Applied Mathematics

Math 312, Section 5632, Winter 2006

MWF 2:40-3:50, Ivers 218


Professor: Doug Anderson, Ph.D.
  Ivers 234G
  299-4453
  andersod@cord.edu

Office Hours: TTh 1:00-3:30, MWF by discovery.

Text: Differential Equations with Boundary Value Problems, 6th edition, by Zill and Cullen. 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 210 Linear Algebra, Math 223 Calculus III, Math 311 Differential Equations.

Content: In this follow-up course to Math 311 Differential Equations, we explore additional techniques for solving ordinary and partial differential equations. Some of the standard models of mathematical physics, including the heat equation, the wave equation, and Laplace's equation, are discussed. Classical solution techniques involve power series, Fourier series, and eigenfunction expansions on bounded domains.

Homework: Homework will be assigned each day for your practice in mastering the material, and will be due two class periods later; if you have questions please ask them the following class period after the homework is assigned, or visit me during office hours. I will allow up to two (2) late submissions without penalty; after that late homework will not be accepted. 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, and clarity of the steps/arguments used to derive your answers; the use of correct grammar and complete sentences is imperative.

Exam: There will be one take-home exam at the end of the block. You are allowed to use your text, class notes, homework, and Mathematica 5.1 where appropriate, but you must work independently. Solutions should first be written out on scratch paper, with the final submitted version neatly written without cross-outs or restarts.

Grading: Points                  Scale
Homework 200 A 90%--100%
B 80%--89%
Exam 100 C 70%--79%
D 60%--69%
F Below 60%



Class Schedule:
      
Date Section Exercises
Jan 4 12.1 Separation of Variables (468) 3,4,5,9,10
6 12.3 Heat Equation (477) 2,3,4; read 12.2: (474) 1-9 odd
      
9 12.4 Wave Equation (480) 1,4,8
11 Math Conference No Class
13 Math Conference No Class
      
16 12.5 Laplace's Equation (486) 2,5,6
18 12.6 Nonhomogeneous Equations (491) 6,9*
20 8.1 Systems (336) 12,14,17,18
      
23 8.2.1 Real Eigenvalues (351) 1,2,4,18
25 8.2.2 Repeated Eigenvalues (351) 20,21*,32
27 8.2.3 Complex Eigenvalues (352) 37*,38,47*
      
30 10.1 Autonomous Systems (400) 3,4,6,9-14,24
Feb 1 10.2 System Stabililty (408) 9-18,20
3 10.3 Linearization (417) 11,12,15,18
      
6 10.4 Systems Models (426) 16,20
8 Phase Plane Analysis Handout
10 Phase Plane Analysis Handout
      
13 Bifurcations Handout
15 Take-home Exam
17
      
20
22 Exam Due
24 Spring Break No Class


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.


  • Doug Anderson's home page.
  • Concordia College Math/CS home page.
  • Concordia College home page.

  • Last update: 1 February 2006