Week

Topics

Reading

Problems

Jan 21

Dynamical systems, mathematical models

Prologue, 1.1

Jan 23

Solutions, direction fields

1.2

Jan 28

Separable ODEs

1.3

Jan 30

Properties of linear ODEs

2.1

Feb 4

Solutions of first order linear ODEs, integrating factors

2.2

Feb 6

Exponential growth and decay models

2.3

Feb 11

First order ODE models: mixing, cooling, harvesting, loans annuities

2.4

Feb 13

Nonlinear models

2.5

Feb 18

Exam 1

Feb 20

Matrices, vectors, geometry

3.1

Feb 25

Systems of linear equations

3.2

Feb 27

Inverses and determinants

3.3, 3.4

Mar 4

Vector spaces

3.5

Mar 6

Basis and dimension

3.6

Mar 11

2nd order ODEs, phase plane, circuits and oscillators.

4.1

Mar 13

2nd order ODEs; real roots

4.2

Mar 18

2nd order ODEs; complex roots

4.3

Mar 20

EXAM 2

Mar 24-28

SPRING BREAK

Apr 1

Non-homogeneous problems and forced oscillations

4.4, 4.5

Apr 3

Linear transformations

5.1, 5.2

Apr 8

Eigenvalues

5.3

Apr 10

Systems of linear ODEs

6.1

Apr 15

Systems with real eigenvalues

6.2

Apr 17

Systems with complex eigenvalues

6.3

Apr 22

Stability and chaos

6.4

Apr 24

EXAM 3

Apr 29

Laplace transforms

8.3

May 1

Laplace transforms

8.4

May 6

Review

May 8

Review

May 13-15

FINAL EXAM