Office hours: MTW 9:50AM - 10:50AM, Hill 525 (the classroom)

You may also catch me in my office at Hill 624, but preferably please send me an email and make an appointment before you come.

Email: cl.volkov at rutgers dot edu

In the Summer of 2015 I will teach 640:244 (Differential Equation for Physics and Engineering) for Sections C1.

I taught the same class in the past. Here are the materials I used for teaching recitations of 244 in Spring 2015, Fall 2014, Spring 2014 and Fall 2013.

Syllabus, Tentative Schedule. Maple Labs

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).

Lecture Materials:

Lecture 1 (May 26): Lecture Notes: 1.1, 1.2. Homework Assignment (If you know how to do #2 and #3 then do it. Otherwise leave it tomorrow since we didn't cover that much)

Reviewing materials: Law of Algebra (link broken), Review Slides of basic formula, Review of Technique of Integration

In case you have time, please also watch MIT Lecture 1 to further understand the geometric interpretation of ODE.Lecture 2 (May 27): Lecture Notes: 1.3, 2.1. Homework Assignment

In case you have time, please also watch MIT Lecture 3 and read Dr. Z's notes for 2.1 for further understanding.Lecture 3 (May 28): Lecture Notes: 2.2, 2.4. Homework Assignment

In case you have time, please also read Dr. Z's notes for 2.2 and Dr. Z's notes for 2.4 for further understanding.

Maple Lab 1 is assigned and is due on Monday, June 8th. Please find the instructions here and the seed file hereLecture 4 (June 1): Course Plan: Part 1, Part 2, Lecture Notes: 2.3. Homework Assignments

More modeling examples with ODE is available in MIT Lecture 7 and MIT Lecture 8Lecture 5 (June 2): Lecture Notes: 2.5. Homework Assignment

In case you have time, please also watch MIT Lecture 5 and read Dr. Z's Notes on 2.5 (Note that Dr. Z used a different method).

Lecture 6 (June 3): Lecture Notes: 2.6. Homework Assignment

In case you have time, please also read Dr. Z's Notes on 2.6 for further understanding.

Lecture 7 (June 4): Lecture Notes: 2.7, 8.1, 8.2, 8.3. Homework Assignment

Notes about the homework set: The original initial value y(1)=0 will make no sense of the problem. As you may observe, there's no error at all. So I have to cancel this homework set since many of you have already struggled enough on the computations.

(Added 6/4/2015 10:11PM: Solving the revised version will result in bonus in grade)

Instead of continuing to do the homework, please watch the MIT Lecture 2 for a much better understanding. Also in case you have time, please also read Dr. Z's Notes on 2.7.

Maple Lab 2 is assigned and is due on Monday, June 15th. Please find the instructions here and the seed file hereLecture 8 (June 8): Hour Exam, Solutions to Hour Exam 1

People not doing well on Hour Exam 1 are welcomed to attend the Second Chance Club. Please find the details here.

Please watch MIT Lecture 6 to get acquainted to complex numbers.Lecture 9 (June 9): Lecture Notes: 3.1, 3.2. Homework Assignment

In case you have time, please also watch MIT Lecture 9 for further understanding. Also you are welcomed to watch also MIT Lecture 10 to prepare for the classes tomorrow.

Also you could read Dr. Z's notes on 3.1 and 3.2Lecture 10 (June 10): Lecture Notes: 3.3, 3.4. Homework Assignment

In case you have time, please read Dr. Z's notes on 3.3 and 3.4. We haven't been able to cover the reduction of order. It shall be done tomorrow in the beginning of the class.Lecture 11 (June 11): Course Plan, Lecture Notes: 3.4, 3.7. Homework Assignment

I forgot the post the MIT Lecture 11 before. In case you have time, please also watch it to further understand the general theory of second order linear ODEs. Next Monday after finishing the leftovers today, we will apply the theory to another type of ODEs. So it would be helpful to keep the knowledge refreshed.Lecture 12 (June 15): Lecture Notes: 3.7, 5.4. Homework Assignment

Maple Lab 3 is assigned today and is due next Monday. Also a bonus problem is asked in the homework assignments.Lecture 13 (June 16): Lecture Notes: 5.4, 3.5. We haven't covered enough to assign new homework. So just finish the rest yesterday. The bonus problem yesterday is still open.

In case you have time, please read Dr. Z's Notes on 3.5 and 3.6 to prepare for further details. Also you can consult the corresponding Recitation Notes I wrote last semester.Lecture 14 (June 17): Lecture Notes: 3.5. Homework Assignments

The set-up we discussed today is refered as first try templates. Its name suggests that one try may not succeed and you may have to try multiple times. We will look into this issue tomorrow. Also the set-up actually works for higher order linear ODEs. So if you have a solid grasp to the current topic, you'll find nothing further difficult in the rest of stuffs before the second midterm.Lecture 15 (June 18): Lecture Notes: 3.5. Please finish the leftovers of homework yesterday and submit it on sakai.

In the exam you should not expect too much computations on such problems. As long as you can figure out the correct template, you are not supposed to spend more than 15 minutes on a single problem.

