Math 267

Differential Equations & Transforms

Course Plan

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Textbook: Differential Equations with Boundary Value Problems
                  by J Polking, A. Boggess and D. Arnold

Chapters to be covered: 

1. First-order Differential Equations,   Lecture 1 -- Lecture 12;
2. Second-order Equations,  Lecture 13--20;
4. The Laplace Transform Methods;  Lecture 21--28;
5. Numerical Methods, Lecture 29--31;
6. Linear Systems of Differential Equations, Lecture 32--45;
7. Nonlinear Systems and Phenomena, Lecture 46-51
8. Power Series Methods;  Lecture 52--54;
Review,  Lecture 55--56  +  3  in-class exams.

Tentative Course Plan:

Week 1 23-27 August 
--- Overview,  examples  of  ODEs;
---  Mathematical models and ODE Solutions; Reading: 1.1;
--- Integrable  equations; Reading: 1.3;
---  Solution Curves; Reading: 2.1;

Week 2   30-03 September
--- Separable equations; Models of motion; Reading: 2.2-2.3;
--- Linear first-order equations; Reading: 2.4;
--- Exact Equations;  Reading: 2.6;
--- Quiz +discussion

Week 3   06-10 September
--- University holiday (no class)
--- Integration factors;   Reading: 2.6;
--- Existence & Uniqueness; Reading: 2.7;
--- Stability issues;   Reading: 2.9;

Week 4  13-17 September
--- Discussion
--- Second-order equations; Reading: 4.1;
--- Quiz2 +discussion;
--- General solution structures; Reading: 4.2;

Week 5 20-24  September
--- Homogeneous equations with constant Coefficients; Reading: 4.3;
--- Harmonic Motion; Reading: 4.4;
--- Inhomogeneous equations: Method of undetermined coefficients; Reading: 4.5;
--- Variation of Parameters; Reading: 4.6;

Week 6   27--01 September-October
-- Forced Harmonic Motion; Reading: 4.7;
--- Exam 1
--- Laplace Transform; Reading 5.1-5.2;
--- Inverse Transform, Reading 5.3;

Week 7  4--8 October
--- Transformation of Initial Value Problems; Reading 5.4;
---- Solution via Laplace Transform; Reading 5.4;
--- An Account of transform properties; Reading 5.4;
--- Discontinuous Forcing terms; Reading 5.5;

Week 8 11-15 October
---The Delta function; Reading 5.6;
---Convolutions; Reading 5.7.
---Numerical Methods; Reading 6.1;
--- Euler's Method; Reading 6.2;

Week 9  18-22 October
-- -Numerical error comparisons; Reading 6.3;
--- The Method of Elimination; Reading 7.3;
--- Matrix and Linear Systems; Reading 7.4;
--- First-order Linear systems; Reading 8.4;

Week 10   25-29  October
---Solution structure; Reading 8.4;
--- Linear system with constant coefficients: techniques; Reading 9.1;
--- Exam 2
--- Planar system; Reading 9.2;

Week 11  01 - 04 November
--- Phase Plane Portraits; Reading 9.3;
--- Continue
--- Higher-D systems; Reading 9.4;
--- The exponential of matrix; Reading 9.5;

Week 12  08-12 November
--- Higher-order linear equations; Reading 9.7;
--- Discussion;
--- Inhomogeneous linear systems; Reading 9.8;
--- Summary

Week 13    15-19 November
--- Nonlinear systems: the linearization; Reading 10.1;
--- Types of equilibrium points; Reading 10.1;
--- Long time behavior of solutions; Reading 10.2;
--- Exam 3;  

22-26 November *** Thanksgiving Break ***

Week 14    29 November ---03 December
--- Conserved quantities; Reading 10.5
--- The method of Lyapunov; Reading 10.7;
--- Discussion;
--- Review of Power Series; Reading 11.1;

Week 15 06 - 10 December
--- Continue
--- Series solutions near ordinary points; Reading 11.2.
--- Review
--- Review

Final  Week 13-17  December