Tutoring room is available Monday-Thursday 3-5pm in 149 Henry, and 7-9pm in 113 Gregory. Office hours are Monday 9:30-10:30am in AH 366 and Thursday 4:00-5:00pm in Altgeld 366.
Homework procedures
Homework should be turned in during class on Friday. All homework must be stapled.
I encourage you to work in groups of two or three on the homework
problems. But each person must write up his/her own
solution individually, to turn in.
Late homework will be accepted only if you have made prior arrangement
with me.
I will drop your 2 lowest homework scores, over the semester.
| Homework # 1 |
Hand in the following: Homework 1 Supplement (print this off) Section 1.1: 13, 19, 33 (and solve for v(t)), 35 Section 1.2: 3, 18 (acceleration is nonconstant, so eq. (11) does not apply) |
Due Friday, January 29 |
| Homework # 2 |
Section 1.3: 15 (Do this for arbitrary initial condition y(a)=b)
Section 1.4: 18, 28, 47 Section 1.5: 14, 19, 29, 38 (In #29, first find the derivative of erf(x), before solving the problem. Comment on #38: cascades arise naturally when studying the Great Lakes, or water purification systems.) |
Due Friday, February 5 |
| Homework # 3 |
Section 1.6: 16, 14, 23, 61
Section 2.2: Consider the following two equations: (a) (dx/dt) = x2 - x - 6 (b) (dx/dt) = cos2x For each equation, (i) find all "equilibrium" x-values (also called "critical points", on p. 91), (ii) draw the phase line (vertically!), (iii) determine the stability or instability of all equilibrium x-values, (iv) plot enough solution curves to make the picture clear in all regions of the tx-plane, (v) find the general solution by hand (for example by using the method of partial fractions to integrate, or by looking up integrals from a table). [Check: do your plots in part (iv) basically agree with your solution formula in part (v)?] |
Due Friday, February 12 |
| Homework # 4 |
Section 2.4: 6
Section 2.5: 5 (do both regular and improved Euler method here, compare the results using the table described in the problem) Section 3.1: 5, 19, 37, 48 Section 3.2: 6, 9, 26 (in problems 6 and 9, use the definition of linear dependence and linear independence from class; thus do NOT use Wronskians) Section 3.3: 22, 41 |
Due Monday, February 22 |
| Homework # 5 | Section 3.4: 3 (write 20cm as 0.2m), 6 (this means the pendulum takes 24 hours 2 minutes and 40 seconds at the equator to complete as many cycles as it does during 24 hours at Paris), 14 (also determine whether the system is overdamped, critically damped, or underdamped.) 23 (here m=100, and you should express omega in radians per second), 31 (you can use the binomial series on page 498; it is just the Taylor series of f(x)=(1+x)alpha around x=0) | Due Friday, March 5 |
| Homework # 6 |
Section 3.5: 3, 10, 29, 43, 50
Section 3.6: 5 (undamped and forced not at natural frequency - beating!), 6 (undamped and forced at natural frequency - resonance!), 11 (damped and forced), 24 (undamped and forced at two frequencies, hint: cos3(u)=(3/4)cos(u)+(1/4)cos(3u) by Section 3.5), |
Due Friday, March 12 |
| Homework # 7 | Download and solve these problems. | Due Friday, March 19 |
| Homework # 8 |
Section 9.1: 26 (just sketch, do not try to find Fourier series)
Section 9.2: 12, 17 |
Due Friday, April 9 |
| Homework # 9 |
Section 9.3: 9, 13, 15 [Hint: for 13 and 15 you might want to use results from
Example 1 in Section 9.3]
Section 9.4 #3, 8, 9, 10. For 8,9, you are not required to explicitly find a particular solution. For 10, I want you to evaluate a particular solution. |
Due Friday, April 23 |
| Homework # 10 | Download Homework 10. | Due Monday, May 3 |
