Differential Equations

Course Description
The practical track of Math 2 focuses on exploring methods of solving differential equations explicitly, and applications to real-world problems. The lectures will contain numerous examples and, compared to the analytic track, fewer derivations and proofs. Even though the content of the two tracks will not be the same, the two tracks of Math 2 will have approximately the same difficulty level and workload.

William E Boyce and Richard C DiPrima, Elementary differential equations and boundary value problems (10th Edition), published by Wiley, ISBN-13: 9780470458310.

There will be approximately 8 problem sets, a midterm exam and a final. Your grade will be determined by: 

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
119 Kerckhoff Laboratory of Biological Sciences (KRK, Building 27)

All recitations take place on Thursday.
 Section Time Location TA
 19:00 - 9:55 am 387 Linde HallAndrei Shubin
 210:30 - 11:25 am 387 Linde Hall Jane Panangaden 
 41:00 - 1:55 pm 187 Linde Hall Ryan Yoo 
 5 2:30 - 3:25 pm310 Linde Hall Jane Panangaden 
 63:00 - 4:00 pm155 ArmsAndrei Shubin
 NA7:00 - 8:00 pm  183 Linde Hall Mark Xu

Course Instructor Contact Information and Office Hours
Lu Wang
360 Linde Hall
Office Hours: Friday 11 am - 12 pm; Monday 4 pm - 5 pm.
Office hours on Monday, November 4 is moved to 7 pm - 8 pm. 
Office hours on October 25 is moved to October 28, Monday 4 pm - 6pm.

TA Contact Information and Office Hours
 TA Office Hours Location Email
 Haoxuan Chen Monday 8 - 9 pmLINDE 183    haoxuan@caltech.edu
 Jane Panangaden Monday 3-5 pmLINDE 289  jpananga@caltech.edu
 Andrei Shubin  Friday 3-5 pmLINDE 289 ashubin@caltech.edu
 Ryan Yoo Tuesday 2-3 pmLINDE 183 gyoo@caltech.edu
 Mark Xu  - mzxu@caltech.edu
Andrei's office hours on November 15th are moved to November 17th from 4-6pm in LINDE 382.

Course Ombudspersons
 House/Residence Ombudsperson Email
 AveryLin Lin Lee  llee3@caltech.edu
 DabneyMarguerite Hewitt  shewitt@caltech.edu
 Fleming Meena Hari mhari@caltech.edu

Course Schedule
We will mostly follow the textbook listed above.

 DateTopic  Reading
 10/02 Overview Ch. 1
 10/04 Separable Equation;
1st Order Linear Equation
  integrating factor 
 10/07 1st Order Linear Equation (Continued) 2.1
 10/09 Modeling with 1st Order Equation 2.3
 10/11 Population Dynamics; Equilibruims; Phase Line 2.5
 10/14 Exact Equation 2.6
 10/16 Existence and Uniqueness 2.4; 2.8
 10/18 2nd order ODE with Constant Coefficients: 
Characteristic Equation with Different Real Roots
 10/21 Characteristic Equation with Complex Roots3.3 
 10/23Characteristic Equation with Repeated Real Roots;
Reduction of Order
 10/25Homogeneous Linear 2nd Order ODE; Wronskian  3.2
10/28 Nonhomogeneous Linear 2nd Order ODE: Variation of Parameters  3.6
10/30 Method of Undetermined Coefficients  3.5
11/01 Motion of a Mass on a Vibrating Spring3.7-8 
11/04Homogeneous Higher Order Linear Equation 4.1-2
11/06 Nonhomogeneous Higher Order Linear Equation 4.3-4
11/08 Series Solutions near a Regular Point  5.1-2
11/11 Series Solutions near a Regular Point, Continued  5.3
11/13 Series Solutions near Regular Singular Point 5.4-5
11/15 Laplace Transform 6.1-2 
11/18  Solve Initial Value Problem by Laplace Transform 6.2
11/20  Step Functions; ODE with Discontinuous Forcing Function 6.3-4

Course Policies
Due dates: Problem sets will be due by 4 pm on Tuesdays, unless otherwise specified. Problem sets will be turned in to (locked) dropboxes which are located at the entrance of Linde Hall. If you are not sure about where to turn in problem sets, please ask Freddy Mora at 156 Linde Hall for help.

You are encouraged to discuss and collaborate with others on problem sets, but you are required to write down solutions on your own.

Late work - Late work won't be accepted without a dean's excuse preferably received in advance. However, the lowest score of problem sets will be dropped when calculating towards course grade.

 Date PostedAssignment Due Date  Solution Common Mistakes
 10/04 Problem Set 1 10/15, 4 pmsolutionscommon mistakes
 10/11 Problem Set 2 10/22, 4 pmsolutions 
 10/18 Problem Set 3 10/29, 4 pmsolutions 
(Updated 11/03)
 Problem Set 4 11/12, 4 pm  
 11/08 Problem Set 5 11/19, 4 pm  
 11/15Problem Set 6  11/26, 4 pm  
 11/22  12/06, 4 pm  
 12/02    No due date  

In order for your problem sets to be returned in the return slot in the lobby of the math building, you must fill out a FERPA waiver and return it to Freddy Mora in the math office. If you do not fill out a FERPA waiver you will have to pick up your problem sets in person. 

Midterm and Final Exam
The midterm exam will be available here on October 30, 2019. It will be due by 4 pm on November 5, 2019. Only open the exam when you have a blue book(s) and a 4-hour time period available. Refer to the Exams column in the Collaboration Table. The honor code applies.

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,
Oct 22, 2019, 10:03 PM
Jane Panangaden,
Oct 17, 2019, 9:16 PM
Jane Panangaden,
Oct 22, 2019, 10:10 PM
Jane Panangaden,
Oct 30, 2019, 12:14 PM
Lu Wang,
Oct 4, 2019, 11:52 AM
Lu Wang,
Oct 4, 2019, 1:36 PM
Lu Wang,
Oct 11, 2019, 4:20 PM
Lu Wang,
Oct 18, 2019, 9:27 AM
Lu Wang,
Nov 3, 2019, 5:18 PM
Lu Wang,
Nov 8, 2019, 12:20 PM
Lu Wang,
Nov 15, 2019, 11:52 AM
Lu Wang,
Oct 30, 2019, 1:57 PM