Math 441: Differential Equations (Spring 2020) - Sec X13/X14


Instructor Partha Dey
ContactBy and from "@illinois.edu" account.
Videos Subscribe to go.illinois.edu/math441_ch
Q&A MWF 9:00-9:50am through Zoom Meetings.
HW upload Upload PDF files through Compass2g.
Websitehttps://faculty.math.illinois.edu/~psdey/Math441SP20.html.

Discussion Board and exam/hw scores are in the Compass2g site.

Textbook Elementary Differential Equations and Boundary Value Problems, Boyce & DiPrima (10th Ed).
A free book on Elementary Differential Equations.
Software Direction field plotter and WolframAlpha for direction fields, solving DEs, and more.
Resources

This is a rigorous study of Ordinary Differential Equations (ODEs) and mathematical modeling. Topics include:

  • solution of first-order ODEs by analytical, graphical and numerical methods;
  • existence, uniqueness and continuity for first-order ODEs;
  • linear second-order ODEs, in particular, with constant co-efficients;
  • undetermined coefficients and variation of parameters;
  • sinusoidal and exponential signals: oscillation, damping, resonance;
  • matrix and first-order linear systems: eigenvalues and eigenvectors; phase plane diagrams and
  • Stability and Liapunov's Method.
See Department Syllabus for Math 441.


Instructor Partha Dey
ContactBy and from "@illinois.edu" account.
Class MWF 12:00-12:50pm in 241 Altgeld Hall
Websitehttps://faculty.math.illinois.edu/~psdey/Math441SP20.html. Discussion Board and exam/hw scores are in the Compass2g site.
Office Hrs Wednesdays 2:00-03:30pm or by appointment made via e-mail in 341A Illini Hall
Textbook Elementary Differential Equations and Boundary Value Problems by Boyce and DiPrima (10th Ed).
If you like to study using a hard copy of the book, then you can buy a used copy of 10th edition of Boyce & DiPrima Elementary Differential Equations (either with or without Boundary Value Problems, since those chapters are not covered in our course).

A free book on Elementary Differential Equations.
Prerequisite MATH 241 or the equivalent. MATH 347 or MATH 348 is recommended
Electronic devices No use of cell phones or other means of electronic communication during the class. In particular, no texting and no emails are allowed during the class. Laptops are Tablets are allowed only for class purposes. Calculators are not allowed in exams and/or quizzes.
DRES Please email your DRES letter to me as early as possible in the semester, so that we can make appropriate accommodations.
Software links
  • Direction field plotter
  • WolframAlpha for direction fields, solving DEs, and more
  • Iode package for direction fields, first and second order ODEs, and first order systems (Iode runs inside Matlab, which students get free from the Webstore)
  • Java applets for vibrating membranes (and other vibrating systems), these are not part of the class but are fun to play around with
Study Resources

Homework Policy Homework will be assigned weekly on Mondays on this website, to be handed in at the beginning of the Friday lecture.

You are encouraged to work together on the homework, but I ask that you write up your own solution (and write name/s of collaborators) and turn them in separately.

Late homeworks will not be graded. If you will be absent when homework is due, you must turn in your homework in advance. Note that I will check my mailbox (250 Altgeld) right after collecting homework in class.

I will drop your lowest hw scores.
Exams There will be three in-class midterm exams on Wednesdays February 19, March 25 and April 22. They will be technically comprehensive, but emphasizing recent material up to the most recent graded and returned homework assignment.

The Final Exam is comprehensive and tentatively scheduled for 8:00-11:00 a.m., Friday, May 15 in 241 AH.
Make-up examMake-up exams will not be given, unless your absence is approved by the Emergency Dean. Travel and leisure plans, even for family events, are never a legitimate reason for missing an exam.
ParticipationA small portion of the grade is the easiest to achieve. Make at least five postings on the Discussion Board about material from the lectures, ask questions in class, find errors in the lecture notes or the homework problems, or the reading from the book, at least two weeks apart. You can post questions about the homework or exams on the Discussion Board, but they will not count in computing your class participation score. Regular attendence will be taken.
Grading Policy Check your grades at compass2g. Grades will be computed by a weighted average:

Participation   5%
Homework 15%
Midterms
45% (lowest scoring midterm is worth 5%, and the other two are worth 20% each)
Final 35%

Tentative curve: A(+/-): 90-100%; B(+/-): 80-89%; C(+/-): 70-79%; D(+/-): 60-69%. I may slightly adjust the curve later to see it fit. Two exceptions to the numerical grading for people who take all four exams: anyone who scores 95% on the Final gets an A and anyone whose scores 75% on the Final will pass. (Experience shows that these exceptions rarely make a difference.)
Remarks Good habits early in the semester will help you succeed in Math 441:
  • Come to the Office Hour.
  • If you are unavailable during all our scheduled office hours and homework sessions, email me to set up a different time to meet!
  • Come to class prepared: re-work your lecture notes before each last class, to check every step and fill in missing calculations.
  • Actually take notes - don't just take pictures of the board. Write them down by hand - sometimes twice.
  • Work through the proofs and examples on paper.
  • Read the textbook after you re-work the notes - the text helps you see the big picture.
  • Ask questions early and often, about steps you don't understand.
  • Start the HW early, and get help on any problems you can't solve.
  • Don’t do the HW by plugging problems into some website. (You won’t learn the material…)
  • Ask about HW questions on Compass2g.
  • When preparing for exams, summarize the important concepts and methods. Learn the definitions (they tell you what the words mean). Then work some problems.
  • Try to rewrite notes for confusing concepts in different ways to help organize thoughts.
  • After reading a theorem or algorithm, try to summarize the important concepts. This creates a mental framework for the problems you work on.
  • Debrief thoroughly on each exam as soon as you get it back.
  • Learn from mistakes.

