Differential Equations

Course Description 

This is meant to be an introductory course on Differential equations. It is meant to be somewhat more serious and interesting than the course you would take at the Pasadena City College on the same subject, but perhaps less single-mindedly rigorous than a course you might take in mathematics graduate school on the subject of ordinary differential equations. A traditional City College style course would focus a little too much on just the question of how to write down explicit solutions to equations. Different equations are different so this might acquire a bit of a cookbook character. My aim is to teach much of the same material but emphasize the underlying concepts. We will also discuss differential inequalities somewhat more than is traditional in a first course. 

The reason is that it is not too hard to do this, and it gives you a way to say things rigorously about solutions to differential equations which you don't know explicitly. The course is more than an algebra course, and more than a calculus course, but it isn't Math 1a either. You may occasionally see me do an epsilon-delta proof, you are still acknowledged to know what one is, but that isn't the emphasis here. The goal is to be able to use your ingenuity and all the background you have , Math 1a,1b, and 1c, to say everything you can about solutions to differential equations. Like every mathematics course at Caltech, Math 2 will be rigorous, you are expected to answer questions on a problem set in complete sentences, and if what you have written makes no sense, it can be counted wrong. But all of this is subject to the aims of the questions you are asked.

There will be no textbook. My lecture notes, found at the bottom of this page will play the role of the textbook.
Eventually, they may be gathered into a single file, with better formatting and a snazzy title like "Differential Equations for Dilettantes" but for now, we have what we have.

Grading

There will be 8 problem sets, a midterm exam and a final. Your grade will be determined by 
  • Problem sets   40%
  • Midterm Exam 30%
  • Final Exam       30%
The grading scale will not be set in advance.

Course Meeting Time and Location
Lectures
Monday, Wednesday and Friday
10:00 - 10:55
B122 Gates Chemical Laboratory (GCL, Building 26)

Recitations 
Thursday
 019:00 - 9:55 am  269 LAU Forte Shinko
029:00 - 9:55 am 119 KRKYuhui Jin 
039:00 - 9:55 amB122 GCLAngad Singh 
0410:00 - 10:55 am 269 LAUNathaniel Sagman 
05 10:00 - 10:55 amB122 GCLAngad Singh 
0610:00 - 10:55 am 119 KRKTamir Hemo 
071:00 - 1:55 pm142 KCK  Josh Lieber
08 1:00 - 1:55 pm 314 ANB Jane Panangaden
09 1:00 - 1:55 pm B101 BBBJim Tao 
10 2:30 - 3:25 pm 142 KCKJosh Lieber 

If you would like to switch your recitation section, please email Meagan with your preferred recitation time.

Announcements
  1. I, Nets Katz, regret deeply that I must be away for the first week of the term. For this reason, the first three lectures will be delivered by Oleg Ivrii. Please be nice to him. He'll be doing his best. If anything goes wrong, it is my fault. The lectures he is meant to be delivering are available at the bottom of the page as lecture1.pdf, lecture2.pdf, and lecture3.pdf. Please read them. They represent my point of view as to what is going on and even the jokes might give you some clues about, e.g., how to approach the problem sets.
Course Ombuds
There will be an Ombuds meeting with Dr. Elena Mantovan on Thursday November 9th, 12 - 1 pm in Room 105 of the Math Building. Your course Ombuds are:
  • Jackie Lodman
  • Camilla Ora
  • Miranda Schwacke
  • Zhengyuan Shang
Please contact them to pass along any feedback you may have about the class.


Course Instructor Contact Information and Office Hours
276 Cahill

Office Hours
Thursday, 7 - 8 pm, Sherman Fairchild Library Room 326
Sunday, 8 - 9 pm, Millikan Library 9th Floor Teaching Resource Room


TA Contact Information and Office Hours
Forte ShinkoThursday 8 - 9 pmSherman Fairchild Library Room 326 
Jane PanangadenFriday 4:30 - 5:30 pmMillikan 9th Floor, Teaching Resource Room
Josh LieberSaturday 3 - 5 pm Millikan 9th Floor, Teaching Resource Room
Tamir HemoFriday 7 - 8 pm Millikan 9th Floor, Teaching Resource Room 
Yuhui JinFriday 8 - 9 pmMillikan 9th Floor, Teaching Resource Room 
Nathaniel SagmanFriday 5:30 - 6:30 pm Millikan 9th Floor, Teaching Resource Room 
Jim TaoSaturday 7 - 8 pm Millikan 9th Floor, Teaching Resource Room 
Angad SinghSunday 6 - 8 pmMillikan 9th Floor, Teaching Resource Room 

There will no office hours the week on 11/30 or on subsequent days. 
If you need help studying for the exam please contact a TA. 



