Differential Equations

Course Description and Grading Breakdown

This course will be an introduction to the study of differential equations.

Topics include:
- Examples of modeling real-life phenomena with differential equations
- Elementary methods for solving simple ordinary differential equations (separation of variables, integrating factors, variation of parameters)
- General solutions to constant coefficient differential equations
- Linear differential equations (homogeneous, inhomogeneous, principle of superposition), relevant linear algebra concepts (span, linear independence, basis)
- Graphical methods (slope fields, direction fields, phase lines)
- Numerical approximation (Euler's method)
- Solving constant coefficient first order linear systems
- Phase portraits for nonlinear systems and linearization of nonlinear systems
- Fundamental local existence and uniqueness theorem
- Fourier Series.


There will be 8 problem sets, one midterm and one final.  Your grade will be calculated based on:

40% Problem Sets
30% Midterm
30% Final

The letter grade scale will not be set in advance.

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

 All recitations take place on Thursday.
 SectionTime Location  TA
9:00 - 9:55 am 310 LindeJane Panangaden
29:00 - 9:55 am 255 LindeNeeraja Kulkarni
39:00 - 9:55 am 187 Linde Bowen Yang
410:00 - 10:55 am 387 LindePraveen Venkataramana
510:00-10:55 am187 LindeAlex Perozim de Faveri
610:00 - 10:55 am 187 LindeAlex Perozim de Faveri
713:00 - 13:55 pm 187 LindeTran Thanh Trung Can
813:00 - 13:55 pm B127 GatesJane Panangaden
914:00 - 14:55 pm 187 LindeAngus Gruen
Note: the location of section 8 recitations has changed. The TAs for sections 4 and 8 have swapped since Week 1. 

Note: the TA for section 5 has changed. 

Notes from the midterm review session can be found here

Course Instructor Contact Information and Office Hours
Prof. Phil Isett
175 Linde Hall
OH: Friday 11AM-12PM; Monday 1:30 PM - 2:30 PM

TA Contact Information and Office Hours
 TA     Office Hours
 Location email
Jane PanangadenFriday 6p-7p, Monday 5p-6p Linde 183, Linde 187 jpananga@caltech.edu
Angus GruenThursday 5p-6p Linde 183 agruen@caltech.edu
Alex Perozim de FaveriThursday 7p-8p Linde 183 afaveri@caltech.edu
Praveen VenkataramanaFriday 4p-5p Linde 183 pvenkata@caltech.edu
Bowen YangFriday 5p-6p Linde 183 byyang@caltech.edu
Tran Thanh Trung CanThursday 6-7 Linde 183 tcan@caltech.edu
Alex Perozim de FaveriMonday 4-5 Linde 187 afaveri@caltech.edu
Neeraja KulkarniMonday 6-7 Linde 187 nkulkarn@caltech.edu
Announcement: Alex is holding office hours from 8-9p on Thursday November 29th in Linde 183.  

Course Ombudspersons
 House/ResidenceOmbud   Contact (@caltech.edu) 
Avery Nathaniel Smith nismith 
 LloydAmy Wang awang3 
Ricketts Maya Mutic mmutic 

Approximate Course Schedule and Reading Material

Primary reading from MIT lecture notes by Bjorn Poonen, see
Search for "Course notes".

We will also be using some course materials (e.g. problem set questions) shared from the MIT 18.03 class made available by MITx.

Supplementary notes may be found here.

The schedule below is an approximation of what will be covered and may be subject to change.

Week 1
 Sec. 1 - 7.14, 28.2-28.4, Supp Note 1
Week 2 
 Sec. 7.15 - 10.8, Supp Note 2, Supp Note 3, Supp. Note 4
Week 3    
 Sec. 10.8-12.11
Week 4
 Sec. 13.1-14.15, Supp. Note 5
Week 5
 Sec. 19.7-21.2, MatrixAlgNote
Week 6
 Sec. 22.1-23.13
Week 7
 Sec 24-26.3, HeatWaveEnergy
Week 8
 Sec 27.1-27.2,  ExistUnique,
Week 9
 Fences, Sec. 27.3-27.5
Week 10
 Centers, Sec. 31.1, 31.5

Course Policies
Due dates:  Problem sets will be due by 4PM on Tuesdays.  It is encouraged that students finish the problem set before the week of class in order to stay on track.

Late work - A late problem set requires a dean's note, preferably received in advance.

 Date PostedAssignment Due Date  Solutions
 9/30/2018PSet 1
 4PM, 10/9/2018 Sol 1 
 10/8/2018 PSet 2
 4PM, 10/16/2018Sol 2
 10/15/2018     PSet 3
Sol 3
 10/21/2018PSet 4
 4PM, 10/30/2018
Sol 4
 11/5/2018     PSet 5
 4PM, 11/13/2018
 Sol 5
 11/12/2018 PSet 6
 4PM, 11/20/2018
 Sol 6
 11/18/2018 PSet 7
 10AM, 11/30/2018 (Fri.)
 Sol 7
 11/27/2018 PSet 8
 10AM, 12/7/2018 (Fri.)
 Sol 8

Posted solutions are password protected. The password has been emailed to you. If you have issues accessing the files, please contact Meagan. These solutions are for your personal use only and should not be posted or distributed. 

Midterm and Final Exam
The midterm is available here. It is due at 1 pm on Tuesday November 6th. If you have issues accessing the file, please contact Meagan. If you have questions about the content please contact your TA or instructor.

The final is available here. It is due at 10 am on Friday December 14th. If you have issues access the file, please contact Meagan. If you have questions about the content, please contact your TA or instructor.

Site directory

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.

Jane Panangaden,
Dec 10, 2018, 1:54 PM
Jane Panangaden,
Oct 31, 2018, 2:13 PM