# Differential Equations

**Winter 2009 Syllabus (For sections: 20, 50)**

Some of the material covered, and some of the dates may be changed at your
instructor's discretion.

You will be informed if this is the case. Key: blue text indicates due dates for
written assignments

to be turned in to your recitation instructor, red text indicates closing times
for the web homework

assignments, and magenta text indicates scheduled exams. Prelab assignments can
be found in the

lab manuals that may be downloaded from the course website. The review of
complex numbers text

supplement may also be downloaded from the course website.

**Week 1:
Wednesday, January 7. Lecture.**

Mathematical modeling with differential equations, solutions given by integrals, and slope fields. Ed-

wards and Penney sections 1.1, 1.2, and 1.3.

**Friday, January 9. Lecture.**

Separable and linear first-order differential equations. Edwards and Penney
sections 1.4 and 1.5.

**Week 2:
Monday, January 12. Lecture.**

Differential equations for population modeling. Edwards and Penney section 2.1.

**Tuesday, January 13. Lab.**

Lab 1.

**Wednesday, January 14. Lecture.**

Equilibria and their stability. Edwards and Penney section 2.2.

**Friday, January 16. Lecture.**

Differential equations for kinematics of velocity and acceleration. Edwards and Penney section 2.3.

Due to recitation instructor by 5 PM: Homework Set 1.

Web Homework Sets 0 and 1 close at 10 PM.

**Week 3:**

Monday, January 19. NO LECTURE (Dr. Martin Luther King Jr. Day)

Tuesday, January 20. Recitation.

Monday, January 19. NO LECTURE (Dr. Martin Luther King Jr. Day)

Tuesday, January 20. Recitation.

Review. (Quiz #1)

**Wednesday, January 21. Lecture.**

Numerical methods for approximating solutions of initial-value problems for
differential equations. Ed-

wards and Penney sections 2.4, 2.5, and 2.6.

**Friday, January 23. Lecture.**

Review.

Due to recitation instructor by 5 PM: Homework Set 2 and Writeup of Lab 1.

Web Homework Set 2 closes at 10 PM.

**Week 4:
Monday, January 26. Lecture.**

Second-order linear differential equations. Edwards and Penney section 3.1.

**Tuesday, January 27. Lab.**

Lab 2. Due at beginning of lab: Prelab assignment for Lab 2.

Wednesday, January 28. Lecture.

Wednesday, January 28. Lecture.

Complex numbers.

**Friday, January 30. Lecture.**

General facts about linear equations. Second-order linear homogeneous equations
with constant coefficients.

Edwards and Penney sections 3.2 and 3.3.

Due to recitation instructor by 5 PM: Homework Set 3.

Web Homework Set 3 closes at 10 PM.

**Week 5:
Monday, February 2. Lecture.**

Edwards and Penney section 3.3, continued.

**Tuesday, February 3. Recitation.**

Review. (Quiz #2)

**Wednesday, February 4. Lecture.**

Differential equations governing mechanical vibrations. Edwards and Penney section 3.4.

**Friday, February 6. Lecture.**

Nonhomogeneous terms, the method of undetermined coefficients, and the method of variation of pa-

rameters. Edwards and Penney section 3.5.

**Week 6:
Monday, February 9. Lecture.**

Edwards and Penney section 3.5, continued.

**Tuesday, February 10. Recitation.**

Review. (Quiz #3)

Wednesday, February 11. Lecture.

Wednesday, February 11. Lecture.

Forced oscillations and resonance. Edwards and Penney section 3.6.

Due to recitation instructor by 5 PM: Homework Set 4 and Writeup of Lab 2.

Web Homework Set 4 closes at 10 PM.

Friday, February 13. Lecture.

Friday, February 13. Lecture.

Review.

**Week 7:**

Monday, February 16. Lecture.

Monday, February 16. Lecture.

Review. Exam 1, 6{8 PM.

**Tuesday, February 17. Lab.**

Lab 3. Due at beginning of lab: Prelab assignment for Lab 3.

**Wednesday, February 18. Lecture.**

First-order systems of differential equations and the method of elimination. Edwards and Penney

sections 4.1 and 4.2.

**Friday, February 20. Lecture.**

Numerical methods for systems of first-order equations. Edwards and Penney section 4.3. Review.

Due to recitation instructor by 5 PM: Homework Set 5.

