MAT244 INTRODUCTION TO ORDINARY DIFFERENTIAL
I. M. SIGAL
Course description: First order ordinary diﬀerential equations: integrating factors, sep-
arable equations, homogeneous equations, autonomous equations, modelling. Higher order
equations: Constant coeﬃcient equations, reduction of order, Wronskian, method of un-
determined coeﬃcients, variation of parameters. Solutions by series and integrals. First
order linear systems, fundamental matrices. Non-linear equations, phase plane, stability.
Applications in life and physical sciences and economics. Existence and uniqueness theorem.
Syllabus (could be adjusted later on):
Week 1: First Order Diﬀerential Equations (Sections 2.1, 2.2, 2.5)
Week 2: Second Order Linear Equations (Sections 3.1-3.2)
Week 3: Second Order Linear Equations (Sections 3.5, 3.6)
Week 4: Series Solutions of Second Order Linear Equations (Sects 5.1, 5.2, 5.4)
Weeks 5-6: Systems of First Order Linear Equations (Sections 7.1-7.7, 7.9)
Week 7: Numerical Methods (Sections 8.1, 8.3, 8.6)
Weeks 8-11: Nonlinear Diﬀerential Equations and Stability (Sections 9.1-9.8)
[BDiP] William E. Boyce, Richard C. DiPrima, Douglas B. Meade, Elementary Diﬀerential
Equations and Boundary Value Problems, Enhanced eText, 11th Edition. (Also possible
to use: William E. Boyce, Richard C. DiPrima, Elementary Diﬀerential Equations and
Boundary Value Problems, 10th Edition)
We will have ten quizzes, midterm test and ﬁnal test.
Quizzes: January 17, 24, 31, Feb 7, 14, March 7, 14, 21, 28, April 3 (in class on Thursdays)
Midterm: February 27, 5-7pm (place to be announced).
Quizzes and midterm and ﬁnal exams will be on the material covered in the lectures. All
the problems for the quizzes and midterm exam most of the problems for the ﬁnal test will
be taken (with possibly minor modiﬁcations) from the homework. The problems in quizzes
and exams will involve proofs.
Breakup of the grade
Quizzes/ midterm/ ﬁnal test 42%/30%/28%.
There will be no make-ups for missed quizzes and missed midterm. The 3 lowest (including
missed) quizzes will be discarded. If more than three quizzes or the midterm are missed,
then the corresponding weight would be placed on the remaining quizzes and ﬁnal exam.
Date: January 10, 2019.