Math 232: Elementary Differential Equations

Lectures: MWF 16:00-16:50 in SC 362
Instructor: Carmeliza Navasca, (cnavasca@clarkson.edu), SC 391
Office Hours: MW 15:00-16:00, F 12:00-13:00, 13:00-14:00

Graduate Student TA: Kelum Dineshanrathma, (dineshhk@clarkson.edu)

Recitation TAs:
Eric Fredette, (fredette@clarkson.edu), Section 11, Tues 9:00-9:50, SC 348
Kevin Mason, (masonka@clarkson.edu), Section 12, Tues 12:00-12:50, SC 340
Christopher Lane, (laneca@clarkson.edu), Section 13, Tues 13:00-13:50, SC 344
Christopher Nycz, (nyczcj@clarkson.edu), Section 14, Tues 14:00-14:50, SC 344

Objectives:
(1) to learn how to solve differential equations and initial value problems quantitatively and qualitatively
(2) to see how differential equations model many physical and biological phenomenon
(3) to learn some basic linear algebra tools

Course Info

Textbook: Farlow, Hall, McDill, and West, Differential Equations and Linear Algebra, Second Edition, Pearson Education, 2007.

Prerequisites: Math 132

Grading Scheme: 10% hw, 10% quiz, 10% project, 20% midterm 1, 20% midterm 2, 30% final exam

Homework: Weekly assignment will be assigned every Monday in lecture and will be collected the following Tuesday in your recitation. No late hw will be accepted. However, one homework grade will be dropped.

Quiz: There will be a weekly quiz on Tuesday. The lowest quiz grade will be dropped.

Project: There will be a project. The project entails advanced topics which can be done in groups of two or more.

Exam: The two midterms are scheduled on February 24 and April 6. There is one comprenhensive exam TBA. No make-up exam will be given unless you have proper documentation. No shows on exams will result on an F grade.

Handouts and Other Info: All other info can be found at moodle.

Reading and Blogging: To acheive our objectives, you must read the sections ideally before lecture. To encourage this activity, you must blog about the reading material weekly. Your blog must have at least three sentences summarizing the sections read and at least one question on something you find unclear, complicated or puzzling.

Course Syllabus

Week 0: Jan 13
Introduction


Week 1: Jan 16-20
Introduction - concept of a DE (1.1)
Slope fields (1.2)
Separable DEs (1.3)

Week 2: Jan 23-27
Linear Theory (2.1)
First order linear equations (2.2)
Grow and Decay (2.3)

Week 3: Jan 30-Feb 1-3
Nonlinear models: logistic equation (2.5)
Review complex numbers and complex-valued functions (Appendix CN)
Harmonic oscillator (4.1)

Week 4: Feb 6-10
Real characteristic roots (4.2)
Complex characteristic roots (4.3)
Undetermined coefficients (4.4)

Week 5: Feb 13-17
Variation of parameters (4.5)
Winter Break!

Week 6: Feb 20-24
Conservation and conversion (4.7)
Review
Midterm Exam I

Week 7: Feb 27-29-Mar 2
Project day!
Matrices (3.1)
Linear systems (3.2)

Week 8: Mar 5-9
Inverses (3.3)
Determinants (3.4)
Vectro Spaces (3.5)

Week 9: Mar 12-16
Basis (3.6)
Eigenvalues and eigenvector (5.3)
Linear DE systems (6.1)

Week 10: Mar 19-23
Spring Break!

Week 11: Mar 26-30
Linear systems with real eigenvalues (6.2)
Linear systems with nonreal eigenvalues (6.3)
Stability and linear classification (6.4)

Week 12: Apr 2-6
Matrix exponential (6.6)
Review
Midterm Exam II

Week 13: Apr 9-13
Project day!
Review partial fractions (Appendix PF)
Introduction to Laplace transform (8.1)

Week 14: Apr 16-20
Solving DEs and IVPs with Laplace transform (8.2)
Step functions and the delta function (8.3)
Feedback control (10.1)

Week 15: Apr 23-27
Optimal control (10.2)
Pontryagin maximum principle (10.3)
Review