Math 320 — Syllabus

Spring 2010

About the exams | Syllabus | Using your computer | Homework assignments

“…thus we will rarely need slugs…”
(Edwards & Penney, page 14)

Instructor. Sigurd Angenent. Office: Van Vleck Hall 609.

Office Hours: Monday–Wednesday–Friday, 1:20-2:20pm.

Lecture time and location. Since our original classroom was very crowded we will henceforth meet in room 105 of the Psychology Building, at the same time as before (9:55–10:45am).

Text book. We will follow the book which is listed in the math department's course description, namely, “Differential Equations and Linear Algebra” (3rd edition) by Edwards and Penney, Prentice Hall.

Exams. There will be two midterm exams which will be held during a regular lecture. The exam dates are

Wednesday Feb 17 for the first midterm, and
Wednesday March 24 for the second midterm.
Mark these dates in your calendar now! There will be no alternate exams.

TAs. There are two TAs associated to this lecture. They are Masanori Koyama and Mark Remmel.

Homework will be assigned every monday in lecture, and later posted here. Homework must be returned in lecture on the following monday. It should be neatly written; separate sheets must be stapled (no paper clips, etc.); your name must appear on each sheet. Homework that does not meet these standards will not be graded.

Grades. You can get up to 100 points throughout the whole semester. The two midterms are worth 20 points each. Your combined homework score counts for another 20 points, and the final exam is worth up to 40 points.

Course content

The course covers two related topics, Linear Algebra (or Matrix Algebra), and Differential Equations (mainly linear differential equations.) Unfortunately there is some overlap between the material presented in the textbook and material covered in math 222, so that it does not make sense to follow the book linearly (no pun intended). We will jump back and forth through the book. The Linear Algebra part of the course, which is assumed to be new to all students in this class, is contained in chapters 3, 4, and 6. The other chapters cover differential equations. Chapter 7 is a milestone in the book, because it is here that we find out why the two topics linear algebra and differential equations appear in the same book.

We will take the following path through the book:

Linear Algebra, in particular, chapters 3 and 4 of the text.
Differential Equations
- The existence and uniqueness theorem (appendix A -- statement only, no proofs.)
- Slope fields, and graphical interpretation of differential equations (§1.3, §9.1)
- How a computer computes approximations to solutions of differential equation (Euler method, §2.4, §2.5)
- Review from math 222: How to solve simple first order linear equations, how to solve linear higher order constant coefficient equations. The “Forced Oscillation and Resonance” example (§5.6) in detail.
We return to Linear Algebra to study ``eigenvalues & eigenvectors'' of square matrices. (Chapter 6)
Differential Equations again: using the theory of eigenvalues we learn how to solve constant coefficient systems of differential equations (Chapter 7.)
To conclude, we read chapter 9, and discover how the theory of linear equations can be used to study the stability properties of equilibrium solutions of nonlinear systems of differential equations. This chapter contains many illustrations and examples of the theory that has been covered in this course.

The course, week by week

---, jan 20, jan 22
§3.1. Introduction to Linear Systems, p. 147.
§3.2. Matrices and Gaussian Elimination, p. 156.
jan 25, jan 27, jan 29
§3.2. Matrices and Gaussian Elimination, p. 156.
§3.3. Reduced Row-Echelon Matrices, p. 167.
§3.4. Matrix Operations, p. 176.
feb 1, feb 3, feb 5
§3.4. Matrix Operations, p. 176.
§3.5. Inverses of Matrices, p. 188.
feb 8, feb 10, feb 12
§3.6. Determinants, p. 202
§3.7. Linear Equations and Curve Fitting, p. 218 [independent reading].
§4.1. The Vector Space R³, p. 227
§4.2. The Vector Space Rⁿ and Subspaces, p. 238
feb 15, feb 17, feb 19 FIRST MIDTERM ON WEDNESDAY FEB p. 17
§4.3. Linear Combinations and Independence of Vectors, p. 245.
feb 22, feb 24, feb 26
§4.4. Bases and Dimension for Vector Spaces, p. 253.
§4.6. Orthogonal Vectors in Rⁿ, p. 269
mar 1, mar 3, mar 5 We switch to Differential Equations!
Appendix A. Existence and Uniqueness of Solutions, p. 685
§1.3. Slope Fields and Solution Curves, p. 19
§2.2. Equilibrium Solutions and Stability, p. 92
§9.1. (Stability and the) Phase Plane, p. 517
§1.5. Linear First-Order Equations, p. 48
mar 8, mar 10, mar 12
§2.4. Numerical Approximation: Euler's Method, p. 112
§7.6. Numerical Methods for Systems, p. 465
§2.5. A Closer Look at the Euler Method, p. 124
mar 15, mar 17, mar 19
§5.2. General Solutions of Linear Equations, p. 301
§5.3. Homogeneous Equations with Constant Coefficients, p. 314
§5.4. Mechanical Vibrations, p. 326
§5.6. Forced Oscillations and Resonance, p. 353
mar 22, mar 24, mar 26 SECOND MIDTERM ON WEDNESDAY.
§6.1. Introduction to Eigenvalues, p. 366
mar 29, mar 31, apr 2 SPRING BREAK
apr 5, apr 7, apr 9
§6.2. Diagonalization of Matrices, p. 376
§7.1. First-Order Systems and Applications, p. 396
apr 12, apr 14, apr 16
§7.2. Matrices and Linear Systems, p. 407
§7.3. The Eigenvalue Method for Linear Systems, p. 418
apr 19, apr 21, apr 23
§7.4. Second-Order Systems and Mechanical Applications, p. 432
apr 26, apr 28, apr 30
§9.2. Linear and Almost Linear Systems, p. 530
may 3, may 5, may 7
§9.3. Ecological Models: Predators and Competitors, p. 545
§9.4. Nonlinear Mechanical Systems, p. 558