Course Schedule and Lecture Notes
 DateTopic 
 9/25/2017 Lecture 1
 9/27/2017  Lecture 2
 9/29/2017         Lecture 3
 10/2/2017     Lecture 4
 10/4/2017 Lecture 5
 10/6/2017 Lecture 6 
 10/9/2017 Lecture 7 
 10/11/2017     Lecture 8 
 10/13/2017 Lecture 9 
 10/16/2017 Lecture 10
 10/18/2017 Lecture 11
 10/20/2017 Lecture 12
 10/23/2017 Lecture 13
 10/25/2017 Lecture 14
 10/27/2017 Midterm Review
 10/27/2017 Lecture 15
 10/30/2017 Lecture 16
 11/1/2017 Lecture 17
 11/3/2017 Lecture 18
 11/6/2017 Lecture 19 
 11/8/2017 Lecture 20
 11/10/2017 Lecture 21 
 11/13/2017 Lecture 22 
 11/15/2017 Lecture 23
 11/17/2017 Lecture 24        
 11/20/2017 Lecture 25
 11/22/2017 Lecture 26
 12/3/2017 Final Review


Course Policies and other remarks by the hacker who is teaching this course:

Problem set due dates and times: Problem sets will be turned in to boxes which are now located somewhere in Downs. The due dates are Mondays. The due times are 2 A.M.  This is so you can get lots of sleep after turning in the set and before class, and so that with each week's  classes, the past week's assignment is already in the rearview mirror so to speak. 

Late work - Late work won't be accepted without a dean's excuse preferably received in advance.

Recitations - Please go to the recitations.  Each week, a portion of the recitation will be dedicated to introducing some computational (or even theoretical) aspect which the instructor will not have time to present in class or possibly to something else entirely. The TA's will not do your problem sets for you under any circumstances but they will do whatever they can to help you understand the course. In theory, all TA's for a course are interchangeable. Students are in the habit of picking favorites and crowding their sections and office hours. This isn't necessarily a good idea. My advice [this is Nets, hacking into the website] is to find the least popular TA you can and follow him or her as an oracle. The less popular your TA is, the more time he or she has to talk to you.

In general, get to know your TA and bug him/her with your questions, and try to fill in all the holes in your understanding. I didn't write that sentence but basically agree with it. In fact, you could try to be in touch with your TA about how to customize the section to meet your preferences. Of course it helps if all the students in the section are with you. Sometimes it is hard to tell. But try to help the TA. If it is obvious

Assignments

 Date PostedAssignment Due Date  Solutions
 9/21/2017Problem Set 1 10/2/2017 Solutions 1
 10/2/2017Problem Set 2 10/9/2017 Solutions 2
 10/9/2017Problem Set 3 10/16/2017 Solutions 3
10/16/2017Problem Set 4 10/23/2017 Solutions 4
 10/30/2017Problem Set 5 11/6/2017 Solutions 5
 11/6/2017Problem Set 6 11/13/2017 Solutions 6
 11/13/2017 Problem Set 7  11/20/2017 Solutions 7
 11/21/2017 Problem Set 8 Extended to 2 am 11/30/2017 Solutions 8


Midterm and Final Exam
Midterm is available. The password for the file was emailed to you. If you have issues accessing the file, please contact Meagan. The exam is due at 4 pm on Tuesday October 31st. 


The final exam is available. The password for the file was emailed to you. If you have issues accessing the file, please contact Meagan. The exam is due at 9 am on Friday December 8th. 

The review session for the final will be on Sunday December 3rd 7-9pm in B122 GCL.


Collaboration Table
 HomeworkExams
You may consult:  
Course textbook (including answers in the back)YESYES
Other booksYESNO
Solution manualsNONO
InternetYESNO
Your notes (taken in class)YESYES
Class notes of othersYESNO
Your hand copies of class notes of othersYESYES
Photocopies of class notes of othersYESNO
Electronic copies of class notes of othersYESNO
Course handoutsYESYES
Your returned homework / examsYESYES
Solutions to homework / exams (posted on webpage)YESYES
Homework / exams of previous yearsNONO
Solutions to homework / exams of previous yearsNONO
Emails from TAsYESNO
You may:

Discuss problems with othersYESNO
Look at communal materials while writing up solutionsYESNO
Look at individual written work of othersNONO
Post about problems onlineNONO
For computational aids, you may use:

CalculatorsYES*NO
ComputersYES*NO

* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work.  For example, "by Mathematica" is not an acceptable justification for deriving one equation from another.  Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them.

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