Homework 1: Due Friday, September 6
1. Burden, Faires & Burden, Section 1.1: #10
2. Burden, Faires & Burden, Section 1.2: #2c, 4a, 5a (i,iii, iv(iii))
3. (a) Find two distinct 3-decimal digit floats in [1,100], say a and b, with a less than b, so that fl( fl(a+b)/2 ) is not in the interval [a,b].
(b) Now with these values of a and b, find fl( a + fl( fl(b-a)/2 ) ).4. Let x be a (normal) float such that x+x overflows. What values can fl(x+x-x-x) take, depending on the order of operations?
Homework 2: Due Friday, September 20
1. Burden, Faires, Section 2.1: #3c
2. Burden, Faires & Burden, Section 2.3: #1, 3a, 13bc (feel free to write code to help with 13, but do 1 and 3a by hand)
3. Burden, Faires & Burden, Section 2.4: #6, for MATH 53803 students, also do 2.4 #7a
4. Let f(x) = x^3 - 4.999x^2 + 6.996x - 2.997. Find the absolute condition number for the problem "find z such that f(z)=0" with z being the root of f nearest x = 1.01.
Homework 3: Due Friday, October 11
1. Burden, Faires & Burden, Section 3.1: #1b, 3b, 21, 17 (Hint for 3b: see example 3, section 3.1 (but our x is fixed, so you don't have to maximize l(x), you just use l(0.45)); hint for 17: see Example 4 in 3.1)
2. Given the (pairwise distinct) nodes x_i, i=0:n, show that Ln,0(x)+ Ln,1(x)+...+ Ln,n(x) = 1 for all x.
Homework 4: Due Friday, November 1
2. Burden, Faires & Burden, Section 3.5: #13
1. Burden, Faires & Burden, Section 4.1: #6b
2. Burden, Faires & Burden, Section 4.3: #5d, 22
3. Burden, Faires & Burden, Section 4.4: #3f
Homework 5: Due Wednesday, December 4
1. Burden, Faires & Burden, Section 5.2, #1c
2. Burden, Faires & Burden, Section 5.3, #1c
3. Using the identity dy/dt = f(t,y), give an expression for d^2/dt^2 { f(t,y(t)) } (for arbitrary, but smooth f) in terms of f and its partial derivatives wrt t and y.
4. Burden, Faires & Burden, Section 5.4, #1c
5. Burden, Faires & Burden, Section 5.6, #1c (explicit 2-step only)