Math 441: Differential Equations (Spring 2020)  Sec X13/X14
Instructor  Partha Dey 

Contact  By and from "@illinois.edu" account. 
Videos  Subscribe to go.illinois.edu/math441_ch 
Q&A  MWF 9:009:50am through Zoom Meetings. 
HW upload  Upload PDF files through Compass2g. 
Website  https://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 firstorder ODEs by analytical, graphical and numerical methods;
 existence, uniqueness and continuity for firstorder ODEs;
 linear secondorder ODEs, in particular, with constant coefficients;
 undetermined coefficients and variation of parameters;
 sinusoidal and exponential signals: oscillation, damping, resonance;
 matrix and firstorder linear systems: eigenvalues and eigenvectors; phase plane diagrams and
 Stability and Liapunov's Method.
Instructor  Partha Dey 

Contact  By and from "@illinois.edu" account. 
Class  MWF 12:0012:50pm in 241 Altgeld Hall 
Website  https://faculty.math.illinois.edu/~psdey/Math441SP20.html. Discussion Board and exam/hw scores are in the Compass2g site. 
Office Hrs  Wednesdays 2:0003:30pm or by appointment made via email 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 

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 inclass 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 8:0011:00 a.m., Friday, May 15 in 241 AH.  
Makeup exam  Makeup 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.  
Participation  A 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:
Tentative curve: A(+/): 90100%; B(+/): 8089%; C(+/): 7079%; D(+/): 6069%. 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:

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, Solution 
Homework 10 (due on 05/01):  Homework 10, TeX, Solution 
Homework 11 (due on 05/06):  Homework 11, TeX, Solution 
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 nth Order Linear DE. Sec. 4.14.3; handout and solution.  
W  Mar 25  MT2  Systems of DEs and Infection Model; handout and solution, Mathematica Code.  
F  Mar 27  Equilibrium Points & Predator Prey Equations; handout and solution.  
11  M  Mar 30  Linear System, Existence and Uniqueness; handout and solution.  
W  Apr 1  Linear Algebra Recap; handout and solution.  
F  Apr 3  HW7  Linear Independence and General Solutions; handout and solution.  
12  M  Apr 6  Constant Coefficient Homogeneous Linear Systems; handout and solution.  
W  Apr 8  Distinct Real or Complex Eigenvalues; handout and solution.  
F  Apr 10  HW8  Phase portraits in 2 dimension; handout and solution.  
13  M  Apr 13  Trace–determinant plane; handout and solution.  
W  Apr 15  Matrix exponentials; handout and solution.  
F  Apr 17  HW9  Matrix exponentials and Putzer's method; handout and solution.  
14  M  Apr 20  Problem Solving. handout and solution.  
W  Apr 22  Info  Midterm 3  
F  Apr 24  Linearization of Autonomous Systems; handout and solution.  
15  M  Apr 27  Linearization, and Longtime Behavior; handout and solution.  
W  Apr 29  Chaos and Strange Attractors; 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 and solution.  
17  F  May 15  Final exam 8:0011:00am  