Math 285 Day-by-day Schedule, Spring 2010

Lecture Date Section Topics
1 Jan 20 1.1 DEs and math models
2 Jan 22 1.2, 1.4 Integrals as solutions, Separable method, and Quiz 1
3 Jan 25 1.3 Direction fields - Iode Lab 1
4 Jan 27 1.3 Direction fields, and Existence and Uniqueness Theorem
5 Jan 29 1.4 Separable DEs, and applications of dx/dt=ax+b
to populations with harvesting, and Newton's law of cooling
6 Feb 1 1.5 First order linear DEs, and application to mixture problems
7 Feb 3 1.6 Substitution methods, and Quiz 2
8 Feb 5 2.2 Autonomous DEs and phase lines, with application to populations
with a capacity constraint (logistic DE) and harvesting
9 Feb 8 2.4 Euler's method - Iode lab 2
10 Feb 10 2.4 Euler's method, and Quiz 3
11 Feb 12 3.1 Second order linear, Superposition, Existence and Uniqueness
y''+k2y=0 (cos and sin solutions) and y''-k2y=0 (cosh and sinh solutions)
12 Feb 15 3.1 Second order linear constant coefficient DEs: solution y=er x
with characteristic equation having real roots, possibly repeated
13 Feb 17 1.1-2.4 Test review
14 Feb 19 1.1-2.4 Test 1
15 Feb 22 Class canceled Furlough Day
16 Feb 24 3.3 Complex numbers (class notes), and second order linear
constant coefficient DEs with complex roots in characteristic equation
17 Feb 26 3.4 Combining sine and cosine, and mechanical and electrical oscillations
18 Mar 1 3.4 Mass-friction-spring systems (equivalent to RLC circuits):
overdamping, critical damping and underdamping
19 Mar 3 3.2 Higher order linear DEs, and linear independence of functions
20 Mar 5 3.3 Higher order linear homogeneous constant coefficient DEs
21 Mar 8 3.3,3.5 Operator notation for DEs
Nonhomogeneous DEs and decomposition of general solution: y=yc+yp
22 Mar 10 3.5 Method of Undetermined Coefficients, for
constant coefficient nonhomogeneous DEs
23 Mar 12 3.5 Undetermined Coefficients, and Variation of Parameters
24 Mar 15 3.5,3.6 Variation of Parameters
Undamped forced oscillations, resonance
25 Mar 17 3.6 Damped forced oscillations, practical resonance
26 Mar 19 3.8 Boundary value problems
27 Mar 29 3.1-3.6 Test review
28 Mar 31 3.1-3.6 Test 2
29 Apr 2 3.8 Orthogonality of Eigenfunctions
30 Apr 5 9.1 Orthogonality and Fourier coefficients
31 Apr 7 9.2 Convergence of Fourier series
32 Apr 9 9.3 Odd and even extensions, sine and cosine series
33 Apr 12 9.2,9.3 Eigenfunctions and generalized Fourier series
34 Apr 14 9.3 Term-by-term differentiation
35 Apr 16 9.4 Mechanical oscillators using Fourier series,
resonance at multiples of forcing frequency
36 Apr 19 9.5 Heat or diffusion equation, and the physical
meaning of Dirichlet and Neumann boundary conditions
37 Apr 21 9.5 Heat equation with Dirichlet boundary conditions
and Separation of Variables
38 Apr 23 9.5 Heat equation with Neumann boundary conditions
39 Apr 26 9.6 Wave equation - standing waves
40 Apr 28 9.6 Wave equation - traveling waves
41 Apr 30 9.6 Waves hitting the boundary
42 May 3 9.7 Steady state temperatures and Laplace's equation
43 May 5 Class canceled Furlough Day