Math 320 — Syllabus

Syllabus

Homework assignments

Using your computer

About the exams

Notes, links and slides 

Mo We Fr
   19 21 Jan
24 26 28
31  2  4 Feb
 7  9 11
14 16 18
21 23 25
28  2  4 Mar
 7  9 11
SPRING BREAK
21 23 25
28 30  1
 4  6  8 Apr
11 13 15
18 20 22
25 27 29
 2  4  6 May
“…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.   We will meet in room 1111 of the Humanities building (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

Friday Feb 18 for the first midterm, and
Friday April 1 for the second midterm.
Mark these dates in your calendar now! There will be no alternate exams.

Your TA is Jonathan Blackhurst.

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

  1. —, jan 19, jan 21
    §3.1. Introduction to Linear Systems, p. 147.
    §3.2. Matrices and Gaussian Elimination, p. 156.
  2. jan 24, jan 26, jan 28
    §3.2. Matrices and Gaussian Elimination, p. 156.
    §3.3. Reduced Row-Echelon Matrices, p. 167.
    §3.4. Matrix Operations, p. 176.
  3. jan 31, feb 2, feb 4
    §3.4. Matrix Operations, p. 176.
    §3.5. Inverses of Matrices, p. 188.
  4. feb 7, feb 9, feb 11
    §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
  5. feb 14, feb 16, feb 18 — FIRST MIDTERM ON FRIDAY FEB 18.
    §4.3. Linear Combinations and Independence of Vectors, p. 245.
  6. feb 21, feb 23, feb 25
    §4.4. Bases and Dimension for Vector Spaces, p. 253.
    §4.6. Orthogonal Vectors in Rn, p. 269
  7. feb 28, mar 2, mar 4 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
  8. mar 7, mar 9, mar 11
    §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
  9. mar 14, mar 16, mar 18 Spring break
  10. mar 21, mar 23, mar 25
    §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
  11. mar 28, mar 30, april 1 — SECOND MIDTERM ON FRIDAY APRIL 1.
    §6.1. Introduction to Eigenvalues, p. 366
  12. apr 4, apr 6, apr 8
    §6.2. Diagonalization of Matrices, p. 376
    §7.1. First-Order Systems and Applications, p. 396
  13. apr 11, apr 13, apr 15
    §7.2. Matrices and Linear Systems, p. 407
    §7.3. The Eigenvalue Method for Linear Systems, p. 418
  14. apr 18, apr 20, apr 22
    §7.4. Second-Order Systems and Mechanical Applications, p. 432
  15. apr 25, apr 27, apr 29
    §7.4 & §8.2. Linear inhomogeneous systems of first and second order
  16. may 2, may 4, may 6
    §7.4 & §8.2. Continuation of Linear inhomogeneous systems of first and second order