Instructor:
Isabelle Camilier
camilier at Stanford dot edu
Office
hours: Mondays 3:15 pm to 4:15 pm.
Tuesdays 3:15 pm to 4:15 pm. Wednesdays noon to 1pm.
Course Assistant:
Daniel Kim Murphy
dmurphy at math dot stanford dot edu
Room
381 K
Office
hours: Wednesdays at 3:05--5:05.
Starting
Week 2.
Meeting times:
Monday, Tuesday,
Wednesday, Thursday, Friday 2:15 pm to 3:05 pm
Room 380W in the
basement of math building.
The
summer quarter begins Monday June 20 and the last lecture is on Thursday August
11.
Midterm exam:
Tuesday,
July 19, 2011
6:00
to 8:00PM
Room:
380-380Y
Material
for midterm exam: topics covered in class between Monday June 20 and Friday,
July 15.
Practice
material:
Past
midterm exams:
Fall 2009
(except Problem 3, we did not cover exact equations).
Suggested
problems.
Textbook
section 2.3: problems 22,23.
Textbook
section 2.4: problems 7,15,20.
Textbook
section 3.2: problems 21,23.
Textbook
section 3.3: problems 2,13,26.
Textbook
section 3.4: problems 3,8,20.
Textbook
section 3.5: problems 2, 15.
Midterm exam solutions Solutions
Final exam:
Saturday, August 13,
12:15-3:15PM. Room Hewlett 102.
Closed book, closed
notes exam. You may bring a calculator.
Additional office hours. Isabelle Camilier: Monday Tuesday Friday 3:05 pm-5:05 pm, room 383FF
Daniel Murphy : Wednesday Thursday 3:05pm-5:05
pm room 381K
Review
in class Wednesday Thursday
Here is a list of all
the topics we covered in this course. Here
Past
exams: Summer 2010 SOLUTIONS
REVIEW
MATERIAL Existence Uniqueness
Textbook:
The
textbook is Differential Equations : an
Introduction to Modern Methods and Applications by James R. Brannan and
William E. Boyce. I follow this textbook in the lectures and use it for some of
the homeworks.
Assignments:
There
will be 6 homeworks. The lowest score will be dropped
from the average. Homework are due on Thursdays at the
beginning of class.
Homework 1 Solutions : HW1 Solutions
Homework 2 Problem 30: Problem
30 Solutions: HW2 Solutions
Homework 3 Solutions: HW3
Solutions
Homework 4 Problems 15 and 16 from Textbook
: here. Solutions: HW4 Solutions
Homework 5 Solutions: HW5
Solutions
Homework 6 Solutions: HW6
Solutions
Course grade:
Homework:
20%
Midterm:
30%
Final:
50%
Prerequisite:
MATH 51 (or equivalent).
You
should be familiar with differentiation of functions. You should also know the
standard tricks for computing integrals of functions of a single variable
(integration by parts, substitution, etc), and be
able to use them in practice.
You
should be familiar with vectors, matrices, systems of
linear equations, determinants, and inverses of matrices.
Syllabus:
Linear
ordinary differential equations, applications to oscillations, matrix methods
including determinants, eigenvalues and eigenvectors, matrix exponentials,
systems of linear differential equations with constant coefficients, stability
of non-linear systems and phase plane analysis, numerical methods, Laplace
transforms.
Here
is a tentative schedule:
June
20: Introduction to ODEs. Notes
June
21: Classification of ODE (1.4), Direction Fields (1.1), Numerical
approximation: Euler's method (1.3)
Notes
June
22: Numerical approximation:
Euler's method (1.3), Solving (some) differential equations (1.2) Notes
June
23: Solving (some) differential equations, method of integrating factors (1.2)
(continued) Notes
June
24: (continued) Notes
June
27:
Separable equations (Section 2.1)
Notes
June
28: General theory of differential equations (existence/uniqueness) 2.3 Notes
June
29: General theory of differential equations (existence/uniqueness) Interval of
existence (2.3
) Notes
June
30: (2.3) continued. HW1 due Notes
July
1: Autonomous equations (2.5) Notes
July
5: Autonomous equations.
Notes
July
6: Systems of first order linear equations (3.2). Linear
algebra review. Notes
July
7: Complex numbers (Appendix B)
HW2 due Notes
July
8: Real eigenvalues (3.3). Notes
July
11:
Phase diagrams (textbook has bits in 3.3, 3.4, 3.5) Notes
July
12: Continued. Complex eigenvalues
(3.4) Notes
July
13: Complex eigenvalues (3.4) Notes
July
14:
Complex eigenvalues. Repeated eigenvalues (beginning)
HW3 due Notes
July
15: Repeated eigenvalues,
generalized eigenvectors (3.5). More on phase portraits. Notes
July
18: Review for Midterm
July
19:
Midterm exam (during the
evening) Notes
July
20:
Second order linear homogeneous equations with constant
coefficients (4.3), damped linear oscillations in mechanics (4.4). Notes
July 21:
General theory of first
order linear systems
HW4 due Notes
July
22:
General theory of first order linear systems Notes
July
25: (continued) Notes
July
26: (continued) Notes
July
27: (continued) Notes
July
28: HW5 due. Review Notes Notes2
July
29: Non homogenous systems. Notes
August
1: Variation of parameters:
example. Superposition principle for nonhomogeneous equations
(Theorem 4.5.1). Notes 08/01 and 08/02
August
2: Method of undetermined
coefficients (4.5). Laplace
Transform: definition.
August
3: Laplace transform: definition
and basic properties; a formula for the Laplace transform of the derivative of
a function (5.1, 5.2), the inverse Laplace transform (5.3) Solving first order
systems and higher order ODE-s using Laplace transform (5.4); Notes
August
4:
Nonlinear systems (Chapter 7) , existence
and uniqueness theory (3.6) HW6 due Notes
August
5: Nonlinear systems (Chapter 7) Notes
August
8: (continued) Notes Notes2
August
9:
(continued) We cover 7.1, 7.2, 7.3, 7.4.
Notes
August
10: Review
August
11: Review
August
13: Final exam