MATH 333
  SPRING 2003
   
Course Syllabus:    [Outline]

  Venue: The class meets Tuesday and Thursday from 1:15 pm to 2:30 pm and Friday from 2:15 pm to 3:05 pm in 304 Reese.

Text: William Boyce and Richard DiPrima, Elementary Differential Equations, seventh edition, John Wiley & Sons, 2001.

Course description: We will study various methods of solving ordinary differential equations and explore some ways in which differential equations and their solutions are used to model real-world phenomena, such as population dynamics, mechanical systems, thermodynamics, radioactive decay, and electrical circuits.

Homework: There will be a problem set each week. Problem set solutions are to be written in complete sentences, and will be graded for presentation as well as correctness.

Exams: There will be three hour exams during the semester, probably during the weeks of February 24, March 31, and April 28. There will be a final exam during final exam period.

Quizzes: Except in exam weeks, there will be a ten-minute quiz each week.

Grading: Your lowest problem-set grade and your two lowest quiz grades will be dropped, and your course grade will be computed as follows:

Problem Sets   40%
Quizzes 20%
Hour Exams 20%
Final Exam 20%

Technology: We will be using calculators and computers from time to time in class. When it is helpful to do so, you are welcome to use a calculator or computer on the problem sets, provided you explain its use in your write-up.

Occasionally, a problem set problem will specifically require the use of a computer or calculator.

Resources: My office hours are listed at my website; you are welcome to make appointments to talk with me at other times.

The Honor Code: You are encouraged to collaborate on problem sets, but only as long as the information flow goes both ways. Each student must write up her own solutions independently. Direct copying from another student's paper will be treated as a violation of the honor code. No collaboration will be permitted on the quizzes, the hour exams, or the final exam.


Course Outline    [Syllabus]

   I. Introduction (B & D 1.1 - 1.3)
  1. Classification of differential equations
  2. Verifying solutions of differential equations
  3. Direction fields
II. Solution of first-order linear DEs
  1. Integrating factors (B & D 2.1)
  2. Separation (B & D 2.2)
III. Modelling with first-order DEs (B & D 2.3, 2.5)
  1. First-order models
    1. Mixing problems
    2. Interest problems
    3. Heating and cooling problems
    4. Radiocarbon dating
    5. Population dynamics; the logistic equation
  2. Qualitative analysis of critical points
IV. Numerical techniques for first-order DEs
  1. Euler's method (B & D 2.7)
  2. Difference equations; stair-step diagrams (B & D 2.9)
V. Second-order constant-coefficient linear DEs
  1. Solutions to homogeneous equations (B & D 3.1, 3.2, 3.4, 3.5)
  2. Linear independence of solutions (B & D 3.3)
  3. Solutions to inhomogeneous equations (B & D 3.6)
VI. Other second-order solution methods
  1. Reduction of order (B & D 3.5)
  2. Variation of parameters (B & D 3.7)
VII. Modelling with second-order DEs
  1. Mass-and-spring models (B & D 3.8)
  2. RLC circuit models (B & D 3.8)
  3. Forced vibrations (B & D 3.9)
VIII. The Laplace transform (B & D 6.1 - 6.6)
  1. Definition and properties of the Laplace transform
  2. Computation of the Laplace transform and inverse Laplace transform
  3. Solution of IVPs
  4. Laplace transforms of discontinuous functions and impulse functions
  5. Solution of IVPs with generalized forcing functions
  6. Convolutions
IX. Series solutions of differential equations (B & D 5.1 - 5.3)