MAT244H1

Introduction to Ordinary Differential Equations

University of Toronto St. George

First order ordinary differential equations: Direction fields, integrating factors, separable equations, homogeneous equations, exact equations, autonomous equations, modeling. Existence and uniqueness theorem. Higher order equations: Constant coefficient equations, reduction of order, Wronskian, method of undetermined 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.
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Israel Michael Sigal

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Israel Michael Sigal
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MAT244H1
Israel Michael Sigal

MAT244H1 Syllabus for Israel Michael Sigal — Winter 2019

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MAT244 INTRODUCTION TO ORDINARY DIFFERENTIAL
EQUATIONS
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)
Textbook:
[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)
Tests
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.
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