Techniques of Ordinary Differential Equations

University credit, 13 assignments, 2 exams, $684 tuition, $75 administration fee, Prerequisites: see below. This is course U600-319.

A first course in ordinary differential equations, concentrating on solution techniques for first- and second-order equations and systems of linear equations. Introduction to partial differential equations and Fourier series. Includes a quick review of the linear algebra needed.

Prerequisites: Standard two-term sequence of differential and integral calculus, and some knowledge of linear algebra. Before registering, please use this link to contact Director of Mathematics.

Course Materials

• Elementary Differential Equations and Boundary Value Problems,7^th ed., Boyce and DiPrima, John Wiley & Sons, New York, 2000. ISBN 0471319996. Search for book.
• Student Handbook, available at learn.wisconsin.edu/il/studenthandbook/studenthandbook.pdf, or on paper by request to Learner Services, toll-free 1-877-UW-LEARN (877-895-3276).
• Syllabus and forms will be mailed by the instructor upon registration.

Format of Course

The course consists of 13 lessons and 2 exams. Each lesson consists of:

• A reading assignment from the text.
• A written assignment, from the text, to submit for grading and feedback.

Exams are mailed to a proctor selected by the student in accordance with Independent Learning's guidelines.

Grading

Score	Letter Grade
NOTE: The grading scale was revised on Nov 13, 2003. This grading scale applies to all students who complete the course after that date.
93-100	A
90-92	AB
83-89	B
80-82	BC
73-79	C
65-72	D
0-64	F

Each lesson and each exam is graded on a 100-point scale. The final score is computed as a weighted average, with the average of the lessons counting for 70%, and the average of the exams counting 30%. The exam average must be at least 40 for a passing grade. Assuming this is the case, the average of all your work is converted to a letter grade as shown in the table.

Course Outline

• Lesson 1: Linear and separable differential equations, modeling with first order equations
• Lesson 2: Nonlinear equations, exact equations, integrating factors
• Lesson 3: Solution of second order homogeneous differential equations, linear independence, the Wronskian
• Lesson 4: Complex and repeated roots of the characteristic equation
• Lesson 5: Solution of non-homogeneous equations by the method of undetermined coefficients and variation of parameters, mechanical vibrations
• Lesson 6: Higher order linear differential equations
• Exam 1
• Lesson 7: Laplace transform: solution of initial value problems
• Lesson 8: Step functions and discontinuous forcing functions
• Lesson 9: Impulse functions and convolutions
• Lesson 10: Matrices, eigenvalues and eigenvectors, systems of first order linear equations
• Lesson 11: Homogeneous linear systems with constant coefficients, complex and repeated eigenvalues
• Lesson 12: Two point boundary value problems, introduction to Fourier series
• Lesson 13: Fourier convergence theorem, introduction to partial differential equations
• Exam 2