Math 325 Winter 2022 | Tsogtgerel Gantumur

Course Record

Institution: McGill
Term: Winter 2022
Level: undergraduate
Topics: ODE

Overview

Honours ordinary differential equations course on first and second order equations, Laplace transforms, series solutions, stability, and boundary value problems.

Schedule and Topics

Date	Topic
R 1/6	Introduction. IVP. BVP. Examples. Classifications. Complex exponentials.
T 1/11	Constant coefficient first order linear equations. Uniqueness. Stability. Duhamel's principle.
R 1/13	Constant coefficient second order homogeneous equations. Uniqueness. Fundamental set.
T 1/18	Wronskian. Abel's formula. Stability. Inhomogeneity. Undetermined coefficients.
R 1/20	Variation of parameters. Forced oscillators. Transfer function.
T 1/25	Discontinuous source functions. Laplace transform.
R 1/27	Laplace transform table. Dirac's delta.
T 2/1	Euler-Cauchy equations. First and second order cases. Abel's formula.
R 2/3	Fundamental sets. Reduction of order. Variation of constants. Sturm's separation theorem.
T 2/8	Sturm's comparison theorem. Power series method.
R 2/10	Frobenius method.

Topic List

First order equations
Second order linear equations
Power series solutions and Frobenius method
Phase space, linearization, stability, and perturbation
Second order linear boundary value problems
Calculus of variations, if time permits
Sturm-Liouville theory, if time permits

Books and Related Pages

Books

Garrett Birkhoff and Gian-Carlo Rota, Ordinary differential equations. Wiley.
William E. Boyce, Richard C. DiPrima, and Douglas B. Meade, Elementary differential equations. Wiley.
Dennis G. Zill and Warren S. Wright, Differential equations. Cengage.
William F. Trench, Elementary differential equations. Trinity.

Assignments and Projects

Assignments and Exams

Homework assignments were part of the course record.

Local Materials

Notes

Constcoeff pdf

Archive Note

The recovered schedule records the first part of the term; later rows in the archived page were blank.

Math 325: Winter 2022