Instructor:
Isabelle Camilier
camilier at stanford dot edu
Office hours:
Tuesdays 3:05-5:05 pm, Thursdays 3:05-4:05 pm.
Room 383FF.
Xiaodong Li : xdli1985 at stanford dot edu
Office hours: Mondays 3-5 pm. Room 380-380 T (math building).
Meeting times:
Monday, Tuesday,
Wednesday, Thursday, Friday 2:15 pm to 3:05 pm
Room McCullough 115
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 5 homeworks. The lowest score will be dropped
from the average. Homework are due on Wednesdays at the
beginning of class.
Course grade:
Homework:
20%
Midterm 1:
25%
Midterm 2: 25%
Final:
30%
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 25: Introduction to ODEs, Classification of ODE (1.4).
June 26: Direction Fields (1.1), Numerical approximation: Euler's method (1.3)
June 27: Numerical approximation: Euler's method (1.3), Solving (some) differential equations (1.2)
June 28: Solving (some) differential equations, method of integrating factors (1.2) (continued)
June 29: (continued)
July 2: Separable equations (Section 2.1)
July 3: General theory of differential equations (existence/uniqueness) 2.3
July 5: General theory of differential equations (existence/uniqueness) Interval of existence (2.3 ) HW1 due
July 6: (2.3) continued.
July 9: Autonomous equations (2.5)
Juliy 10: Autonomous equations
July
11: Systems of first order linear equations (3.2). Linear
algebra review.
July 12: Complex numbers (Appendix B)
July 13: Real eigenvalues (3.3).
July 16: Phase diagrams (textbook has bits in 3.3, 3.4, 3.5)
July 17: Midterm exam (during the evening)
July 18: Phase diagrams
July 19: Complex eigenvalues(3.4).
July 20Complex eigenvalues(3.4)
July 23: Repeated eigenvalues.
July 24: Repeated eigenvalues, generalized eigenvectors (3.5). More on phase portraits.
July 25: Second order linear homogeneous equations with constant coefficients (4.3), damped linear oscillations in mechanics (4.4). HW3 due.
July 26: General theory of first order linear systems
July 27: General theory of first order linear systems
July 30:General theory of first order linear systems(continued)
July 31: (continued)
August
1: Laplace
Transform: definition.
August 2: Midterm 2. 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).
August 3: Non homogenous systems.
August 7:Variation of parameters:
example. Superposition principle for nonhomogeneous equations
(Theorem 4.5.1).
August 8: Method of undetermined coefficients (4.5). HW4 due
August 9: Nonlinear systems (Chapter 7) , existence and uniqueness theory (3.6)
August 10: Nonlinear systems (Chapter 7)
August 13: Nonlinear systems (continued) HW5 due
August 14: (continued) We cover 7.1, 7.2, 7.3, 7.4.
August
15: Review
August 16: Last day of classes. Final exam due.