1. 1 Class #15 of 30 Exam Review Taylor 7.50, 7.8, 7.20, 7.29, ODE’s, 4.4, 4.7, 4.15, 4.19, 4.20 :72

2. 2 Test #2 of 4 Thurs. 10/17/02 – in class Bring an index card 3”x5”. Use both sides. Write anything you want that will help. You may bring your last index card as well. Anything on last 3 homeworks Lagrangian method (most of exam) Line integrals / curls Generalized forces / Lagrange multipliers / constraint forces Tuesday 10/15 – Real-time review / problem session :08

3. 3 Taylor 7-50 A mass m1 rests on a frictionless horizontal table. Attached to it is a string which runs horizontally to the edge of the table, where it passes over a frictionless small pulley and down to where it supports a mass m2. Use as coordinates x and y, the distances of m1 and m2 from the pulley. These satisfy the constraint equations f(x,y)=x+y=const. Write down the two modified Lagrange equations and solve them for x’’, y’’ and the Lagrange multiplier Lambda. Find the tension forces on the two masses. :12 m2m2 m1m1

4. 4 m1m1 m2m2 Atwood’s Machine Lagrange Multiplier Recipe -- CORRECTED :40

5. 5 Class #14 Windup - CORRECTED Exam next Thursday :72

6. 6 ODE Summary :55 Math Physics

7. 7 Class #15 Windup HW due Thursday Tues 3-5, Wed 4-5:30 Bring up to two index cards Midterm grades will be posted on web Only one (hard) HW problem Happy 49ers! :72