Please find Dr. Goonetilleke's syllabus, schedule and 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 (Jan. 20): Law of Algebra, Review Slides of basic formula, Review of Technique of Integration

Surveillance Quiz, SolutionsWeek 2 (Jan. 27): No recitation due to the snow. Please watch MIT Lecture 1 and MIT Lecture 3, and try the Attendance Quiz 1.

In case you run into trouble, please consult an old recitation note I wrote last semester. There will be enough information for you to gauge your way.

Maple Lab 0 will be due next week. Please find the assignments on the maple website above.

If you are in trouble, please consult Maple Intro for 244 and Maple TutorialWeek 3 (Feb. 3): Recitation Notes, Quiz 1

The MIT Lecture 7 and MIT Lecture 8 shows more details concerning modeling.

Week 4 (Feb. 10): Recitation Notes, Quiz 2

The old recitation notes provides a good supplement: Notes from 2.2 to 2.4, Notes from 2.5 to 2.6

For numerical methods, please also watch MIT Lecture 2 for further understanding the local truncation error (especially, why second derivative).Week 5 (Feb. 17): Recitation Notes, Quiz 3

The old recitation notes: Notes for local truncation error (only the first part), Notes from 3.1 to 3.4

Dr. Goonetilleke's study guide and practice problems

Week 6 (Feb. 24): Recitation Notes. Solutions to Tricky Homework Problems in Chapter 3 (from old Rec. Notes)

Solution and Grading Schemes to Midterm 1 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).

(Only for interested students) About Reduction of Order: Note (I), Note (II) (both from the old notes)Week 7 (Mar. 3): Recitation Notes, Quiz 4

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

Also the old recitation notes may also be helpful: Notes on 3.5 and 3.6Week 8 (Mar. 10): Recitation Notes, Quiz 5

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 exponential powers, 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 (Mar. 17): No recitation during the spring break. Enjoy!

Week 10 (Mar. 24): Recitation Notes, Quiz 6

Please refer to the book for the graphs of solutions corresponding to different types of vibrations.Week 11 (Mar. 31): Recitation Notes, Quiz 7

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 12 (Apr. 7): Recitation Notes, Quiz 8 (Take-home)

Week 13 (Apr. 14): Recitation Notes, Quiz 9

Week 14 (Apr. 21): Recitation Notes Part I: Phase Portraits (real eigenvalues), Part II: Phase Portraits (repeated and complex eigenvalues)

, Quiz 10

Related MIT Lectures: Lecture 24, Lecture 25, Lecture 26, Lecture 27Week 15 (Apr. 28): No more quiz this week.

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

Some techniques of integration are summarized in this hand-written notes: Brief review of integrating techniques

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 or exams on these rules WILL SUFFER SERIOUS 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 homogeneous ODEs.

Fei Qi

Room 624, Hill Center

Department of
Mathematics

Rutgers University

110 Frelinghuysen
Road

Piscataway, NJ USA 08854