MATH 20D: Introduction to Differential Equations
Section C00
Spring quarter, 2005

Tentative Schedule and Topics of Lectures

Date Lecture Sections Topics Covered
Monday 3/28 1 11.1   Sequences: concepts, Squeeze Thm, Monotonic Seq Thm
Wednesday 3/30 2 11.2, 11.3   Geometric and harmonic series, integral test
Friday 4/1 3 11.4, 11.5   Comparison and alternating series tests
Monday 4/4 4 11.6   Absolute convergence, ratio and root tests
Wednesday 4/6 5 11.8, 11.9   Power series, radius of convergence, examples
Friday 4/8 6 11.10   Taylor series and remainder estimate
Monday 4/11 7 11.12   Applications of Taylor series and remainder estimate
Wednesday 4/13 8 1.1, 1.2   Introduction to ODE and linear growth/decay models
Friday 4/15 9 1.3   Linear first-order ODE
Monday 4/18 10 2.1, 2.2   Separable ODE, exact form and integrating factors
Wednesday 4/20 11 2.3   Graphical analysis of ODE
Friday 4/22 - Midterm 1   Stewart: 11.1-11.6, 11.8-11.10, 11.12. Conrad: 1.1-1.3, 2.1.
Monday 4/25 12 2.4   Initial value problems (IVP) in ODE
Wednesday 4/27 13 2.5   Nonlinear growth models and asymptotic behavior
Friday 4/29 14 3.1, 3.2   Systems of ODE and the phase plane
Monday 5/2 15 3.4, 3.5   Autonomous systems; Interacting population models
Wednesday 5/4 16 4.1   IVP for linear systems of ODE
Friday 5/6 17 4.2   Systems with constant coefficients
Monday 5/9 18 4.4   General solution of a linear system
Wednesday 5/11 19 4.4   Complete example from 4.4 and some related examples from 4.1 and 4.2
Friday 5/13 20 4.3, 2.2   Complex numbers and eigenvalues, exact form and integrating factors
Monday 5/16 21 5.1   IVP for 2nd-order ODEs
Wednesday 5/18 22 5.2, 5.3   Homogeneous equations, and the case of constant coefficients
Friday 5/20 - Midterm 2   Conrad: 2.4, 2.5, 3.1, 3.2, 3.4, 3.5, 4.1-4.4, 5.1.
Monday 5/23 23 5.5   Inhomogeneous equations (method of undetermined coefs)
Wednesday 5/25 24 5.8   Variation of constants/parameters
Friday 5/27 25 6.1, 6.3   Definition and properties of the Laplace transform
Monday 5/30 - Holiday   Memorial Day
Wednesday 6/1 26 6.4   Inverse transforms of rational functions
Friday 6/3 27 7.1, 7.2   Series solutions of ODE at a regular point
Friday 6/10 - Final Exam   Cumulative!

Last updated by Bo Li on March 27, 2005.