Math 13, Fall 2005


Math 13 Home | Course Information | Assignments
Schedule | ODE Software | Expectations

This day-by-day schedule will be modified as we go along.
Green numbers indicate sections of Borrelli and Coleman's book.

Week 1
  • Fall Break: No class on Monday
  • Introduction: DEs, IVPs, modeling, solving, interpreting;
    Sections 1.1, 1.2
  • Refining the fish model, Classification of DEs, skydiver model, qualitative methods, ODE Architect demo;
    1.2, 1.3
Week 2
  • Linear first-order DEs, analytic methods of solving, method of Integrating Factors; 2.1
  • Structure of solutions, ODE Architect demo, existence and uniqueness of solutions, Cold Medication;
    2.2, 2.3, Spotlight from Ch 1
  • Visualizing solution curves, direction fields, ODE Architect demo, approximate numerical solutions; 2.4, Spotlight from Ch 2
Week 3
  • Separable DEs; 2.5
  • A predator--prey model: the Lotka--Volterra system; 2.6
  • Models of springs, undriven constant-coefficient linear DEs; 3.1, 3.2
Week 4
  • Undriven constant-coefficient linear DEs (cont.), visualizing solutions;
    3.2, 3.3
  • Complex-valued solutions, periodic solutions, simple harmonic motion. 3.3, 3.4
  • Friday: In-class Midterm
Week 5
  • Existence and uniqueness, Wronskians, basic solution sets; 3.7
  • Linear independence, Abel's Theorem, Wronskian reduction of order; 3.7
  • Driven linear DEs, undetermined coefficients; 3.5
Week 6
  • Undetermined coefficients (cont.), variation of parameters; 3.5
  • Interpretation for driven spring--mass systems, including beats and resonance; 4.2
  • Thanksgiving: no class on Friday
Week 7
  • Compartment models: tracking lead in the human body; 6.1
  • Eigenvalues, eigenvectors, eigenspaces, undriven linear differential systems, real eigenvalues; 6.2, 6.3
  • Complex eigenvalues, orbital portraits for planar systems; 6.4, 6.5
Week 8
  • Guest lecture by Tara Martin '04, UCLA, on S.I.R. models
  • Evaluations, Romeo and Juliet
  • Introduction to Partial Differential Equations (PDEs)
  • Takehome Final


Last modified December 2005, by ward