Math 110.302 - Differential Equations

Spring 2018 Course page Math 302 Differential Equations with Applications Spring 2018

Announcement about course grade:
After curve, the grade percentage breakdown is as follows:
         F 52D, 56D+, 60C-, 64C, 68C+, 72B-,76B, 80B+, 84A-, 88A, 94A+
I have spent hours to find every possible grade lifts following the criteria: within 1% to the next level AND have shown improvements over the semester (or have been active in class).  I have also taken into account your extra credits from homework if there is any.

The grades have been submitted to SIS. I can not change it.

If you are sure that I made a mistake in your grade assignment, please email me with your section number and all your scores. We will go to SIS to make the change. This process will be recorded by paperwork. The JHU Ethics Statement below applies. 

If you do not get the grade you wished: I am sorry that your grade does not work for you. You may consider retaking the course in summer or other semesters. When you take the course again, please do talk with your teacher (and TA) about your situation early. More importantly, please do put a reasonable amount of efforts in the course. Your grade is determined by you, not by us. As teacher, following the JHU policies and ethics, we are here to help you to learn and to earn a better grade. But in the end it is your efforts that determines the grade.
Any efforts asking for a better grade than reasonable will be ignored. Your grade is determined by your efforts, not by me or your TA. I can not arbitrarily change your grade. We must follow the policies. The JHU ethic statement applies to you, as well as me and your TA. Please do not keep on contacting me for an unreasonable grade, such an action is disrespectful and is unethical.

Instructor: Fei Lu
  Krieger 301 
Office Hours:
MF 11--12 + after classes in classrooms: 12:50-1:15, and 2:20-2:50 
Email:  feilu##           (Here and in the following,  ## =

Lectures and sections:

Recitation Sections

Sec #
Office hr
Email, office

MWF 12:00 - 12:50PM
Levering Arellano
T  1:30--2:20
Maryland 309
Jeffrey Marino
Th 1-2
jmarino9##, Krieger 211

T  3:00-3:50
Maryland 217 Patrick Martin

mmart152##, Krieger 211

Th 3:00-3:50 Gilman 55
Emily Stoll
T11:15-1:15, Krieger 207

Th 4:30-5:20
Maryland 217 Emily Stoll T11:15-1:15
MWF 1:30--2:20 PM
Maryland 110
T   4:30-5:20 Maryland 217 Cheng Zhang
czhang67##, Krieger 211

Th 1:30--2:20
Gilman 17
Xiaoqi Huang
Th 4-5
xhuang49##, Krieger 200

Th 3:00-3:50 Hodson 313
Xiaoqi Huang
Th 4-5 xhuang49##, Krieger 200

Textbook: Elementary Differential Equations and Boundary Value Problems (10th Edition or later) William E. Boyce and Richard C. DiPrima.
We will basically cover the material detailed in the official 110.302 Differential Equations Course Syllabus. I may slightly alter this material depending on the progress of the class, and I strongly recommend to take notes in class.

Grade Policy: There will be weekly homework sets (10%), two in-lecture midterm exams (50%) and a final (40%).  The schedule of these exams is given with the homework problems below. There will be no make-ups on homework or exams. 

Academic Support: Besides attending the lectures and the recitation sections I encourage you to use the following opportunities for additional academic support:

Special Aid: Students with disabilities who may need special arrangements within this course must first register with the Office of Academic Advising. I will need to have received confirmation from the Office of Academic Advising. To arrange for testing accommodations please remind me at least 7 days before each of the midterms or final exam by email.

JHU Ethics Statement: The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Cheating is wrong. Cheating hurts our community by undermining academic integrity, creating mistrust, and fostering unfair competition. The university will punish cheaters with failure on an assignment, failure in a course, permanent transcript notation, suspension, and/or expulsion. Offenses may be reported to medical, law, or other professional or graduate schools when a cheater applies.

Violations can include cheating on exams, plagiarism, reuse of assignments without permission, improper use of the internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Ignorance of these rules is not an excuse.

In this course, as in many math courses, working in groups to study particular problems and discuss theory is strongly encouraged. Your ability to talk mathematics is of particular importance to your general understanding of mathematics. You should collaborate with other students in this course on the general construction of homework assignment problems. However, you must write up the solutions to these homework problems individually and separately. If there is any question as to what this statement means, please ask the instructor.

Homework assignments: Homework based on the week's lectures will be posted as official on the course schedule below on each Friday (sometimes may be earlier, but may change as the lectures evolve for the week). That assignment will be due at the beginning of class the next Friday (Once the class starts, late assignments will not be accepted). Please hand your homework set into the bin corresponding to your section. You will receive your graded homework back from your section teaching assistant in the following week.  If you absolutely cannot make it to class, please arrange for someone else to hand it in for you. However, you may miss up to two homework assignments without grade penalty, as the lowest two homework scores will be dropped from the final grade calculation.
Homework is an absolutely essential educational part of the course. You should make every effort to solve the assigned problems using the concepts learned from the lectures and readings. You will be graded mostly on your ability to work problems on exams. If you have not practiced the techniques within the homework problems, you will have difficulties to work problems on exams. You are strongly encouraged to collaborate in the analysis and study stage of homework preparation. However, you are required to submit completely original work, however, and must write up your homework for final submission alone. Both parties of copied homework will be assigned score 0.

Please turn in homework assignments in the following format:
Announcement:  Blackboard is available now! 18/2/7.

