Math 110.302 Differential Equations

Fall 2015 Course Syllabus

http://www.math.jhu.edu/~brown/courses/f15/302.html

 

Dr. Richard Brown

MWF 12:00pm - 12:50pm: Bloomberg 272

brown@math.jhu.edu

MWF 1:30pm - 2:20pm: Krieger 205

403 Krieger Hall

 

410-516-8179

 

Office Hours:

 

M

3:00-4:00 pm

by appt. other times

W

3:00-4:00 pm

 

Text Elementary Differential Equations, 10th Edition, Boyce, William E. and DiPrima, Richard C., New Jersey: Wiley, October 10, 2012 0470458321 978-0470458327

 

Current Recitation Sections:

Section

Time

Place

Instructor

1

Tuesday 1:30pm

Shaffer 304

Wang

2

Tuesday 3:00pm

Maryland 110

Wang

3

Thursday 3:00pm

Olin 305

Su

4

Thursday 4:30pm

Krieger 308

Su

5

Tuesday 4:30pm

Maryland 217 Ginsberg
6

Thursday 1:30pm

Shaffer 304 B Zhao
7

Thursday 3:00pm

Shaffer 100 B Zhao
8

Tuesday 3:00pm

Olin 305 Ginsberg
9 Thursday 3:00pm Maryland 201 Mehrle

Course Material: The core of the course will center on the text material, and will basically cover the material detailed in the syllabus link below.  I may add and/or slightly alter this material depending on how the semester plays out.  But the core set of material that I will cover will be what is on the syllabus:

 

Official Syllabus for 110.302 Differential Equations

In addition to this, you should be aware that the prerequisite for this is a full year of single variable calculus.  With an Advanced Placement BC exam score of 5, or the equivalent credits of the course 110.109 Calculus II (Phys Sci & Eng), you are considered prepared for this course.  If there is a question, please come see me.  For now, what we consider prerequisite content is everything on the syllabus for 110.109.  The link is here:

Official Syllabus for 110.109 Calculus II (Phys Sci & Eng)

Grade Policy:  There will be weekly homework sets and projects (10%), 2 in-lecture 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.  If you will not be present when homework is submitted, please submit the assignment early.  If you miss a homework or project deadline, you can talk to the TA for late acceptance, but I have instructed them to not accept late submissions.  If you miss an exam, you will have to be cleared by me to be excused from the exam, a process that will include documentation and a valid excuse.  In this case the ultimate grade for that exam will be calculated based on your performance on future exams and the final. 

Homework: Homework based on the week’s lectures will be posted as official on the course web site sometime on Friday (Homework may be posted earlier, but may change as the lectures evolve for the week). That assignment will be due in lecture at the end of the following week.  See below for the due dates.  Homework is an absolutely essential educational part of the course. You will be graded mostly on your ability to work problems on exams. You cannot work problems on exams if you have not practiced the techniques and become comfortable applying the concepts within the homework problems. If you misuse homework by not doing it yourself, or not checking that you can solve a problem on your own after having been shown how to do it, then your exam scores and corresponding grade will reflect this. Trust me on this last point.  Talk to your section Teaching Assistant about how to turn in a homework if you cannot go to class. Some additional points:

  • 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.

  • You will be graded on your PROCESS in homework construction rather than simply your ability to calculate.  You must present your homework solutions and not simply answer questions. 

  • Here is a brief idea of how one should construct homework problems for submission:

How to construct homework problem solutions:  Example 1: Calculus I Bio, Example 2: Linear Algebra

Also, here is an excellent quick article on good mathematics writing.  It is worth the read....

Course Policy: You are responsible for lecture notes, any course material handed out, and attendance in class.  While I will not formally record your attendance, I will get to know you and your rate of presence over time.  The lectures will be conducted as if you have already read the material and attempted some homework problems.  In this manner, you can focus mainly on those parts of the lectures that cover the areas of your reading you found difficult to understand. My teaching style is that of interactive discussion and I will rely on your input in developing the material.  Active participation in the classroom is a great way to generate the discussion necessary to fully grasp the material.

 

Help Room:  213 Kreiger Hall.  The hours are 9am  9pm on Monday through Thursday, and 9am  5pm on Friday.  This free service is a very valuable way to get one-on-one help on the current material of a class from other students outside the course.  It is staffed by graduate students and advanced undergraduates.

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 see the professor or the grader.

For more information, see the guide on "Academic Ethics for Undergraduates" and the Ethics Board web site (http://ethics.jhu.edu).

Students with Disabilities:  Students with documented disabilities or other special needs that require accommodation must register with the Office of Academic Advising. After that, remind me of your needs at least 5 days prior to each exam; we will need to have received confirmation from Academic Advising.

Fall 2015 Tentative Schedule

The details of this material will be updated and reformed as the semester progresses. 

