Math 217 Fall 2015

Lectures: MWF 10:10am-11:00am and 11:10am-12:00noon Wilson 214

Instructor: Songhao Li        Office: 207A Cupples I

Phone: (314)935-4208        email: sli (at) math (dot) wustl (dot) edu

Office Hours: Monday 1pm-2pm, Tuesday 1pm-2pm and Wednesday 2pm-3pm or by appointment

Office Hours for the Final Exam: Tuesday Dec 8 1:30pm-5pm, Wednesday Dec 9 2:30pm-5:00pm

Note: TA office hours are as usual on Monday Dec 7 and on Thursday Dec 10

TA: Gong Cheng

TA Office Hours: Monday 3pm-5pm Thursday 3:30pm-4:30pm Lopata 323

Calculus help room:

Grader: Fan Zhang, Taylor Lau, Augus Gu, Amritha Gourisankar

Course Webpage:

Textbook: Elementary Differential Equations 10ed by Boyce and DiPrima

Suggested: Elementary Differential Equations with Boundary Value Problems by Edwards and Penney

Note: Boyce and DiPrima has a different version Elementary Differential Equations and Boundary Value Problems 10ed.

As far as I checked, the first nine chapters are just the reproduction of our textbook.

Edwards and Penney is optional. I listed it here because it has been used for this course at this university in the past.

It is preferrable if you can get the 10th edition of Boyce and DiPrima.

If you elect to use an earlier edition, it is your responsibility to check the possible different numbering in homework assignments.


If time permits, we will cover up to Chapter 7 of Boyce and DiPrima, possibly skipping some sections.

More details to follow...



There will be four exams, three of which will be written on weekday evenings during the semester, plus the final exam.

The final exam is accumulative.

There will be weekly homeworks, except on the weeks preceeding the exams.

Instead, there will be a webwork during the week before each exam.

Each of the homework assignments and the webworks will be counted equally.

Update: The point grade for the course will be the greater of the following two options:

1. 20% homework/webwork + 20% E1 + 20% E2 + 20% E3 + 20% F

2. 100% F

Your point grade is then translated into the letter grade, with the class average being at least B.

Midterm point grade is calculated as follows:

0.2 x E1 + 0.2 x E2 + 0.05 x A1 + 0.05 x A2 + 0.05 x A3 + 0.05 x A4 + 0.05 x A5

The maximum point grade is 50.

Ave: 36.989, Median: 37.65

Range: A: 40-50, B: 34-39.99, C: 28-33.99, D: 22-27.99, F: 0-21.99

Distribution: A: 61, B: 60, C: 34, D: 17, F: 3

Note that for convenience, I did not add + or - to the letter grades, and I did not include the one and only webwork in the calculation.

I will add +/- and include the webwork for the end-of-course grades.


The exam dates:

Exam 1: Sept 17, Thursday 7pm-9pm

Exam 2: Oct 20, Tuesday 7pm-9pm

Exam 3: Nov 17, Tuesday 7pm-9pm

Final Exam: Dec 11, Friday 10:30am-12:30pm

You can look up your seating here.

The following exam sessions are lead by our TA Gong Cheng

Exam 1 review session: Sept 14, Monday 6pm-8pm Wilson 214

Exam 2 review session: Oct 15, Thursday 6pm-8pm Wilson 214

Exam 3 review session: Nov 13, Friday 6pm-8pm Wilson 214

Final exam review session: Dec 9, Wednesday 6pm-8pm Wilson 214

Exam 1  Exam 1 Solution  Histogram Ave: 69.986, Median: 72

Exam 2 Exam 2 Solution  Histogram Ave: 71.069, Median: 72

Exam 3 Exam 3 Solution  Histogram Ave: 60.305, Median: 59

Table of Laplace Tranform

Final Final Solution  Ave: 55.825, Std Dev: 15.047

Note: The answer for #2 is B, not A as indicated on the grading site. The discrepency will be resolved later.

Also no matter what you choose for #8, you will get the credit.



Print the homework sheet and use it as the cover sheet.

Write your student number and your name clearly on the cover sheet.

Please use letter sized papers only, and remember to staple your homework.

Anyone who fail to do this will be subjected to a 10% penalty.

Homework 1  due Sept 4, 2015

Homework 2  due Sept 11, 2015

Note: For the direction fields and the graphs of solutions, you may use the printouts from a software or a website, or you may simply hand draw them.
In either case, do not spend too much time on the pictures.
The pictures are supposed to help building intuition.
They are not meant to waste your valuable time.

Webwork 1 is posted, due Sept 18, 2015

Homework 3  due Sept 25, 2015

Homework 4  due Oct 2, 2015

Homework 5  due Oct 9, 2015

Homework 6  due Oct 19, 2015

Homework 7  due Oct 30, 2015

Homework 8  (now complete!) due Nov 13, 2015

Note: To limit the workload, I have not assigned too many problems in Assignment 8.
Try practising with similar problems in the textbook and in past exams to prepare for Exam 3.

Homework 9  due Nov 30, 2015

Homework 10  due Dec 4, 2015

Homework 11  Not to be handed in

Progress of the course:

Week 1

Aug 24: Direction fields

Aug 26: Solutions of differential equations

Aug 28: Classification of differential equations

Week 2

Aug 31: 1st order linear ODEs

Sept 2: Cont'ed...

Sept 4: 1st order separable ODE's

Week 3

Sept 7: Labour Day

Sept 9: Modelling

Sept 11: Uniqueness and existence of solutions as in Sec 2.4

Week 4

Sept 14: Exact equations

Sept 16: 2nd order linear homogeneous equations with constant coeffients

Sept 18: Characteristic equation: b^2-4ac > 0

Week 5

Sept 21: Wronskian

Sept 23:  Wronskian continued...

Sept 25:  Characteristic equation: b^2-4ac < 0

Week 6

Sept 28: Characteristic equation: b^2-4ac = 0

Sept 30: Reduction of order

Oct 2: Methods of undetermined coefficients

Week 7

Oct 5: Variation of parameters

Oct 7: Dampened variations and dampened variations with external force

Oct 9: nth order linear equations, determinants, Wronskian and linear indepedence

Week 8

Oct 12: nth order homogeneous equations with costant coeffients

Oct 14: Methods of undetermined coefficients

Oct 16: Fall break

Week 9

Oct 19: Variation of parameters

Oct 21: Review of power series

Oct 23: Solution near an ordinary point

Week 10

Oct 26: Continued... 

Oct 28: Convergence of solution near an ordinary point

Oct 30: Euler equation revisited

Week 11

Nov 2: Regular singular points

Nov 4: Solution near a regular singular point

Nov 6: Case: two root do not differ by an integer

Week 12

Nov 9: Case: two root do not differ by an integer

Nov 11: Bessel equation of order zero

Nov 13: Beseel equation of order a half

Week 13

Nov 16: Definition of Laplace transform

Nov 18: Solution of IVP

Nov 20: Laplace transform of step functions

Week 14

Nov 23: Examples from mechanics

Nov 25: Happy Thanksgiving!

Nov 27: Happy Thanksgiving!

Week 15

Nov 30:  Laplace transform of impulse functions

Dec 2: Convolution integral

Dec 4: Review