MATH 215 -- Elementary
Differential Equations I/
MATH 255 -- Ordinary
Differential Equations
Session: 2012W Term 1 (Sept.-Dec. 2012)
NOTE: The Math Club, sells packages for
10$ in the Math Annex one week before the Final Exams.
The packages contain solutions of past Final Exam problems (a few
solutions in the past contained some errors).
- Pre-requisite: Mathematics 101 (integral calculus) or
equivalent, Math 152
(linear algebra) or equivalent
- Co-requisites (crucial): Mathematics 200 or 253 (multivariable
calculus)
- Textbook: Boyce & DiPrima, Elementary
Differential Equations and Boundary Value Problems, 9th Edition
(2008)
SECTIONS:
GRADING: Your final grade
will be based on your Term mark (50%) and common Final Exam
(50%) for all sections. No notes, books or calculators will
be allowed for the Midterms or the Final Exam. Please
note that the median Term mark of your section may be scaled
to match the median Final mark of your section.
Midterms: There will be two Midterms
approximately based on weeks 1-4 and weeks 4-9. See you Section's website for the
exact time and location of your Midterms. The Midterms will worth 30-40% of
your overall grade. See your Section for details.
Homework Assignments and/or
Quizzes: The will be weekly problem sets which
either has to turned in or alternatively short quizzes written in
class. The homeworks/quizzes will worth 10-20% of your overall mark. Please consult your section for
details.
Policies: Missing a midterm or an assignment will normally
result in a mark of zero. Exceptions may be granted in
two cases: prior consent of the instructor or a medical emergency. In the latter case, the
instructor must be notified as soon as possible (preferably before
the test), and presented with a doctor’s note immediately upon the
student’s return to UBC.
COURSE OUTLINE - SUGGESTED
PROBLEMS
I. Introduction
1.
Week
of September 3: what
is a DE, order, linear and nonlinear, solution, general
solution, particular solution, direction field
Reading: Chapter 1.
Suggested Problems: p.7: 1,6 p.15: 7,8,12; p.24: 18, 20.
Due: Sept. 14th
II. First order equations
2.
Week
of September 10: Solutions of basic first order DE:
separable, linear and exact equations
Reading: 2.1, 2.2, 2.6 (no integrating
factors)
Suggested Problems: p.39:.
3(c), 8(c), 16, 30 p.47: 1, 6, 9, 32(b) p.99: 1,
2, 13, 15
3.
Week
of September 17: Modeling
with DE, autonomous equations, existence and uniqueness of
solutions
Reading: 2.4, 2.3, 2.5
Suggested Problems: p.75: 1,3,28
p.59:
2, 4, 16, 18b, 23a-c p.88: 3, 5, 15, 20 a-c, 22
III. Second order linear equations
4.
Week
of September 24: Second
order linear homogeneous equations, fundamental set of
solutions, Wronskian
Reading: 3.1, 3.4.
Suggested Problems: ; p.144:
1, 9, 13, 17, 23, 28; p.155:
1, 2, 12, 13, 26
5.
Week
of October 1: Constant
coefficient linear homogeneous equations (characteristic
equation: simple and double real roots)
Reading: 3.2, 3.3
Homework Problems: p.163:
2, 7, 17, 25 a-c, 35; p.171:
1, 14, 23, 25; Due: Oct.
17th
6.
Week
of October 8: complex
roots, reduction of order
Reading: 3.3-3.4 (continued)
Homework Problems:
7.
Week
of October 15: linear
non-homogeneous equation: undetermined coefficients,
variation of parameters, Midterm I: Oct. 19th Friday
Reading: 3.5, 3.6
Suggested Problems: p.183:
1, 8, 17, 27, p.189:
1, 5, 13, 17, 19
IV. The Laplace transform
8.
Week
of October 22: Applications to spring-mass systems
(no electrical circuits, resonance or beat), Laplace
transform: definition and
examples, initial value problems
Reading: 3.7-8, 6.1, 6.2
Homework Problems: ; p.202:
3, 7, 11, 17, p.215: 5,
12. p.311: 5 a-b, 6, 7, 15; p.320: 3, 10, 12, 23
Due:
Nov 2nd
9.
Week of October 29: step
functions, discontinuous
forcing functions, systems of first order equations: homogeneous case
Reading: 6.3, 6.4, 7.5, (no matrix
exponentials)
Suggested Problems: p.328:
9, 13, 17, 21, 27; p.336: 6a-b, 7a-b, 9,
p.398: 1(a), 4(a), 15, 18, 24, 26, 31
Calculators can be used for graphing!
V. Systems of first order linear
equations
10. Week of November 5: systems of first order equations:repeated and complex eigenvalues,
Reading: 7.6, 7.7, 7.8,
Suggested Problems: p.409:
3, 5, 17, p.420: 3a,
6a-b, 12, p.428: 2, 4, (for parts a-b you just have to
sketch the phase portrait and indicate its type), 6, 8a;
VI. Nonlinear systems
11.
Week
of November 12: Midterm II: Nov. 14th
Reading: 7.9, 9.1 non-homogeneous case: undetermined
coefficients, variation of parameters, classification of linear
systems Conservative systems,
Suggested Problems: p.439 5,
6, 11 (variation of parameters); 1, 3, 7
(undetermined coefficients)
p.494: 2, 3, 6 (only
parts (a) (b) (c) only the phase portraits, don't have to sketch
x_1 versus t), 14, 16
12.
Week
of November 19: fixed points, linear
approximations to non-linear systems,
simple pendulum,
Reading: 9.2, 9.3,
Suggested Problems:
p.506: 2, 4, 6, 21, 24 p.516: 5,
7, 9, 13, 19a,c (find H(x,y))
13.
Week
of November 26:
competing species
equations, Review
Reading: 9.3,
9.4 (in part) Review
Suggested problems: p.531:
2(b-e), 4(b-e), 15c,
Further
information/resources
- Heres is a little applet
which can plot direction
fileds as well as solutions
to ODE's.
- Here you can look at Past
Final Exams.
- The Final
Exam
schedule will be available mid October.
- The last day of withdrawal with a mark W is October 12th.