# Courses

## Math 2700 - TH 12:30-1:45 (15996) and MWF 10:10-11 (31849)

**Office Hours (633 Boyd): **Monday 11:30-12:30; Tuesday 10-11, and Wednesday 9-10.

**Homework**:

(1) Section 1.1: 2, 4, 6, 7, 10, 12; Section 1.2: 6, 14, 18, 22, 30, 34, 42

Due at the beginning of class on (31849) Wednesday 8/24; (15996) Thursday 8/25.

Solutions to Homework 1

(2) Section 1.3: 6 (skip parts b and c), 14, 16, 20, 22; Section 1.4: 5, 6, 14, 18; Section 1.5: 2, 4, 15, 18 (use interval 0<=t<=pi and step size =pi/12)

Solutions to Homework 2

(3) Section 1.6: 4, 16, 22, 24, 28; Section 1.7: 4, 10, 20.

Due at the beginning of class on (31849) Friday 9/9; (15996) Thursday 9/8.

Solutions to Homework 3

(4) Section 1.8: 2, 12, 23, 30; Section 1.9: 2, 10, 14, 20, 24

Quiz on Thursday/Friday: solving a linear ODE.

(5) Section 2.1: 2, 3, 4, 19, 20, 22; Section 2.2: 4 (skip c), 10, 11; Section 2.4: 1, 4, 7, 13; Section 1.8: 33

To turn in: 1.9: 24; 2.1: 20, 22; 2.4: 1, 4.

Due in class Tuesday 10/04 or Wednesday 10/05.

Solutions to Homework 4

Remark: Error on Section 1.9 #24 on integration step. The term 30 should be replaced with 30t which affects the following numbers in the computation as well.

(6) Section 2.5: 2, 8; Section 3.1: 16, 18, 24, 26, 34

(7) Study guide for Exam 2: 1.8 #2; 1.9 # 2, 10; Ch. 1 Review Exercises #54; 2.4 #7, 2.5 # 8; 3.1 #16, 26.

(8) Green-square problem on exam 2. No partial credit. 3.2 # 10 (for part (c), plot corresponding straight-line solutions and direction vectors at following 4 points: p1 = (3, 1), p2 = (-1, 1), p3=(-3, -1), p4 = (1, -1)). #14(skip part c).

Due at the beginning of class on (31849) Wednesday 10/26; (15996) Thursday 10/27.

(9) Suggested Exercises: 3.2 #2, 8, 15, 22; 3.3# 2, 6, 3.4 #4 (skip e), #10

(10) Suggested Exercises: 3.6: #10, 14, 22, 39; Trace-Determinant plane: Use the TD plane to determine the type of system (sink, source, saddle, spiral sink, spiral source, periodic) given in 3.2#3, 6 and 3.4 #5, 9; 4.1:#3,6, 4.2: #6, 23.

(11) Study guide for Exam 3:

- For the systems 3.2 #3, 7, (a) find the general solution (b) sketch the phase portrait
- For the system 3.4 #5, 9, Use the TD plane to determine the type of system (sink, source, saddle, spiral sink, spiral source, periodic). If spiral or periodic, determine direction of oscillation: clockwise or counterclockwise.
- For 3.6 #15, (a) write the second order differential equation, (b) find general solution y(t) (DON'T change to system and solve system.) (c) classify oscillator: overdamped, underdamped, critically damped, or undamped.
- Find the general solution for 4.1 #5, 4.3 #1
- Think about it: does linearity principle hold for a non-homogeneous second order linear equation?

(12) Optional homework to replace lowest homework grade. 6.1 #16, 18; 6.2 #10; 6.3 #28; Will not be accepted after 4pm on 12/07. You may turn it in in class, my office, or slip under office door if I'm not present.

(13) Study guide for Final Exam:

- 1.3 #22 (a) solve using separation of variables (b) solve using Laplace transform
- 1.5 #9; 1.6 #7, 19; 1.7 #19; 1.8 #11
- 3.2 #11; 3.3 #7; 3.4 #11
- 4.3 #9 (a) solve using guessing (b) solve using Laplace transform

**Exams** - you may use a scientific calculator; no graphing calculators.

T/Th: Review for exam 1, 9/13 (Bring questions!); Exam 1, 9/15.

Review for exam 2, 10/11; Exam 2, 10/13.

Review for exam 3, 11/15; Exam 3, 11/17.

Final Exam: 12:00 - 3:00 pm, Thur., Dec. 8.

MWF: Review for exam 1, 9/14 (Bring questions!); Exam 1, 9/16.

Review for exam 2, 10/12; Exam 2, 10/14.

Review for exam 3, 11/16; Exam 3, 11/18.

Final Exam: 8:00 - 11:00 am, Mon., Dec. 12.

If you have a final exam conflict or three exams scheduled within a 24 hour period, here's the protocall to get things rescheduled:

https://curriculumsystems.uga.edu/curriculum/final-examination-schedule-conflicts

**Helpful links**:

About disposing of radioactive materials in hospitals safely.. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3068798/

About capacitors and circuits... A capacitor charging and How capacitors work.

About how raindrops form.. Raindrops

Some Harmonic Oscillators..

Pendulum wave video

Making sine waves with hose, speaker, and tone generating software..

Here's what you can do with oscillations in higher dimensions.. Vibrating Plates

(To glance at the math involved, see Wiki - Vibration of plates. Note that we need partial differential equations to model this situation.)

Slow motion glass breaking under resonance