heather at math dot utk dot edu Math231TR Home Math231TR Calendar Math231 Office Hours Math231 Miscellaneous |
Which Assignment? |
When? |
What
to do? |
reading #1 |
due 8/25 |
[Write definitions *carefully*.
I will be checking them carefully. Plagerism is
allowed here, but please don't turn this into just busy
work. The point is for you to get the *meaning* of
the definitions and theorems into your head before we
discuss them in class, so think about their meaning and if
you can state them clearly and well in your own words,
feel free to. This is intended to set the stage for
greater learning in lecture, and better retention of the
material in the long term.] define- ordinary differential equation, order of a differential equation, linear differential equation, nonlinear differential equation, explicit solution to a differential equation, implicit solution to a differential equation, unique solution Theorems- section 1.2 - Theorem 1 |
reading #2 |
due 8/27 |
define(1.4)- Euler's method define(2.1,2.2)- technique of separation of variables, the general solution to a differential equation [note: some of these are not explicitly defined in the text, but you can deduce their definitions from what the text has to say about these terms..] Read the chapter summary on page 29. define- difference between a function and a relation as used in this course |
|
8/27 |
1.1:
1,2,4,5,7,8,9,10, 13--16 (For 1-12, state it's order,
the independent/dependent variable names, and whether or
not it is linear, and include a brief statement on WHY
it is linear or nonlinear. you do not need to
classify it as an ODE or PDE as i have left all PDE's
out) 1.2: 2ac,4,5,8,
9--13,14,16, 17,24,25,26,27 |
reading #3
|
9/1 |
define(2.3)- linear first order equation, standard form of a linear first order equation Write out- Method for Solving Linear Equations (pg 48) Also, compute the partial derivatives indicated for the following functions: 1. f(x,y) =y*x^2 + cos(xy), find df/dx and df/dy 2. f(t,x) = (t+xcos(t))/(t+sin(x)), find df/dt and df/dx 3. f(x,y)= e^(xy) + xtan(y), find df/dx and df/dy (NOTE: this assignment will be out of 5 points rather than 2, there will be 2 for the defs and 1 for each of the partial derivs) |
quiz #2 |
9/3 |
1.4:
2,3, 5,6, 9,10 (use code),
12, 15 read problem 16 (don't have to do it) 2.2: 1--5,7,12,13,16,18 (hint: to integrate tan(x) write in sines and cosines and use substitution), 22--26, 28, 29,30,34,38 |
reading #4 |
9/8 |
2.4 - total differential of F, exact
equation, theorem 2 (test for exactness), method for solving
exact equations (pg 59). 2.5 - Def 3, Method for finding special integrating factors (pg 66) |
quiz #3 |
9/10 |
2.3: 1--6, 7, 9, 12, 14, 15, 18, 20, 22, 37,
39 2.4: 1,2,4,5,6,9,12,13,14,17,21,22,29 |
reading #5 |
9/10 |
2.6 - Def 4 (homogeneous eq'n), Def 5
(Bernoulli eq'n) |
Exam
1 |
9/15 |
Prep Problems: 2.5: 2,5,7,11 2.6: 1,3,7,9,11,18,19,21,25 I also recommend working exercises from the Chapter 1 and 2 review problems. These are particularily good since you are not told which method to use, but have to discern that yourself. |
quiz #4 |
9/24 | 3.2: 1,3,4,6,7,13,14,15,19,21 3.3: 1,2,3,5,7,8,9,13 3.4: 1,5,7,9,13 |
reading #6 |
9/29 |
4.2- Theorem 1, Def 1, Theorem 2, Lemma 1, General solution of a linear second order ODE with constant coefficients in the case of distinct real roots, and the case of a repeated root (both on pg 163) 4.3- Euler's formula, Lemma 2, General solution of second order linear ODEs with constant coefficients in the case of complex roots for the auxiliary equation (pg 169) |
quiz #5 | 10/1 | 4.1: 2, 3, 4, 5, 6 4.2: 1-17 e.o.o.(every other odd), 26, 28,29, 32, 37,41,43 4.3: 1-17 e.o.o, 23, 25 |
reading #7 |
