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
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