In the Fall of 2013 I taught recitations of 640:244 (Differential Equations for Physics and
Engineering) for Section 1 - 3.

Please find Dr. Z's
official course website for the course
here:

http://www.math.rutgers.edu/~zeilberg/math244_13.html

for
handouts, homework problems, due dates and answers, exam dates, etc..

Please find the quizzes and some answers here:

Quiz
1, Answer

Quiz
2

Quiz
3

Quiz 4,
Answer (Dropped for low performance)

Quiz 5, Answer
(Typo Contest Winner: Samantha Heller, Donald Chawla, Kevin Albertson, Honorable Mention: Alexander
Kong)

Quiz 6, Answer
(Typo Contest Winner: Jonathan Chang, Kelsey Hickey. Honorable mention: Grace Gunawan [awarded already] )

Quiz 7, Answer

Quiz 8, Answer

Quiz 9 (Due to a failure of copy machine, the quiz is cancelled)

Quiz 10 & 11 (Take-home)

Quiz 12, Answer (Dropped for low performance)

Please find the memorandum of the materials in the first recitation, where we reviewed differentiation and integration.

Brief review of basic formulas(Typo Contest winner: Neha Bhat)

You are welcomed to attend the typo contest that will be kept open for all the material I uploaded. There is one and only one rule: For each typo, the first one who finds it will take the 2-point-award.

The second chance project for quiz will be open on Oct 31.

- Who can attend: People who had the score strictly lower than 6.
- What you should do: I will post the second chance quizzes below before class. Print it after class, do it and submit it with your homework in the next class.
- What you can get: 2 point proration up to 6 points.

In detail: Let x be your original grade. If x <= 4, then your grade will be prorated to x+2. If x=5, then your grade will be 6.

- Only a 100% correct answer will earn you the award.
- After submission you won't have any chance to revise it.
- I won't advise the second chance quiz problems. But you can ask for advice on the original quiz. This will be helpful in achieving the award.
- Overdue submissions will not be graded.

Please find the second chance quizzes and due date here:

Second Chance of Quiz 1, due Nov. 7.

Second Chance of Quiz 5 & 7, due Nov. 14.

Second Chance of Quiz 2 & 3, due Nov. 21.

Please find information of maple labs
here:

http://www.math.rutgers.edu/courses/244/maple244_s13.html

There
is no Fall 2013 version at this moment.

Please find the basic rules of algebra and logarithm
rules here:

http://www20.csueastbay.edu/library/scaa/files/pdf/Alg%20rules.pdf

It is required that you know these rules well. ANYONE making ANY mistakes in quizzes on these rules WILL SUFFER PENALTY!

If you have difficulties, a series of link is provided for help. Please definitely check with them.

If you don't know how to manipulate logarithm, please find

http://people.ucsc.edu/~miglior/chapter%20pdf/Ch10_SE.pdf

Please read**Section 10.5**on page 45 in the pdf file (page 733 in the book), try all example problems, and do**Exercise 44 - 61**on page 51 in the pdf file (Page 740 in the book).

If you are not very fluent with the quadratic equations (e.g. always use the root formula), please find

http://people.ucsc.edu/~miglior/chapter%20pdf/Ch08_SE.pdf

Read**Section 8.1, 8.2**, try all example problems, and do**Exercise 66 - 83**on page 23 in the pdf file (Page 573 in the book). Make sure you understand all the related methodsIn particular, if you have never seen criss-cross factorization before, please check the youtube videos

Criss-Cross Method 1, Criss-Cross Method 2, Criss-Cross Method 3 and Criss-Cross Method 4.If you have never seen matrices before, please find

http://people.ucsc.edu/~miglior/chapter%20pdf/Ch03_SE.pdf

Read**Section 3.6**, try all example problems, and do**Exercise 15 - 23, 46 - 49**on page 51 - 52 in the pdf file (page 227 - 228 in the book).

Read**Section 3.7**, try all example problems, and do**Exercise 2 - 7, 20 - 25, 35 - 40**on page 63 - 64 in the pdf file (page 239 - 240 in the book).

After you work on this topic, try the problems of the attendence quiz at Lecture 15 and you will find it easy to play.If you keep on making mistakes on exponentials, please find

http://people.ucsc.edu/~miglior/chapter%20pdf/Ch01_SE.pdf

Read**Section 1.8**, try all example problems, and do**Exercise 59 - 84**on page 88 in the pdf file (page 88 in the book).If you don't know how to divide a polynomial, please find

http://people.ucsc.edu/~miglior/chapter%20pdf/Ch05_SE.pdf

Read**Section 5.3**, try all example problems, and do**Exercise 27 - 42**on page 31 in the pdf file (page 339 in the book).

After you have done the work, please compare to the technique I used on dealing with t/(t+1) or -2-t/(t+1) in class. You will see that this is actually the simplest example of division.If you are not fluent on simplifications of rational functions, please find

http://people.ucsc.edu/~miglior/chapter%20pdf/Ch06_SE.pdf

Read**Section 6.1 - 6.4**, try all example problems, and do**Exercise 29 - 48**on page 61 - 62 in the pdf file (page 463 - 464 in the book).If you are not fluent on playing with trigonometric functions, please find

http://www.eht.k12.nj.us/~staffoch/Textbook/chapter04.pdf

Read**Section 4.3**, make sure you**memorize the table of the values of sine, cosine and tangent on usual special angles**on page 23 of the PDF file (page 279 in the book)

and do**Exercise 17 - 26**on page 28 of the pdf file (page 284 in the book)

Read**Section 4.5**, make sure you can**recognize, distinguish different graphs of the trignometric functions and manipulate them by scaling and translation**, and do**Exercise 3 - 14, 23 - 16**on page 48 in the pdf file (page 304 in the book)If you are not fluent on factorizing polynomials, please find

http://people.ucsc.edu/~miglior/chapter%20pdf/Ch05_SE.pdf

Read**Section 5.4**, try all example problems and do**Exercise 51 - 70**on page 40 of the pdf file (page 348 of the book) .

Read**Section 5.5**, try all example problems and do**Exercise 9 - 46**on page 52 of the pdf file (page 360 of the book).

Read**Section 5.6**, try all example problems and do**Exercise 43 - 70**on page 61 of the pdf file (page 369 of the book).

Read**Section 5.7**, try all example problems and do**Exercise 1 - 66**on page 67 of the pdf file (page 375 of the book).

If you really do all the exercises, then after that you may probably find yourself addicted to playing such a game. I don't recommend to resist such an addiction. Just do all other exercises and it will accelerate your speed greatly in solving problems in Lecture 8 - 16.

Useful links:

Please find the famous Russian book: 3193 Problems in
Mathematical Analysis
here:

http://mpec.sc.mahidol.ac.th/radok/physmath/mat12/start.htm

If
you feel that your computation skills is insufficient or you need a
review on Calc 1, 2 or 3, please read the corresponding chapters and
do the example problems. I have the full solution to ALL the exercise
problems. If you are in trouble with ANYTHING please come to me for
help.

Please find the very well-prepared video lectures on differential equation offered by Arthur Mattuck in MIT Spring 2010 here:

http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures

In partcular, in the
Lecture 27 you will see nice sketches for the integral curves around four different classes of critical points. That will help to understand Lecture 22 in our course. It is a pity that due to limitation of time we cannot really talk about this in class.

Please find the demonstration of stability of 2x2 system of first order linear differential equation (developed by Housam Binous and Ahmed Bellagi) here:

http://demonstrations.wolfram.com/StabilityOfALinearTwoDimensionalAutonomousSystem/

It would help to understand the classification of critical points.