**Web Homework Set 5 closes at 10 PM.**

Winter Break: Saturday, February 21 { Sunday, March 1

**Week 8:
Monday, March 2. Lecture.
**

Linear algebra, eigenvalues and eigenvectors. Edwards and Penney section 5.1.

**Tuesday, March 3. Recitation.**

Review. (Quiz #4)

**Wednesday, March 4. Lecture.**

Edwards and Penney section 5.1, continued.

**Friday, March 6. Lecture.**

Edwards and Penney section 5.1, continued.

Due to recitation instructor by 5 PM: Homework Set 6 and Writeup of Lab 3.

Web Homework Set 6 closes at 10 PM.

**Week 9:
Monday, March 9. Lecture.**

Homogeneous constant-coefficient linear systems and eigenvalues. Edwards and Penney section 5.2.

**Tuesday, March 10. Lab.**

Lab 4. Due at beginning of lab: Prelab assignment for Lab 4.

**Wednesday, March 11. Lecture.**

Edwards and Penney section 5.2, continued.

**Friday, March 13. Lecture.**

Mechanical vibrations governed by second-order systems of differential equations. Edwards and Penney

section 5.3. Review.

Web Homework Set 7 closes at 10 PM.

Due to recitation instructor by 5 PM: Homework Set 7.

**Week 10:**

Monday, March 16 Lecture.

Monday, March 16 Lecture.

Phase portraits for autonomous systems, and stability of equilibria. Edwards and Penney section 6.1.

Tuesday, March 17. Recitation.

Review. (Quiz #5)

**Wednesday, March 18. Lecture.**

Linear and almost linear systems. Linearization and the Jacobian matrix. Edwards and Penney section

6.2.

**Friday, March 20. Lecture.**

Review.

**Week 11:
Monday, March 23. Lecture.
**

Review. Exam 2, 6{8 PM.

**Tuesday, March 24. Recitation**.

Review.

**Wednesday, March 25. Lecture.**

Ecological models of predators and prey. Edwards and Penney section 6.3.

**Friday, March 27. Lecture.**

Nonlinear mechanical systems. Edwards and Penney section 6.4.

Due to recitation instructor by 5 PM: Homework Set 8 and Writeup of Lab 4.

Web Homework Set 8 closes at 10 PM.

**Week 12:**

Monday, March 30. Lecture.

Monday, March 30. Lecture.

Review.

**Tuesday, March 31. Lab.**

Lab 5. Due at beginning of lab: Prelab assignment for Lab 5.

**Wednesday, April 1. Lecture.**

Laplace and inverse Laplace transforms. Edwards and Penney section 7.1.

Friday, April 3. Lecture.

Application of Laplace transforms to initial-value problems for constant-coefficient linear equations and

systems. Edwards and Penney, section 7.2.

Due to recitation instructor by 5 PM: Homework Set 9.

Web Homework Set 9 closes at 10 PM.

**Week 13:**

Monday, April 6. Lecture.

Monday, April 6. Lecture.

Laplace transforms involving translation in time and in the transform variable, and use of partial fraction

representations. Edwards and Penney section 7.3.

**Tuesday, April 7. Recitation.**

Review. (Quiz #6)

**Wednesday, April 8. Lecture.**

Products of Laplace transforms and convolution integrals. Differentiation and
integration of Laplace

transforms. Edwards and Penney section 7.4.

**Friday, April 10. Lecture.**

Laplace transforms of periodic and piecewise continuous functions. Edwards and
Penney section 7.5.

Due to recitation instructor by 5 PM: Writeup of Lab 5.

Web Homework Set 10 closes at 10 PM.

**Week 14:
Monday, April 13. Lecture.**

Impulses (delta functions) and impulse response. Edwards and Penney section 7.6.

**Tuesday, April 14. Recitation.**

Review. (Quiz #7)

Wednesday, April 15. Lecture.

Wednesday, April 15. Lecture.

Review.

**Friday, April 17. Lecture**.

Review.

Web Homework Set 11 closes at 10 PM.

Due to recitation instructor by 5 PM: Homework Set 10

**Week 15: (Last Week of Classes)**

Monday, April 20. Lecture.

Monday, April 20. Lecture.

Review.

**Tuesday, April 21. NO RECITATION OR LAB.**

Thursday, April 23.

Final Exam, 8-10 AM.

Thursday, April 23.

Final Exam, 8-10 AM.