I taught the same class in the past. Here are the materials I used for teaching recitations of 244 in Spring 2014 and Fall 2013.

Please find Dr. Goonetilleke's syllabus either on sakai or here.

Please find the schedule and the homework assignments either on sakai or here.

Please find the information concerning maple labs here.

All announcements are to be posted on sakai. Please make sure that you can have the right email registered to the system.

You may find the following resource useful for this course:

- MIT OCW Lectures on Differential Equations (Note that they have a different syllabus)
- Dr. Z's Calc 4 Lecture Handouts (The mathematical central topic is covered and emphasized, with marginal topics discarded)
- Maple Tutorial (Found and shared by Mr. Joshua Vigoureux).

Recitation Materials:

Week 1 (Sep. 4): Recitation Notes, Quiz 1, Solutions

Review Slides, Basic rules of Algebra and Logarithmic Functions, Maple Intro for 244Week 2 (Sep. 11): Recitation Notes, Quiz 2, Solutions

Also if interested, please watch MIT Lecture 1 and MIT Lecture 3 for more details concerning direction fields and first order linear ODEs.Week 3 (Sep. 18): Recitation Notes, Quiz 3, Solutions

Also if interested, please watch MIT Lecture 7 and MIT Lecture 8 for more details concerning modeling.

For 2.2 and 2.4, Dr. Z's notes may also be helpful: Notes for 2.2 Notes for 2.4.Week 4 (Sep. 25): Recitation Notes, Quiz 4, Solutions

More Practice for 2.6, Solutions, Dr. Z's Notes for 2.5, 2.6

For numerical methods, please also watch MIT Lecture 2 for further understanding the local truncation error (especially, why second derivative).Week 5 (Oct. 2): No quiz this week due to the coming midterm exam.

Dr. Goonetilleke's study guide and extra practice problems

Recitation Notes (with Comments to all extra practice problems), Review Questions

Week 6 (Oct. 9): Recitation Notes, Quiz 5, Solutions (seriously?!)

Exam 1, Solutions with Grading Schemes

For linear homogeneous ODEs, the MIT Lecture 9, MIT Lecture 10 and MIT Lecture 11 cover 3.2 to 3.4 (without reduction of order).Week 7 (Oct. 16): Recitation Notes Part I Part II: Solutions to Tricky Homework Problems, Quiz 6

For 3.5 and 3.6, Dr. Z's notes may also be helpful:Notes on 3.5, Notes on 3.6

In case you are struggling with past due homework, please focus on 3.1, 3.3 and 3.4 before attempting 3.5 and 3.6. Dr. Z's notes on these sections may also help: 3.1, 3.3, 3.4Week 8 (Oct. 23): Recitation Notes, Quiz 7

The principle I talked about in the recitation notes applies to Chapter 4 as well. You should keep in mind that

1. First try templates, as well as characters, are determined ONLY by the right hand side of the ODE.

2. To determine how many times your template fails, you have to look at the characteristic roots, which are determined ONLY by the left hand side of the ODE.

Please understand this set of recitation notes thoroughly.Week 9 (Oct. 30): Recitation Notes, Quiz 8, Solutions

In case you need more exercises on factorizing polynomials, at the bottom of the page you will find some resource (just Ctrl+F factorization).Week 10 (Nov. 6): Recitation Notes Part I: Linear Algebras, Part II: Vibrations

Dr. Goonetilleke's Study Guide for Midterm 2, Extra Practice Problems, Solutions

Review Questions for Midterm 2Week 11 (Nov. 13): Quiz 9

Due to the medical condition of my wife, I am unable to write recitation notes.Week 12 (Nov. 20): Quiz 10

Due to the medical condition of my wife, I am unable to write recitation notes.Week 13 (Nov. 25): No quiz this week. Happy Thanksgiving!

Recitation Notes 11, 12 and 13 Part I: Computations, Part II: Phase Portraits (real distinct eigenvalues), Part III: Phase Portraits (repeated and complex eigenvalues)

Related MIT Lectures: Lecture 24, Lecture 25, Lecture 26, Lecture 27Week 14 (Dec. 4): Quiz 11

I am not sure if I have time to write any more recitation notes. Please watch the following video lectures

Regarding nonlinear systems: MIT Lecture 31

Regarding series solutions: Old MIT Lecture by Herbert Gross Well-worked example by Houston Math Prep

~~Regarding convergence of series: Summary of Theorems of Convergence / Divergence, Finding region of convergence~~

Regarding radius of convergence: How to make an easy estimate

Solution to Some Chapter 5 Problems

For 244 students, I have two requirements

- Please make sure you know how to differentiate and integrate and you can play with the elementary functions. You can review the issue through the slides I wrote

Brief review of basic formulas

Also you can consult the famous Russian book

3193 Problems in Mathematical Analysis

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 basic rules:
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 in these algebra issues, a series of link is provided for help.

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.

Fei Qi

Room 624, Hill Center

Department of
Mathematics

Rutgers University

110 Frelinghuysen
Road

Piscataway, NJ USA 08854