Math 441 Syllabus
Text: Boyce and DiPrima, Elementary differential equations
and boundary value problems, 8th edition, John Wiley and Sons Inc.
(2001).
Following is a tentative syllabus for 441. Some details could still
change.
Introduction (1 lecture)
First-Order Equations (roughly 7 lectures):
Basic techniques for first order ODE's
- Linear equations (Sec. 2.1)
- Seperable equations (Sec. 2.2)
- Exact equations (Sec. 2.6)
- Homogeneous equations (Sec. 2.9)
- Existence and uniqueness (Sec. 2.8)
General theory of first order equations
- Linear versus non-linear equations (Sec. 2.4)
- Applications - Population dynamics (Sec. 2.5)
The Picard Existence Theorem (roughly 5 lectures)
- Review of uniform convergence
nth Order Linear Differential Equations (roughly 14 lectures):
General theory of second and nth order
equations
- Second order constant coefficient (Sec. 3.1)
- Fundamental solutions (Sec. 3.2, 4.1)
- Linear independence, Wronskian (Sec. 3.3, 4.1)
Linear constant coefficient equations
- Complex roots of the characteristic equation (sec. 3.4, 4.2)
- Repeated roots and reduction of order (Sec. 3.5, 4.2)
Non-homogeneous equations
- Undetermined coefficients (Sec. 3.6, 4.3)
- Variation of parameters (Sec. 3.7, 4.4)
Euler equations (sec 5.5)
Applications
- Mechanical and electrical vibrations (Sec. 3.8)
- Forced vibrations (Sec. 3.9)
Power series methods (roughly 3 lectures)
- Review of power series (Sec. 5.1)
- Series solution near an ordinary point (Sec. 5.2, 5.3)
Instructors choice (Material from Chapter 9)
Lectures: (37 lectures)
Exams: 2
Leeway: 3