10/1 |
4.4- Method of Undetermined Coefficients (blue box, pg 180) |
reading #8 |
10/6 |
4.5- Theorem 3, theorem 4 4.6-blue box "Method of Variation of Parameters" pg 19 |
quiz #6 |
10/8 |
4.3: 28,31abc, 32, 33, 35 4.4: 1,2, 3,5,7,8,9,11,13,15,17,19,22,24,25, 27-32 4.5: 1,9,11,13,15,17, 19,20, 22, 27, 29, 30, 31, 36, 43 |
reading
#9 |
10/8 |
4.7- Def 2, Theorem 5, Lemma 3, theorem 6,
theorem 8 |
Exam 2 |
10/13 |
Prep Problems: 4.6: 1, 3, 5, 9 11,13, 15, 18 4.7: 7, 11, 13, 19, 21, 30, 37, 39, 41, 43, 45,47 |
reading
#10 |
10/22 |
5.4- Autonomous systems, phase plane
equation, trajectory of the solution pair, phase plane, Def
1, asymptotically stable critical point (see top of
269), unstable equillibrium (see top of 269),
can you discern the difference between a stable equillibrium
and an asymptotically stable equillibrium from the sketches
at the bottom of 268? |
quiz #7 |
10/22 |
5.2: 2, 3, 7,9, 11, 13,19, 23, 25, 31, 35,
38 |
quiz #8 |
10/29 |
5.4: 1,2, 3, 5,
7,8,9,11,13, 16,18,29 (16 and 18 are to be done by hand, not
with software) 5.5: 5,10 5.6: 2 |
MINI
PROJECTS |
report due 11/17 |
Topic List: (Note - these are
written with the expectation that they will be done in a
group of three, please talk to me if that is not your
situation) A. Nuisance Beaver Trapping - Claimed! B. Rangeland Ecosystems - Claimed! C. Managing Erosion through vegetation - (9:40am unclaimed, 11:10am - 2 people) E. Infectivity and the spread of disease - Claimed! F. Why Dominance of Right-Curling Snails? - (9:40am 2 people, 11:10am unclaimed) G. Managing Insurgencies - Claimed! H. Price/Quantity Economic Model - (9:40am unclaimed, 11:10am claimed) I. Spread of Staph Infections in hospitals - (9:40am unclaimed, 11:10am 2 people) J. Romeo and Juliet: Love in Adolescent times - Claimed! K. When Zombies Attack: Surviving the Undead - (9:40am claimed, 11:10am 2 people) L. Modeling the Heartbeat - Claimed! M. Microparasites and their hosts! - (9:40am - claimed, 11:10am 2 people) File for help with MATLAB: 231Project_MATLABHelp.pdf |
reading
#11 |
11/12 |
7.2- Def 1, Thm
1, Def 2, Def 3, Thm 2, table of Laplace transforms pg 359 7.3- thm 3, thm 4, thm 5, thm 6 |
reading #12 | 11/17 | 7.4- Def 4, Thm 7, Partial Fraction
general forms for all three cases: Nonrepeated linear
factors, repeated linear factors, quadratic factors. |
quiz #9 |
11/19 |
7.2:
1,5,9,11,13,17,19,21,23,29abcdhj 7.3: 1,5,9,13,17 |
reading #13 |
11/19 |
7.5- Method of Laplace Transforms (blue box, pg 376) 8.1- formula for a Taylor series |
Extra Credit |
11/21 & 11/22 |
NIMBioS Conference: The 7th Annual Undergraduate Research Conference at the Interface of Biology and Mathematicshttp://www.nimbios.org/education/undergrad_conf2015You can attend at least one talk at this conference that is related to ODE's, write up a short 1-2 page summary and turn it in for 5 points extra credit on your homework total. It must be well written and clear, include relevant equations that the speaker used and explain what the questions/issues were they were addressing through their research and what their conclusions were. It is important that you stop by the registration desk and let them know that you are with my class. I use the register for verification of attendence AND it will help them to not want to kick you out :) . |
reading #14 |
11/24 |
8.2- Thm 1,2,3,and 4, and Def 1 8.3- Def 2 |
quiz #10 |
11/24 |
7.4: 1,3,7,9,12,14, 21, 23, 25, 27 7.5: 1,3,5,7,9,11,23,25,29,32, 35 |
quiz #11 |
12/1 |
8.1: 1,2,5,8,10acd 8.2: 1,3,5,17,18, 21,22, 30, 32, 34, 38 |
Final Exam |
9:40am
Section: Dec 8, 8am- 10am 11:10am Section: Dec 7, 10:15am- 12:15pm |
Comprehensive! problems from chapter 8 to prepare: 8.3: 1,3,5,11,13,15,19,20, 25,27 |