MATH 231 FALL 2007- COURSE LOG
Th, 8/23 Course policies/ exponential function
HANDOUT 1 (PDF)
(includes HW problems-due Aug. 30)
Tu, 8/28 Exponential models
Examples solved in class
Exponential models- HW problems
(due Sept 6)
Th 8/30 Exponential models (remaining examples)
discussion of HW problems 3 and 4, handout 1
general facts: autonomous equations, the geometric meaning of the
E/U theorem
summary of discussion- handout 2
(includes 6 HW problems, due Sept. 11)
Tu 9/4 general linear first-order equations (sect 1.2 in [Braun])-first examples
(steady-state slns; amplitude and phase shift for periodic
functions)
examples solved in class (linear equations)
linear equations- HW problems
(due Sept 13)
Th 9/6 1st order equations w/ non-constant coefficients (cont.)
discussion of HW problems
Tu 9/11 The existence-uniqueness theorem- statement, geometric interp.
separable equations- general solution, domain of existence,
finite-time blowup
(contrast between linear and nonlinear eqns)
The E-U theorem and separable equations- HW problems
Due date: Sept 20
Th 9/13 separable equations- final examples, homogeneous equations
graphical analysis of autonomous equations
(includes homework problems, due Sept. 25)
Tu 9/18 autonomous eqns. (cont.)
solution of HW problems
exact differential equations
(includes 6 homework problems, due Sept. 25)
Th 9/20 exact diff equations (end)
Bernouilli equations
Tu 9/25 discussion of HW problems
Th 9/27 Exam 1
Tu 10/2 Three applications of first-order equations
Exam 1 returned (inc. written solutions)
Policy on oral exams. Minimal requirements for an oral exam will be:
(i) attendance to every class
beginning on 10/4
(ii) turn in at least 6 complete
homework problems per set (from now on), of which at least 4 correct
(iii) solve all 20 problems in
the following problem set on first-order equations (at least 80%
correct):
Supplementary problems
Due date: 10/18
Remark: these problems will not count towards the homework grade- they are meant as a review for
those students interested in taking an oral exam.
Th 10/4 Linear second-order equations (sect 2.1, 2.2 in [Braun])
E-U theorems in the linear and non-linear cases (contrast)/
homog. equations with constant
coefficients: general solutions (3 cases)/ method of
"reduction of order"
Tu 10/9 Non-homogeneous linear 2nd-order equations (const. coeffs.); De Moivre's formula
Non-homogeneous equations- examples
Homework problems-2nd order equations (due date: 10/16)
Th 10/11 Fall break (no classes)
Tu 10/16 Non-homogeneous equations (examples)
Second-order equations and mechanics
(First version: includes only material presented on 10/16-
continuation, including HW
problems, to be added soon.)
Th 10/18 Simple harmonic motion-examples
Homework problems
(due date: 10/25)
Tu 10/23 Discussion of homework problems; method of variation of constants
Damped harmonic motion
Th 10/25 Forced oscillations/resonance
Damped forced oscillations/resonance frequency, amplification
factor
Homework problems
(Source: Tenenbaum-Pollard; DUE DATE: 11/1)
Tu 10/30 Motion under a central force/
Newton's derivation of Kepler's laws
From elliptical orbits to the inverse-square law
(includes proposed problems)
Th 11/1 Power-series solutions of second-order equations
Homework problems
(due date: 11/8)
Tu 11/6 Power -series solutions (final examples)
Discussion of homework problems
Th 11/8 Discussion of HW problems/ solution of 2X2 1st order systems by substitution
EXAM 2: Tu 11/13, topics included: lectures from 10/2 to 11/6 (inc. problems and theory in 10/30 handouts)
Tu 11/13 Exam2
Th 11/15 Laplace transforms: basic properties; Heaviside's formula
Homework problems
(due date: 11/27)
Tu 11/20 Laplace transforms:
convolution formula, transfer function/impulse response function,
solution of systems
Exam 2 returned (inc. written solutions)
Th 11/22 Thanksgiving holiday
Tu 11/27 The heat equation and the wave equation/ eigenvalue problems in an interval/
example (initial-boundary value problem for the heat
equation)
Homework problems
(due date: 12/4)
Th 11/29 Example: wave equation
(Neumann) BC. Infinite series of eigenfunctions: Fourier series,
Fourier sine and cosine series/ Solution of PDE
using Fourier series (example: wave eqn, Dirichlet BC)/
Example: an eigenvalue problem w/ eigenvalues found
`graphically'.
Course evaluations filled out.
Tu 12/4 Discussion of HW problems (last 2 sets)
FINAL EXAM: Tuesday, Dec.11, 12:30-2:30 (in the usual classroom)
Topics: the exam will consist of six problems: 2 based on problems in Exam 1, 2 based on problems in Exam 2
and 2 based on the material taught in the lectures from 11/8 (inclusive) to 12/4, especially the last two homework sets
(posted 11/15 and 11/27).
Final exam