Math 4242, Fall 2018

Homework 9

Due Friday, November 30

The problem set is due at the beginning of class on Friday. Remember that a full answer to a True/False exercise is not merely a T or F, but must include a detailed explanation of the reason, e.g., a proof, or a counterexample, or a reference to a result in the text, etc.

Reading: Text: Sections 6.1 (from p. 309), 6.2 (ignoring batteries and power within Electrical-Mechanical Correspondence), 8.2 (through p. 417)

Assigned Problems:

Section 6.1: 13(c), 16(b,c), 18, 20

Hint and notes for 6.1.16(b,c): The problem should have been worded as "Describe mass-spring chains that give rise to..." To solve the equation Ku = f, you do not need to find the inverse of K. You may just use Gaussian elimination to find u, as in 5.2, see Example 5.3. Note also that the answer for the equilibrium configuration in Exercise 6.1.16(c) in the Students' Solutions Manual is incorrect.

Hint for 6.1.18: Use the equation the equilibrium solution u* satisfies.

Hint for 6.1.20: See my correction to the wording of 6.1.16 above...

Section 6.2: 2, 4, 13(ii)

Hint for 6.2.2: As in computations on page 316, the equation Ku = f in 6.2.2(c) may just be solved using Gaussian elimination. The answer given for 6.2.2(e) in the Students' Solutions Manual is actually an answer to 6.2.2(d).

Section 8.2: 1(d,f), 7(c), 14, 21, 22

Challenge Problems (for digging deeper into Linear Algebra -- not to be turned in):

Section 6.2: 18, 19
Section 8.2: 24, 32, 35

Last modified: (2018-11-27 14:33:48 CST)