Differential Equations

Math 311, Section 5633, Fall 2004

MWF 1:20-2:30, Ivers 221

Professor: Dr. Doug Anderson
  Ivers 234G
  299-4453 (office), 299-4151 (math department)
  e-mail: andersod@cord.edu

Office Hours: MWF 2:35-3:35; Tuesday 10:30-12, 1-3:00; Thursday 1-4; 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, 5th edition, by Zill and Cullen, ISBN 0-534-38002-6. We will also be using Mathematica, a computer algebra system. Mathematica 5.0 is available on the campus network, and can be downloaded onto the personal computer of any Concordia student free of charge.

Prerequisite: Math 122 (Calculus II) or equivalent; Math 210 (Linear Algebra) is strongly encouraged.

Homework/Projects: Homework will be assigned each day for your practice in mastering the material. Homework that is turned in should be neat and organized. You will not only be graded on correct answers but also on the neatness, organization, 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. Even-numbered problems with be due the second class period after they are assigned. Up to four (4) late assignments will be allowed, but no more than four.

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, which must be made up in a timely manner (to be discussed with me individually).

Homework, Labs 
Exam I 
Exam II 
Exam III 
Final Exam

150
100
100
100
200

  Every class 
  September 29 
  October 29 
  November 29 
  December 17 (Friday), 10:30


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 3 1.1 Intro to ODEs (11) 11,12,15,17,18,23,25,26,40,46
      
5 Mathematica Lab Sunday 6pm-8pm, Ivers 222
6 2.2 Separable Variables (57) 4,7,13,16,25,30,32,37,38
8 2.3 Linear Equations (69) 3,4,11,14,17,18,33,34,50
10 2.4 Exact Equations (78) 1,4*,6,8*,11,21,24*,42(b)
      
13 2.6 Euler's Method (91) 1,2,7,8,14; (416) 12
15 3.1 Linear Models (103) 1,2,7,8,13,14,19,20,38
17 Bifurcation Diagrams Handout
      
20 Lab 1 Handout
22 4.1 Linear Equations: Theory (151) 5,6,9,10*,23,24,26*,28
24 4.3 Constant Coefficients (164) 7,13,17,19,37,39,49
      
27 Review (92) 1,6,12,13,15,18,19,22; (131) 4,5
29 EXAM I
Oct 1 4.4 Undetermined Coefficients (176) 1,2,4,5,8,9,12,17,27,34
      
4 4.6 Variation of Parameters (192) 1,4,8,12,19,20
6 4.7 Cauchy-Euler Equation (199) Case(ii),1,2,3,12,14*,19,20
8 4.9 Nonlinear Equations (211) 3,4,10,14,18
      
11 5.1.1 Free Motion (229) 1,2,9,10,17-20,22
13 5.1.3 Sinusoidal Forcing (233) 29,30,35(read),36
15 5.1.3 Undamped Forcing Beats and Resonance Handout
      
18 5.2 Boundary-Value Problems (243) 15,21,25
20 Lab 2 Handout
22 Fall Break No Class
      
25 5.3 Nonlinear Pendulum (254) read 24
27 EXAM II Take-home test
29 Exam due at 4 pm
      
Nov 1 Fall Symposium No Class
3 6.1 Ordinary Points (279) 13,16,22,28
5 Nebraska Workshop No Class
      
8 6.2 Singular Points (289) 1-6,24
10 Legendre Polynomials Handout
12 Hermite Polynomials Handout
      
15 7.1 Laplace Transform (312) 3,4,7,8,12,18,34
17 7.2 Inverse Transform (322) 1,3,6,8,35,36,38
19 7.3 Translation Theorems (333) 3,9,13,16,27,28,41,46,47,49-54,66,67
      
22 7.4 Additional Properties (347) 1,3,9,13,17,19,31,43
24 7.5 Dirac Delta Function (354) 1,3,5,7
26 Thanksgiving No Class
      
29 EXAM III Take-home test
Dec 1 Exam due at 4 pm
3 11.1 Orthogonal Functions (488) 11,15,17,21
      
6 11.2 Fourier Series (494) 5,17
8 11.3 Cosine & Sine Series (501) 11,13,37
10 11.4 Sturm-Liouville Problems (510) 1,3,7
      
13 No Class
17 Final Exam Due Friday 10:30 am


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: 6 December 2004