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.