PART 1- Systems of differential equations

1/10 Examples of plots of solution curves (transparencies)

1/12: Non-linear systems: classification, vector fields

1/17:Sketches of vector fields and solution curves on the plane; examples

1/19:solution curves, the local E/U theorem, vector fields on the line

1/22: a Predator/prey system with periodic solutions (Lotka-Volterra)

1/24 Potential motion on the half-line: phase space, conserved quantities, bounded/unbounded motions

1/26 Motion under central force fields: reduction of the phase space

1/29 Motion under central force fields: Kepler's laws

1/31 Review of part I

2/2 Exam 1

6.1 Graphical representation
of systems

1(e)(f) (hand sketches)

2(b)(g) (hand/computer)

4(b)(c) (computer plot of vector fields)
HW1 1/22

6.2 Basic existence
theorems (proofs omitted)

Vector fields on the real line

6.3 A predator/prey system
(example)

4
HW2 1/29

6.5 Mechanical systems with one
degree of freedom

2,3,7,9
HW2 1/29

(Analysis of "bead sliding on wire": not needed)

6.7 Central force fields

1(a)(b)(c) , 4, 5(a)
Exam 1 2/2

Sections 6.4 and 6.6 will not be covered in class (except
for

"central forces" in 6.6), but should be read individually
for completeness.