At the end of the notes I included an improved method of computation, just for people who are interested. But for the problems in your exams, the improved method will not make a significant difference, compared to the method I talked in class.

If you are still interested, you can check out the following links: MIT Lecture 13, MIT Lecture 14, Old Recitation Notes in Spring 2014.Lecture 16 (June 22): Lecture Notes: 3.8, 3.6. Homework Assignments

In case you have time, please read Dr. Z's Notes on 3.6. Also Dr. Gross posted his old MIT lectures on youtube. Here are the links Method of Undetermined Coefficients and Variation of ParametersLecture 17 (June 23): Lecture Notes: 4.1, 4.2, 4.3. Homework Assignments

In case you have time, please read Dr. Z's Notes on 4.1, Notes on 4.2, Notes on 4.3 for further understanding.Lecture 18 (June 24): I used chalkboard instead of iPad. Anyone willing to share his or her notes to the class will be highly appreciated by everyone.

Lecture 19 (June 25): Hour Exam, Solutions to Hour Exam 2

People not doing well on Hour Exam 1 are welcomed to attend the Second Chance Club. Please find the details here.

Lecture 20 (June 29): Lecture Notes: 5.1, 5.2 Homework Assignments

Here is the video I played in class: Old MIT Lecture by Herbert Gross. Here is another video lecture that might be helpful: Well-worked example by Houston Math Prep

In case you have time, please read Dr. Z's Notes on 5.2 for further understanding. Also you could use the following materials to recall the knowledge of power series: Summary of Theorems of Convergence / Divergence, Finding region of convergenceLecture 21 (June 30): Lecture Notes: 5.2, 5.3 Homework Assignments

The solution to the last example problem can be found here: Old Recitation Notes on Series Solutions

Here is a more formal notes regarding Estimating the radius of convergenceLecture 22 (July 1): I tried to use IPad but it is annoying to write matrices. So I switched to chalkboard. As a result, no lecture notes are available. We covered 7.2 and 7.3.

Basically I went over the Old Recitation Notes on Linear Algebra. In case I have time, I'll edit the notes to make it easier to read (turned out I didn't).

Since we didn't cover eigenvalues and eigenvectors, for the Homework Assignment tonight you don't have to do Problem 3.Lecture 23 (July 2): We finished the leftovers of eigenvalues and eigenvectors yesterday, then talked about the general theory in 7.1 and 7.4, and covered 7.5 when we applied the theory to the case when the matrix has real distinct eigenvalues. In case you have taken detailed notes, you are very welcomed to share.

Here is the Homework Assignment. In case you have time, please also watch MIT Lecture 24 for better understanding.Lecture 24 (July 6): We basically covered 7.5, 7.6 and 7.8, In the Old Recitation Notes you'll find the problems I covered in class, plus some more problems. Here is the Homework Assignment

In case you have time, please also watch MIT Lecture 25 and MIT Lecture 26 for better understanding.Lecture 25 (July 7): We started 9.1 on the phase portraits. The Old Recitation Notes talks about how to draw the phase portrait in detail.

A better resource is certainly the MIT Lecture 27. In case you are confused, please watch it.

Maple Lab 4 is assigned today and will be due on the last day of class. Due to the limitation of time, we won't have time for Maple Lab 5. The 2 percent credit will be set for free.Lecture 26 (July 8): Hour Exam 3, Solutions

No second chance club will be held for Hour Exam 3 because many of you are already stressing out. The compensation plan is: the grade for this Hour Exam will be set as Max(Exam 3, Final Exam) in percentage. So there's more stake on the final than this exam.

Please make sure you watched MIT Lecture 27 before the class tomorrow.Lecture 27 (July 9): Lecture Notes (Thank Ms. Shawnie Caslin for sharing): 9.1, 9.2, 9.3. Homework Assignments.

We briefly started 9.3 today. An application will be shown next Monday. It will be helpful if you could watch MIT Lecture 31 ahead of time, since we may not have time to cover that in great detail.Lecture 28 (July 13): Lecture Notes (Thank Ms. Shawnie Caslin for sharing): 9.3, 9.4 Homework Assignments.

The SIRS survey form can be found from this link and is due by 11:59PM by July 15, 2015. In case you are not happy with my teaching, this is the last chance you can make me pay.Lecture 29 (July 14): Lecture Notes (Thank Ms. Shawnie Caslin for sharing): 9.4. Review

Please find the Review Questions and make sure you are comfortable on the questions concerning the notions.

Please find the exam problem arrangement on sakai announcements. Also please check the gradebook and inform me if any errors occur.Lecture 30 (July 15): We went over all the stuffs we have learned. I failed to cover the series solution in class due to the limit of time. Please review that part yourself.

I'll be around in the afternoon from 2PM on. In case you have any questions, feel free to drop by my office at Hill 624.

The SIRS survey is due tonight 11:59PM. Seize your last chance to revenge!Lecture 31 (July 16): Final Exam, Solutions

All letter grades are submitted. Enjoy the rest of your summer!

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