(lecture postponed to X-hr Thurs; HW6 due then)
week | date | reading | daily topics & demos | worksheets |
---|---|---|---|---|
1 | Sep 26 W | website, 1.1-1.3 | HW1 assigned. Direction fields, introduction to initial-value problems, starting with computing | miceowls |
27 Th X-hr | intro.m
| Overview of Matlab, important to install it and try simple commands | ||
28 F | 2.1, 2.2 | First-order ODEs: linear, and separation of variables | intfac | |
Oct 1 M | 2.4, 2.6 | Existence and uniqueness, exact equations. | exact | |
2 | 3 W | 2.7 | 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 F | 2.3, 2.5 | Modeling and autonomous equations. | tank | |
8 M | 3.1 | Second-order linear homogeneous ODEs: characteristic equation | 2ndconst | |
3 | 10 W | 3.2 | Quiz 1. Quiz 1 (on Ch.2, no Matlab; solutions). Fundamental solutions. | |
11 Th X-hr | refresher on 2-by-2 matrices | 2by2 | ||
12 F | 3.2, 3.3 | Wronskian, linear independence | wronskian | |
15 M | 3.4 | Complex roots | spiral | |
4 | 17 W | 3.5, 3.6 | Repeated roots, method of undetermined coefficients. | undetcoeff |
18 Th X-hr | (nothing yet planned) | |||
19 F | 3.7 | Variation of parameters. | varpar | |
22 M | 3.8 | Mechanical vibrations. Links: unforced | ||
5 | 24 W | 3.9, 5.1 | Driven oscillators and resonance. Q-factor, Resonance, forcing 1, 2, Tacoma videos 1, 2, 3. Power series. | resonance |
25 Th X-hr | Quiz 2 on Ch. 3 (up to 3.7), no Matlab (solutions). | |||
26 F | 5.2 | series solutions, Matlab Taylor convergence demo (calls show_zser), power series applet. | ||
29 M | 5.3, 5.5 | Series solutions about an ordinary point, Euler equations | series | |
6 | 31 W | 7.1 | Systems of first-order equations, existence and uniqueness review | |
Nov 1 Th X-hr | review for midterm. practise midterm (only 65 mins), solutions | |||
Midterm: Thurs Nov 1st, 6-8pm.
(on everything so far up to 5.3) | ||||
Nov 2 F | 7.2 | Linear algebra: 3x3 matrices, inverse, row reduction. | rowredinv | |
5 M | 7.3 | Eigenvalues, eigenvectors. Applet to visualize Ax. | ||
7 | 7 W | |||
8 Th X-hr | 7.4, 7.5 | Homogeneous systems. Applets: click pplane, and local | saddleflow | |
9 Fr | 7.6 | Handling unusual eigenvalues | spiral2d | |
12 M | 7.8, 9.1 | Degenerate eigenvalues, phase portraits of linear systems. | ||
8 | 14 W | 9.1 | Review linear systems, stability and asymptotic stability. | stablinsys |
15 Th X-hr | Quiz 3 (on Ch. 7, excluding 7.7 and 7.9) | |||
16 Fr | 9.2, 10.1 | non-linear systems, pendulum, Boundary-value problems | twopoint | |
19 M | 10.2 | ODE eigenvalue problems, Fourier series. | ||
.................................. Nov 21 W - 25 Su Thanksgiving recess ............................... | ||||
9 | 26 M | 10.3, 10.4 | convergence, even and odd functions | evenodd |
28 W | 10.5 | Separation of variables. PDEs: heat equation, applet, and. | ||
29 Th X-hr | 10.6, 10.7 | Heat w/ mixed boundary conditions. Wave equation, applet (maximize # masses), odd modes and pulse. | ||
30 F | (no lecture - Alex out of town | |||
10 | Dec 3 M | 10.8 | Laplace's equation | laplace |
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. |