Syllabus for Math 2700, Spring '04

Our text is 'Differential Equations with Boundary Value Problems', by Conrad.

We will cover Sections 1.1-1.3, 2.1-2.4, 3.1-3.4, 4.1-4.3, 8.1-8.2, 4.4-4.5, 5.1-5.6,5.8, 6.1-6.7, 7.1, 7.5, 8.3

Week 1-2, Chapter 1, Intro to linear differential equations, homogeneous and inhomogeneous equations, variation of constants, form of general solution.

Week 2-3, Chapter 2, Intro to nonlinear differential equations, separable equations, form and integrating factors, graphical analysis, initial value problems, existence and uniqueness.

Week 3, Chapter 3, Intro to systems of differential equations, the phase plane, ivp solvers.

Week 4, Chapter 3, autonomous systems, Chapter 4, Systems of linear differential equations, matrices and vectors, systems in matrix form, systems with constant coefficients.

Week 5, Chapter 4, systems with oscillating solutions, Chapter 8, Phase portraits of linear systems, stability of linear systems.

Week 6, Chapter 4, General solution of a linear system, variation of constants, exponential of a matrix

Week 7, Chapter 5, Second order equations, initial value problem, phase plane analysis, homogeneous equations, homogeneous equations with constant coefficients, free vibrations.

Week 8, Chapter 5, Inhomogeneous second order equations, forced vibrations, variation of constants.

Week 9-10, Chapter 6, The Laplace transform, electrical circuits, propertiese of the Laplace transform.

Week 10-11, Chapter 6, Inverse Laplace transforms of rational functions, the unit step function, the delta function.

Week 12-13, Chapter 6, Convolution. Chapter 7, Linear differential equations with variable coefficients, power series, solutions at an ordinary point, Cauchy-Euler equations, regular singular points.

Week 14, Chapter 7, Bessel functions. Chapter 8, Stationary points of nonlinear systems

Homework will be assigned at the end of class on Fridays and will be due the following Friday, unless it is a holiday, in which case I will announce when the homework is due.

Grading will be based on homework, short quizzes, a midterm and a final exam.

On Fridays, we have a computer laboratory reserved. When we are discussing numerical solutions of differential equations, we will meet in the lab. I will announce whether we meet in the lab or in the classroom in the previous class, or by email announcement.

Office Hours: Mondays, 1:10-2:10

Wednesdays, 4:00-5:00

Thursdays, 3:15-4:15