 

Week

Sections

Homework

Due in Lecture

August 28

Course Orientation

 

September 11

2.1.28 Solution

August 31 - September 4

8/31, 9/2, 9/4

9/2Math

ExampleLinearODE

1.1 Basic Models:  Direction Fields

1.2 Solutions to Some ODEs

1.3 Classification of ODEs

2.1 Linear Equations

4,6,12,15-20,26 (JODE1)

3,12,16

1-6,8,12,18,20

12,14,20,24,28,30,36

September 7 Labor Day:  No Class

September 9 -- 11

9/9, 9/11

ExampleSeparableODE

2.2 Separable Equations

2.3 Modeling with 1st Order ODEs

2.4 Linear/Nonlinear Differences

2,6,14,22,30

 

2,6,8,9,16,22,23

September 18

2.2.30 Solution

September 14 -- 18

9/14, 9/16, 9/18

ExampleExactODE

MathPitchforkBifurcation

2.5 Autonomous Equations

2.5 Bifurcation Diagrams

2.6 Exact Equations

2,3,11,12,13,14,16,17,22

27,28,Fish Problem 

September 25

Fish Problem Solution

September 21 -- 25

9/21, 9/23, 9/25

ExUniqWorksheet

ExampleExactSepODE

LectureQuestions

2.6 Exact Equations

2.8 Existence and Uniqueness

3.1 Homogeneous Equations 2

4,6,10,14,15,18

 

2,6,8,10,12,18,20,22

 

October 2

2.6.16 Solution

September 28 -- October 2

9/28, 9/30, 10/2

Wronskian

Abel's Thm

3.2 The Wronskian

3.3 Char. Eqn. Roots:  Complex

3.4 Char. Eqn. Roots:  Repeated

4,6,8,12,14,26,28,32

4,6,10,14,32

10,12,18,24,28

October 9

October 5 -- 9,

10/5, 10/7, 10/9

3.5 Undetermined Coefficients

3.6 Variations of Parameters

4,6,12,14,16,18,30

4,8,10,16,21,28,30

October 15

3.6.17 Solution

3.6.6 Solution

October 12 Exam 1 (Sections covered to 3.4)

October 14 -- 15

10/14, 10/15

4.1 nth Order Linear Equations

4.2 Homogeneous Eqns

4.3 Undetermined Coefficients

7.1 Introduction to Systems

3,5,8,14,18,19

12,14,32

1,2, Resonance

2,3,6,8,15

October 23

4.4.3 Solution

Resonance Solution

October 16 Fall Break:  No Class
October 19 -- 23

10/19, 10/21, 10/23

7.2 Review of Matrices

7.3 Linear Algebraic Eqns

7.4 First Order Linear Systems

7.5 Homogeneous Linear Systems

2,10,22,24

2,7,8,16,17,18

4,6

1,4,8,15,16

October 30

October 26 -- 30

10/26, 10/28, 10/30

7.5 Homogeneous Linear Systems

7.6 Complex Eigenvalues

24,25,26,27,29,31

2,6,10,13,28 (By Monday, you will be able to do this.  See lecture notes for 10/30)

November 6

November 2 -- 6

11/02, 11/04, 11/06

 

7.7 Fundamental Matrices

7.8 Repeated Eigenvalues

9.1 The Phase Plane

3,4,6,7,12

3,9,15

1,4,6,7,17,18

November 13

November 9 -- 13

11/09, 11/11, 11/13

9.2 Autonomous Systems

9.3 Locally Linear Systems

9.4 Competing Species

9.5 Predator-Prey Equations

5,7,17,23

1,3,11,20,27

3,17

2,11

November 20

The Pendulum

Competing Species

November 16 -- 20

11/16, 11/18, 11/20

 

9.7 Periodic Solutions and Limit Cycles

8.1 Euler Method

 

 

 

6.1 Definition of Laplace Transform

2,4,9,16

1a,2a,3a

Also solve 1,3 and graph both numerical and analytical solutions together

November 30

November 23 -- 27

Thanksgiving Break:  No classes

November 30  11/30

6.2 IVP Solutions

1,3,5,11,14,18

Homework not to be handed in

December 2

Exam 2 All sections covered from 10/05 to 11/18.  No Laplace Transform.

December 4

Course Review  

 

 

 

December 9

Final Exam

9:00am - 12:00pm:  1,2,3,4,9 in Bloom 272

9:00am - 12:00pm:  5,6,7,8 in Mudd 26

Special Notes:

  1. For any needed problems, use a slope field calculator like JODE to create the direction fields.  Do not do them by hand.  You can print them out from JODE or screenshot them in another app.  But do edit the images if you screenshot to excise out all unneeded extra stuff.

  2. For the problem set on Homogeneous second order differential equations, assume that the 2-parameter family of solutions we developed in class IS the general solution.