Tentative schedule:
Topic and Sections
Additional Exe(to PILOT)
1.1 Basic Models:  Direction Fields 
1.2 Solutions to Some ODEs
1.3 Classification of ODEs
2.1 Linear Equations
1.1: 6, 14, 15-20
1.2: 3, 8, 13, 15
1.3: 2,4,6,9
2.1: 10,20,21,28,30,35
 Friday 2/9
by Patrick Martin
Tools to plot slope fields:

Bluffton U
1.1: 25       
1.2: 9,16            [5,6]
1.3: 14
2.1: 22. 29, 34  [37,38]
*[] is more challenging.
2/5  2/7 2/9
2.2 Separable Equations
2.3 Modeling with 1st Order ODEs
2.4 Linear/Nonlinear Differences
2.5 Autonomous Equations
2.2: 2,5,14,22,25,29
2.3: 11
2.4: 4,5,14,15,26,27
2.5: 3,4,7,9,14,16,17
2/16 Friday 2/9:
last day to add courses
2.2: 11,21    [30,32]
2.4: 25         [32]
2.5: 2, 13
2/12   2/14
2.5 Bifurcation Diagrams
2.6 Exact Equations
3.1 Homogeneous Equations
2.5: 26,27
2.6: 2,6,8,12,14,16
3.1: 5,7,14,17,20,21
2.6: 5, 15, 17
3.1:18, 22
2/19  2/21
3.1 Homogeneous Equations
3.2 The Wronskian
2.8 Existence and Uniqueness
3.1: 24, 26
3.2: 1,4,8, 14,18,26,28,31, 33,37 
(2.8: read 13,14)

3.1: 25
3.2: 15,21,24,32
2/26   2/28
3.3 Char. Eqn. Roots:  Complex
3.4 Char. Eqn. Roots:  Repeated
3.5 Undetermined Coefficients
3.3: 10, 14,19,26
3.4: 4,8,18,24,27
3.5: 3,10,12,14,17,30
Exam 1 Sample

3.3: 17
3.4: 10,25
3.5: 9
3/7   3/9
Exam 1 on Monday: Covers to 3.4
3.6 Variation of Parameters
4.1 nth Order Linear Equations
4.2 Homogeneous Eqns

3.6: 4,8,12,16,21,28,30
4.1: 3,8,14,18,19
4.2: 12,14,32
Sunday 3/11:
last day to drop the course
3.6: 19,29
4.1: 7
4.2: 31
3/12  3/14
4.3 Undetermined Coefficients
7.1 Introduction to Systems
7.2 Review of Matrices
7.3 Linear Algebraic Eqns
4.3: 1,2
7.1: 3,6,8,15
7.2: 2,10,12,22,24
7.3: 2,7,8,15,16,17,18

4.3: 31
7.1: 10
7.2: 12,21
7.3:  4
Spring Vacation

3/26   3/28
7.4 First Order Linear Systems
7.5 Homogeneous Linear Systems
7.4: 4,6
7.5: 1,4,8,9,12,16,24


7.4: 7
7.5: 10,15,25
4/2    4/4
7.6 Complex Eigenvalues
7.7 Fundamental Matrices
7.8 Repeated Eigenvalues
7.6: 2,7,10,15,22
7.7: 3,4,6,7,12
7.8: 3,9,15
7.6: 15 -- do it after 4/6 lecture
7.6: 4,21
7.7: 2,11
7.8: 2
4/9   4/11
7.8 review of Chapter 7
9.1 The Phase Plane
9.2 Autonomous Systems
9.1: 1&6(abc), 14,18,20,21
9.2: 5,7,17,23

9.1: 15
9.2: 6,18
4/16    4/18

9.3 Locally Linear Systems
9.4 Competing Species

9.5 Predator-Prey Equations

9.3: 1,3,11,20,27
9.4: 3,7

9.3-20 (c): draw a phase portrait only, discard the other parts
9.3: 2, 8
9.4: 6

4/25    4/27

Exam 2 on Monday: covers to 9.4
9.7 Periodic Solutions, Limit Cycles

6.1 Definition of Laplace Transform
9.7: 2,4,9,16
6.1: 2,5,9,14,23,28
Sample Exam 2 Solution to SE2 (corrected #4)
solution to E2 P4b
9.7: 3, 10
6.1: 3,10,13,23
4/30     5/2
5/4: review
6.2 IVP Solutions
6.3 Step Functions
6.4 ODEs with Disc. Forcing Func.
6.2: 12, 21
6.3: 13,20,21
6.4: 3(a),5(a)
Practice Exam (updated)

Solution (Thank Patrick Martin)  [Corrected #2]
Important: course evaluation. *** 

Final Exam Period
Wed. May 9th, 9am-12pm Hodson 110

Wed. May 9th, 9am-12pm at Hodson 110  (for those with conflicts and disabilities, your will be contacted by Professor Brown or SDS about time and location of your exam).
Your grades will be available in Blackboard two-three days after the exam.  ***
*** "Students who do not complete their course evaluations by May 18th will be able to access their final grades and transcripts beginning June 1st, 2018."

Related courses:

ODE Applets: On the following web page you can find several Java applets that are helpful in understanding the behavior of solutions to ordinary differential equations (ODEs): Java Applets for ODEs (JOde). (Your browser must support Java for the applets to work) You may also want to check out the MIT Mathlets and you may want to use Wolfram Alpha to plot slope fields.

Scientific Computing: Differential Equations by Professor Greg Eyink