UNIVERSITY OF BRITISH COLUMBIA
MATH 215
JANUARY–APRIL 2010
ELEMENTARY DIFFERENTIAL EQUATIONS I
Purpose: This course is an introduction to ordinary differential equations (ODEs) and models that involve
ODEs in several areas of application including biology, ecology, engineering, and physics. It is expected
that a successful student passing this course will:
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understand the background theory of linear/nonlinear systems of DEs,
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be able to solve analytically a range of first order DEs and linear second order DE’s,
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be able to understand the qualitative behaviour of some nonlinear DEs, through the phase plane and
methods such as linearization, and
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have familiarity with the concept of numerical solution of a DE.
Prerequisite: Calculus II (one of MATH 101/103/105/121, SCIE 001).
Corequisite: Calculus III (one of Math 200/217/226/253/263) and Linear Algebra (one of Math 152/221/223).
Textbook: Elementary differential equations and boundary value problems, 9th ed., by W. E. Boyce and
R. C. DiPrima, published by Wiley. The 8th edition is fine, but homework problems will be assigned from
the 9th edition.
Grading:
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Weekly homework (10%) with the lowest score dropped (the first is due January 20);
Two 50-minute midterm exams (20% each) on Wednesdays February 3 and March 24;
One 150-minute final exam (50%).
Exam marks may be scaled.
Policies:
1. No calculators or notes are allowed in the midterm and final exams.
2. Homework assignments are to be handed in at the beginning of class on Wednesdays. Solutions will
be posted on web. A selection of the problems will be graded. No late homework accepted.
3. Permission to shift the weight of your missed midterms to other exams, or to ignore missed assignments, may be granted only in the following circumstances: (a) prior notice of a valid, documented
absence (e.g. out-of-town varsity athletic commitment with a letter from a coach) on the scheduled
date; or (b) notification to the instructor of absence due to a medical condition with a doctor’s note
or declared on the Student Service Centre (SSC) at www.students.ubc.ca/ssc . Otherwise, a score of
0 will be given for the missed midterms/assignments.
Instructor: Dr. Tai-Peng Tsai, Math 109, phone 604-822-2591, ttsai@math.ubc.ca.
homepage: http://www.math.ubc.ca/∼ttsai/215/
Topics:
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Introduction
1. First order equations
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(Ch. 1-2, 8hr)
Linear and separable equations 2.1–2.2
Applications 2.3
Existence and uniqueness 2.4
Exact equations 2.6
Euler’s method 2.7
2. Second order linear equations
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(Ch. 3, 9hr)
Homogeneous equations with constant coefficients 3.1
Fundamental solutions, Wronskian 3.2
Complex and repeated roots, reduction of order 3.3-3.4
Nonhomogeneous equations 3.5–3.6
Mechanical and electrical vibrations 3.7–3.8
3. Laplace transforms
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(Ch. 6, 5hr)
Definition and examples 6.1
Solution of initial value problems 6.2
Discontinuities 6.3-6.4
Impulses and convolution 6.5-6.6
4. Linear systems
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(Ch. 7,9, 6hr)
Introduction 7.1
Homogeneous systems and fundamental matrices 7.5–7.8
Nonhomogeneous systems 7.9
5. Nonlinear autonomous systems
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(Ch. 9, 5hr)
Phase portrait for 2 × 2 linear systems 9.1
Autonomous systems, steady states and stability 2.5, 9.2
Locally linear systems and applications 2.5, 9.3–9.5
Midterms and review
Total
2
3 hr
36 hr