Homework: Math 231  MWF sections (Finotti)

heather at math dot utk dot edu

Math231MWF Home

Math231MWF Calendar

Math231 Office Hours

Math231 Miscellaneous








General Guidelines 

**Please look at the following interesting graph of material retention vs. time lapse from first exposure until review (retention curve) and the subsequent tips for textbook reading

**On homework quizzes and exams, solutions need to be well written and explained in order to obtain credit, answers only are not accepted. 

**The purpose of the homework sets are for you to work through the understanding of the material and see what it is you do and do not understand so that you can fine tune your understanding from there -- it is to your advantage to keep this viewpoint in mind when working through problems. 

**Educational research shows that studying and learning in peer groups often leads to better comprehension of the material.  Get to know your classmates and form study groups. 

**The other side of the coin is that just as beneficial to your learning is time spent grappling with the material alone.  Always do your final homework writeups on your own, and feel free to reach for help when you need it.  This helps you to know what it is that you really do or don't understand

**If you are suspected of plagerism (think solution manual) or copying/cheating, you will get a zero for the homework set, and will be reported to University authorities.  The exception to this rule is for the definition/theorem assignments, as you are allowed to copy the statements as is from the text.


Keep this in mind when writing up your homework solutions -- it IS as important to practice clearly and correctly explaining your solutions as it is to find them! 


*Mathematics is a language.*

Which Assignment?

 When?

What to do?

reading #1




due
8/21


 [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.  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
  
   8/26
define(1.4)- Euler's method

Read the chapter summary on page 29.
define- difference between a function and a relation as used in this course

quiz #1


quiz
8/26

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
8/28
 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..]

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)
    reading#4
9/2
 define(2.3)- linear first order equation, standard form of a linear first order equation

Write out-  Method for Solving Linear Equations (pg 48)
quiz #2
 9/2
 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 #5
 9/4
 define(2.4)- total differential of F, exact equation, theorem 2 (test for exactness), method for solving exact equations (pg 59).
reading #6 9/11 2.5 -  Def 3, Method for finding special integrating factors (pg 66)
2.6 -  Def 4 (homogeneous eq'n), Def 5 (Bernoulli eq'n)
 quiz #3
 9/11
 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
Exam 1
9/14
 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
 9/23 3.2: 1,3,4,6,7,9,13,14,15,19,21
3.3: 1,2,3,5,7,8,9,13
3.4: 1,5,7,9,13
reading #7
 9/25
 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)
reading #8
 9/28
 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
9/30 		4.1: 2, 3, 4, 5, 6
4.2: 1-17 e.o.o.(every other odd), 26, 28,29, 32, 37,41,43
reading #9
  10/2
 4.4- Method of Undetermined Coefficients (blue box, pg 180)
quiz #6
  10/5
 4.3: 1-17 e.o.o.,23,25,28,31abc, 32, 33, 35
4.4: 1,2, 3,5,7,8,9,11,13,15,17,19,22,24,25, 27-32
reading #10
 10/7
 4.5- theorem 3, theorem 4
4.6-blue box "Method of Variation of Parameters" pg 19
quiz #7
 10/9
 4.5: 1,9,11,13,15,17, 19,20, 22, 27, 29, 30, 31, 36, 43
4.6:  1, 3, 5, 9, 11, 13, 15, 18
reading #11
 10/9
 4.7- Def 2, Theorem 5, Lemma 3, theorem 6, theorem 8
Exam 2
 10/12
 Prep Problems:
4.7: 7, 11, 13, 19, 21, 30, 37, 39, 41, 43, 45, 46, 47
reading #12
 10/21
 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)
quiz #8
 10/23
 5.2: 2, 3, 7,9,11,13,19, 23, 25, 31, 33, 35, 38
quiz #9
 10/30
 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:  1,2
MINI PROJECTS
 report due
on
11/16
 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 
C. Managing Erosion through vegetation  Claimed!
E. Infectivity and the spread of disease Claimed!
F. Why Dominance of Right-Curling Snails? 
G. Managing Insurgencies  Claimed!
H. Price/Quantity Economic Model -  Claimed!
I. Spread of Staph Infections in hospitals  claimed!
J. Romeo and Juliet: Love in Adolescent times  - (2 people 11:15 am, 12:20 claimed)
K. When Zombies Attack: Surviving the Undead   Claimed!
L.  Modeling the Heartbeat  - Claimed!
M.  Microparasites and their hosts!  Claimed!


File for help with MATLAB: 231Project_MATLABHelp.pdf
reading #13
 11/11
 7.2- Def 1, Thm 1, Def 2, Def 3, Thm 2
reading #14
 11/13
 7.2- table of Laplace transforms pg 359
7.3- thm 3, thm 4, thm 5, thm 6
quiz #10
 11/16
 7.2: 1,5,9, 11, 13, 17, 19, 21, 23, 29abcdhj
reading#15 11/18 7.4- Def 4, Thm 7, Partial Fraction general forms for all three cases:  Nonrepeated linear factors, repeated linear factors, quadratic factors.
quiz #11 11/20
 7.3: 1,5,9, 13, 17
7.4:  1,3,7, 9, 12, 14,  21, 23, 24, 25, 27
reading #16
 11/18
 7.5- Method of Laplace Transforms (blue box, pg 376)
Extra
Credit
 11/21
&
11/22

NIMBioS Conference: The 7th Annual Undergraduate Research Conference at the Interface of Biology and Mathematics

http://www.nimbios.org/education/undergrad_conf2015

You 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 registration as verification of attendance, AND they won't want to kick you out :) .
reading #17
 11/23
 8.1- Formula for a Taylor serios
8.2-  Thm 1,2,3, and 4, and def 1
quiz #12
 11/23
 7.5: 1,3,5,7,9,11,23,25,29,32, 35
reading #18
 11/25
 8.3- Def 2
quiz #13
 11/30
 8.1: 1,2,5,8,10acd
8.2: 1,3,5, 17,18,21, 22, 30, 32, 34, 38
prep for final
8.3: 1,3,5,11,13,15, 19, 20, 25, 27




Final Exam
 11:15-12:05 section: Dec 10, 10:15am-12:15pm

12:20-1:10 section: Dec 8, 10:15am-12:15pm



Comprehensive!