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.


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
Monday, Wednesday and Friday
10:00 - 10:55
B122 Gates Chemical Laboratory (GCL, Building 26)

 019:00 - 9:55 am  269 LAU 
029:00 - 9:55 am 119 KRK 
039:00 - 9:55 amB122 GCL 
0410:00 - 10:55 am 269 LAU 
05 10:00 - 10:55 amB122 GCL 
0610:00 - 10:55 am 119 KRK 
071:00 - 1:55 pm142 KCK  
08 1:00 - 1:55 pm 314 ANB 
09 1:00 - 1:55 pm B101 BBB 
10 2:00 - 2:55 pm B122 GCL 
11 2:00 - 2:55 pm 142 KCK 

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


  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 Instructor Contact Information and Office Hours
276 Cahill

TA Contact Information and Office Hours

Course Schedule and Lecture Notes
 9/25/2017 It is unfortunate that this box is here but the lecture notes are at the bottom of the page. Thank Google.


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


 Date PostedAssignment Due Date 

Midterm and Final Exam

Collaboration Table
You may consult:  
Course textbook (including answers in the back)YESYES
Other booksYESNO
Solution manualsNONO
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:


* 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.

Caltech Math,
Sep 21, 2017, 9:04 AM
Caltech Math,
Sep 21, 2017, 3:36 AM
Caltech Math,
Sep 21, 2017, 3:36 AM
Caltech Math,
Sep 21, 2017, 3:37 AM
Caltech Math,
Sep 21, 2017, 3:37 AM