Lectures to date

Date	Section (roughly)	Topic
Wed. Sept. 3, 2003	1.1	direction fields
Fri. Sept. 5, 2003	1.2, 1.3	solutions, classification
Mon. Sept. 8, 2003	2.2	separable equations
Wed. Sept. 10, 2003	2.3	Modeling, Undetermined Coefficients
Fri. Sept. 12, 2003	2.5	Autonomous Equations
Mon. Sept. 15, 2003	2.6	Exact Equations
Wed. Sept. 17, 2003	2.3	Homogeneous Equations of order Zero
Fri. Sept. 19, 2003	2.6	Integrating Factors
Mon. Sept. 22, 2003	2.1	Linear Equations
Wed. Sept. 24, 2003	2.4	Bernoulli Equations
Fri. Sept. 26, 2003	3.2	Reduction of Order
Mon. Sept. 29, 2003	2.8	Existence and Uniqueness
Wed. Oct. 1, 2003	Ch. 1&2	Review for Exam #1
Fri. Oct. 3, 2003		Exam #1
Mon. Oct. 6, 2003	8.1	Euler
Wed. Oct. 8, 2003	8.2	Improved Euler
Fri. Oct. 10, 2003	8.3,8.4	Runge-Kutta and Predictor/Corrector
Wed. Oct. 15, 2003	3.1	2nd Order ODEs: Homogeneous equations with constant coefficients
Fri. Oct. 17, 2003	3.2,3.3	The Wronskian
Mon. Oct. 20, 2003	3.4	Complex Roots
Wed. Oct. 22, 2003	3.5	Repeated Roots
Fri. Oct. 24, 2003	3.6	Undetermined Coefficients; Nonhomogeneous Equations
Mon. Oct. 27, 2003	3.7	Variation of Parameters
Wed. Oct. 29, 2003	3.8	Vibrations 1
Fri. Oct. 31, 2003	3.9	Vibrations 2
Mon. Nov. 3, 2003	Ch. 4	Higher Order Extensions
Wed. Nov. 5, 2003	Ch. 3,4, &8	Review for Exam #2
Fri. Nov. 7, 2003		Exam #2
Mon. Nov. 10, 2003	6.1	Laplace Transform
Wed. Nov. 12, 2003	6.2	Laplace and IVPs
Fri. Nov. 14, 2003	6.6	Convolution
Mon. Nov. 17, 2003	ch. 6	Laplace and IVPs
Wed. Nov. 19, 2003	6.3, 6.4	Step Functions
Fri. Nov. 21, 2003	ch. 6	Partial Fractions
Mon. Nov. 24, 2003	ch. 6	Applications of the Laplace Transform
Mon. Dec. 1, 2003	5.1	Power Series Overview
Wed. Dec. 3, 2003	5.2,5.3	IVPs with Ordinary Points
Fri. Dec. 5, 2003	5.4,5.6,5.7	IVPs with Regular Points
Mon. Dec. 8, 2003	5.5,5.8	Euler and Bessel's Equations
Wed. Dec. 10, 2003	Ch. 5 and 6	Review
Fri. Dec. 12, 2003	Ch. 1-6, 8	Review, Optional
Mon. Dec. 15, 2003		Final Exam, 2pm

Syllabus

The course will following the first chapters of Boyce and DiPrima's Elementary Differential Equations, 7th ed.. We will begin with first order differential equations, then second order linear equations. We will follow with a study of series solutions and higher order methods. Time permitting, Laplace Transformations will be investigated.

First Order Differential Equations

Approx. 3-4 weeks

Linear Equations: Variable Coefficients
Separable Equations
Nonlinear Equations: Compared to linear equations
Autonomous Equations: Equilibrium, stability, etc.
Exact Equations
Numerical Approximation: Euler's Method
Difference Equations
Existence and Uniqueness

Second Order Differential Equations

Approx. 3-4 weeks

Homogeneous Equations: Real and different roots to the characteristic equation
Homogeneous Equations: Fundamental Solutions
Theory: Linear independence and the Wronskian
Homogeneous Equations: Complex roots
Homogeneous Equations: Repeated roots and reduction of order
Nonhomogeneous Equations: Method of Undertermined Coefficients
Nonhomogeneous Equations: Variation of Parameters (general)
Application: Mechanical and Electrical Vibrations
Application: Forced Vibrations

Series Solutions to Second Order Linear Equations

Approx. 3 weeks

Power series
Series solutions: near an ordinary point
Regular singular points
Application: Euler equations
Series solutions: near a regular singular point

The Laplace Transform

Approx. 2 weeks