Homework for Math 3020, Spring 2008

Prof. Anna Vainchtein


Due date
Homework
Friday, January. 18 HW1: p.32, #5, 8, 14, 15, 18
Friday, February 8 HW2: Click here for this assignment
Friday, February 22 HW3: Ch. 2:  #12, 13, 14, 18, 22 and Ch. 3   #3, 5, 12, 15, 17
Friday, March 7 HW4: Ch. 4, #2, 3, 5, 8, 11 (in the last problem, just derive the equation for geodesics - don't need to show that a surface of revolution is a Liouville surface).
Friday,  March 28 HW5: Ch. 5, #7, 8, 10, 11, 12, 13 (explain!)
Friday, April 11 HW6: Ch. 6, #1, 3, 5, 7, 8. Hint: In #1, to solve the Euler-Lagrange equation, use substitution x=exp(z); then you should obtain a linear ODE with const coefficients for y(z).
Monday, April 21 HW7: 

1) Ch. 7, #1, 2.

2) Use the Fourier method (separation of variables) to solve the problem of small vibrations of a string with free ends (ux vanishes at the ends). Your final answer should be in the form of a sum, each term of which contains two unknown constants, which could be determined from initial conditions.

3) Ch. 8, #2, 4, 5.