13,15,23,27,35
      
18 2.6 Euler's Method (84) 1,3,7,9,11; (372) 1,9
20 Review (85) 1-8abcefh,11-13,17-20,22,23
22 Exam 1
      
25 3.1 Linear Models (98) 1,5,7,11,13,17,19,21,41
27 4.1 Linear Equations: Theory (137) 3,5,7,9,13,19,21,23,27
29 4.3 Constant Coefficients (147) 7,13,17,19,37,39,49
      
Oct 2 4.4 Undetermined Coefficients (158) 1,3,5,7,9,13,17,27,33
4 4.6 Variation of Parameters [PROJECT DUE: Swimming] (172) 1,5,7,15,19,21
6 4.7 Cauchy-Euler Equation (178) 1,3,5,13,15,19,21,27
      
9 5.1.1 Free Motion (207) 1,5,9,11,17,19,21,25
11 Review (99) 14; (120) 2,4,7; (230) 12
(189) 1-4,7,9-11,17,18,20,21,24,36
13 Exam 2
      
16 5.1.3 Sinusoidal Forcing (209) 29,31
18 5.1.3 Undamped Forcing (210) 39,41
20 Fall Break No Class
      
23 Fall Break No Class
25 7.1 Laplace Transform (283) 3,5,7,9,11,17,33
27 No Class Nebraska Workshop
      
30 7.2 Inverse Transform [PROJECT DUE: Bungee] (292) 1,3,5,7,9,35,37,41
Nov 1 7.3 Translation Theorems (301) 3,9,13,17,27,29,41,43,47,49-53,65,67
3 7.4, 7.5 Dirac Function (312) 1,3,11,13,17,19,31,43; (318) 1,3,5,7
      
6 Review (230) 1-8,11,12,14-18; (324) 1,2,6,7-21,33,37,38
8 Exam 3
10 5.2 Boundary-Value Problems (217) 15,17,25
      
13 11.1 Orthogonal Functions (434) 11,15,17,21
15 11.2 Fourier Series [PROJECT DUE: Galloping Gertie] (439) 5,17
17 11.3 Cosine & Sine Series (446) 11,13,37
      
20 11.4 Sturm-Liouville Problems (454) 1,3,7
22 12.1 Separation of Variables (468) 3,4,5,9,10; read Section 12.2
24 Thanksgiving No Class
      
27 12.3 Heat Equation (477) 2,3,4; read 12.2: (474) 1-9 odd
29 Review (230) 9,10,23; (462) 1-8,10,13; (501) 1,11
Dec 1 Exam 4
      
4 12.4 Wave Equation (480) 1,4,8
6 12.5 Laplace's Equation [PROJECT DUE: Mayfair] (486) 2,5,6
8 Review (501) 5,7-9
      
11 Review Exams 1-4
14 Final Exam 8:30-10:30


Link for Phase Portraits

ODE Phase Portrait: This website from Penn State University, developed by Richard Mansfield and Frits Beukers, will draw the nullclines and solutions for various initial conditions in phase space for systems of two ordinary differential equations. For a single differential equation, let x' = 1 and y ' = right-hand side.


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  • Updated: 28 November 2006