Homework 1 (due on 01/31): Homework 1, TeX, Solution
Homework 2 (due on 02/07): Homework 2, TeX, Solution
Homework 3 (due on 02/14): Homework 3, TeX, Solution
Midterm 1 (due on 02/19): Information, Midterm 1, Solution
Homework 4 (due on 02/28): Homework 4, TeX, Solution
Homework 5 (due on 03/06): Homework 5, TeX, Solution
Homework 6 (due on 03/13): Homework 6, TeX, Solution
Midterm 2 (due on 03/28): Information, Midterm 2, Tex, Solution
Homework 7 (due on 04/03): Homework 7, TeX, Solution
Homework 8 (due on 04/10): Homework 8, TeX, Solution
Homework 9 (due on 04/17): Homework 9, TeX, Solution
Midterm 3 (due on 04/22): Information, Midterm 3, Tex, Solution, Quiz
Homework 10 (due on 05/01): Homework 10, TeX, Solution
Homework 11 (due on 05/06): Homework 11, TeX, Solution
Final (due on 05/15): Information, Final, TeX, Solution, Quiz


Week Date Due Content






1 W Jan 22 Some Basic Mathematical Models & Direction Fields; Sec. 1.1;
handout and solution; and calculus review problems and solution.
F Jan 24 Classification of DEs & Integrationg Factors; Sec. 1.3, 2.1; handout and solution.






2 M Jan 27 More First Order Linear ODEs; Sec. 1.2, 2.3; handout and solution.
W Jan 29 Separation of Variables. Sec. 2.2; handout and solution.
F Jan 31 HW1 Applications. Existence and Uniqueness for Linear DE. Sec. 2.2, 2.4;
handout and solution.






3 M Feb 3 Existence and Uniqueness for Nonlinear DE, Bernoulli DE. Sec. 2.4;
handout and solution.
W Feb 5 Autonomous Equations and Population Dynamics. Sec. 2.5;
handout and solution.
F Feb 7 HW2 Autonomous Equations and Second Order Reduction Methods. Sec. 2.5;
handout and solution.






4 M Feb 10 Euler’s method. Sec. 2.7; handout and solution.
W Feb 12 Homogeneous Equations with Constant Coeff. Sec 3.1; handout and solution.
F Feb 14 HW3 Solution of Linear Homogeneous Equations. Sec. 3.2; handout and solution.






5 M Feb 17 Problem Solving. handout and solution.
W Feb 19 Info Midterm 1
F Feb 21 Complex Roots of the Characteristic Equation. Sec. 3.3; handout and solution.






6 M Feb 24 Repeated Roots; Reduction of Order. Sec. 3.4; handout and solution.
W Feb 26 Method of Undetermined Coefficients. Sec 3.5; handout and solution.
F Feb 28 HW4 Variation of Parameters. Sec. 3.6; handout and solution.






7 M Mar 2 Mechanical Vibrations. Sec. 3.7; handout and solution.
W Mar 4 Mechanical and Electrical Vibrations. Sec. 3.7; handout and solution.
F Mar 6 HW5 Forced Vibrations. Sec. 3.8; handout and solution.






8 M Mar 9 Series Solution for Homogeneous Linear DEs. Sec. 5.2; handout and solution.
W Mar 11 Existence & Uniqueness proof for First order DEs. Sec 2.8; handout and solution.
F Mar 13 HW6 Existence & Uniqueness (contd). Sec 2.8; handout and solution.






9 M Mar 16 No class. Spring Break.
W Mar 18 No class. Spring Break.
F Mar 20 No class. Spring Break.






10 M Mar 23 General Theory of n-th Order Linear DE. Sec. 4.1-4.3; handout and solution.
W Mar 25 MT2 Systems of DEs and Infection Model. Sec 7.1; handout and solution, Mathematica.
F Mar 27 Equilibrium Points & Predator Prey Equations. Sec 9.5; handout and solution.






11 M Mar 30 Linear System, Existence and Uniqueness. Sec 7.4; handout and solution.
W Apr 1 Linear Algebra Recap. Sec 7.2-7.3; handout and solution.
F Apr 3 HW7 Constant Coefficient Homogeneous Linear Systems. Sec 7.5; handout and solution.






12 M Apr 6 Complex or Repeated Eigenvalues. Sec 7.6,7.8; handout and solution.
W Apr 8 Phase portraits in 2 dimension. Sec 9.1; handout and solution.
F Apr 10 HW8 Trace–determinant plane. Sec 9.1; handout and solution.






13 M Apr 13 Matrix exponentials. Sec 7.7; handout and solution.
W Apr 15 Matrix exponentials and Putzer's method. Sec 7.7; handout and solution.
F Apr 17 HW9 Linear System of DEs. Sec 7.9; handout and solution.






14 M Apr 20 Midterm Review.
W Apr 22 Info Midterm 3
F Apr 24 Linearization of Autonomous Systems. Sec 9.2; handout and solution.






15 M Apr 27 Linearization, and Long-time Behavior. Sec 9.3; handout and solution.
W Apr 29 Chaos and Strange Attractors. Sec 9.8; handout and solution.
F May 1 HW10 Conserved and Dissipated Energies; handout and solution.






16 M May 4 Conserved and Dissipated Energies (contd.); handout and solution.
W May 6 HW11 Review. handout.






17 F May 15 Info Final exam.