# Math 23: Schedule, topics and worksheets

(lecture postponed to X-hr Thurs; HW6 due then)
week  date      readingdaily topics & demosworksheets
1Sep 26 W website, 1.1-1.3 HW1 assigned. Direction fields, introduction to initial-value problems, starting with computingmiceowls
27 Th X-hr`intro.m` Overview of Matlab, important to install it and try simple commands
28 F2.1, 2.2 First-order ODEs: linear, and separation of variables intfac
Oct 1 M2.4, 2.6 Existence and uniqueness, exact equations. exact
23 W2.7 Introduction to numerical methods, Euler's method.
4 Th X-hr(free) [consider 4-6pm Intro to Matlab class, Berry Instr Ctr; sign-up reqd]
5 F2.3, 2.5Modeling and autonomous equations.tank
8 M3.1Second-order linear homogeneous ODEs: characteristic equation2ndconst
310 W3.2 Quiz 1. Quiz 1 (on Ch.2, no Matlab; solutions). Fundamental solutions.
11 Th X-hrrefresher on 2-by-2 matrices2by2
12 F3.2, 3.3Wronskian, linear independencewronskian
15 M3.4Complex rootsspiral
417 W3.5, 3.6 Repeated roots, method of undetermined coefficients.undetcoeff
18 Th X-hr(nothing yet planned)
19 F3.7Variation of parameters. varpar
524 W3.9, 5.1Driven oscillators and resonance. Q-factor, Resonance, forcing 1, 2, Tacoma videos 1, 2, 3. Power series.resonance
25 Th X-hrQuiz 2 on Ch. 3 (up to 3.7), no Matlab (solutions).
26 F5.2series solutions, Matlab Taylor convergence demo (calls show_zser), power series applet.
29 M5.3, 5.5Series solutions about an ordinary point, Euler equationsseries
631 W7.1Systems of first-order equations, existence and uniqueness review
Nov 1 Th X-hrreview for midterm. practise midterm (only 65 mins), solutions
Midterm: Thurs Nov 1st, 6-8pm. (on everything so far up to 5.3)
Nov 2 F7.2Linear algebra: 3x3 matrices, inverse, row reduction. rowredinv
5 M7.3Eigenvalues, eigenvectors. Applet to visualize Ax.
77 W
8 Th X-hr7.4, 7.5 Homogeneous systems. Applets: click pplane, and local saddleflow
9 Fr7.6Handling unusual eigenvaluesspiral2d
12 M7.8, 9.1Degenerate eigenvalues, phase portraits of linear systems.
814 W9.1Review linear systems, stability and asymptotic stability.stablinsys
15 Th X-hrQuiz 3 (on Ch. 7, excluding 7.7 and 7.9)
16 Fr9.2, 10.1non-linear systems, pendulum, Boundary-value problemstwopoint
19 M10.2ODE eigenvalue problems, Fourier series.
.................................. Nov 21 W - 25 Su Thanksgiving recess ...............................
926 M10.3, 10.4convergence, even and odd functionsevenodd
28 W10.5Separation of variables. PDEs: heat equation, applet, and.
29 Th X-hr10.6, 10.7 Heat w/ mixed boundary conditions. Wave equation, applet (maximize # masses), odd modes and pulse.
30 F(no lecture - Alex out of town
10Dec 3 M10.8Laplace's equationlaplace
5 W Review session. Recurring themes, Review choosing methods; practise Quiz 4 from 2005 (solutions); practise Final from 2005 (solutions) sepvar, choosingprac
Final Exam (solutions): Friday December 7th at 8:00 am - 11:00 am, Kemeny 007. Single side of notes allowed, no algebraic/graphing calculators. Note this exam will not be given early to accommodate travel plans.