Numerical Analysis Homework

Numerical Analysis Homework Assignments

Date Due Reading and Problems

Wed., Jan. 18 Do the following from Section 1.2, page 28, for study problems (not to be turned in). Since some of you don't have books yet I'm including the problem.

#1(a),(b),(c)
Compute the absolute and relative error in approximations of p by p*.
(a) p = pi and p* = 22/7; (b) p = pi and p* = 3.1416; (c) p = e and p*=2.718
#2(a), (c)
Find the largest interval in which p* must lie to approximate p with relative error at most 10^-4 for each value of p.
(a) p = pi; (c) p = square root of 2
#3 (a), (c)
Suppose p* must approximate p with relative error at most 10^-3. Find the largest interval in which p* must lie for each value of p.
(a) p = 150; (c) p = 1500

Fri., Jan. 20 Study/Practice Problems: pages 28 - 30 #4(c),(d), 5(e), (g), 17

Mon. Jan. 23 Study/Practice Problems: pages 29 - 30 #13(a),(d), #21

Wed., Jan. 25 Study/Practice Problems: Pages 54-55 #1, 5(b), 9

Fri., Jan. 27 Hand in:Pages 29-31 #17 (be sure to explain why the method you say is best really is), 18 (the "why" question in part (c) is important!), 24; page 39 #1(a) ("why" again!); pages 54-55 #6(a), 12, 14, 16; pages 64-65 #6 (do the following variation): - Find two different functions g such that a fixed point of g is a root of the equation given in #6. Try to pick at least one function that will probably converge (see #5 for example or the examples on page 61 or our example in class as a model for functions that may be a good choice). Perform 4 iterations of the fixed point algorithm for each of your functions starting at p0 = 1.

Wed., Feb. 1 Page 75 #1, 2, 5(a) (Find the number of iterations needed - to do this start by finding the k in fixed point iteration.)

Fri., Feb. 3

page 65 #11

Write a program for the false position method (just modify the secant method program). Click here to save these programs:
Secant1.java
Newton1.java
Use your false position program and the secant program on page 75 #4

Mon., Feb. 6 page 86 #6, 7, 8, 10

Wed., Feb. 8 Complete the Root Finding Lab

Mon., Feb. 13 Hand-in the problems at the end of Wednesday's lab (this includes both labs).

Mon., Feb. 27 Section 7.1 pages 441-442 #1, 4, 5;
Section 7.5 #1 a,d, 3 a, d

Wed., Mar. 14 Section 7.3 #1(a), 3(a)

Fri., Mar. 16 Section 7.3 #9(a), #11(a),(b), #12(a),(b)Section 9.1 #3

Wed., Mar. 28 Section 3.1 #1ab, 3ab, 5c, 7c

Fri. Mar. 30 Section 3.3, #4a, 7a, 10, 11, 16

Mon., Apr. 2 Section 3.5, #1, 3c, 5c, 7c

Wed., Apr. 4 Hand in the homework (listed above) for Sections 3.1, 3.3, and 3.5 plus:
Section 4.1, #1, 3, 5a, 7a, 18a, 27
For #27 you can use the program described here.

Mon., Apr. 9 Section 4.3, page 202, #1e, 3e, 5e, 7e, 9e

Wed., Apr. 11 Section 4.3, page 202, #13, 14, 16, 18

Fri., Apr. 13 Section 4.4, pages 210-211, #1a, 3a, 5a, 13.

Fri. Apr. 20 Integration Assignment

Date Due	Reading and Problems
Wed., Jan. 18	Do the following from Section 1.2, page 28, for study problems (not to be turned in). Since some of you don't have books yet I'm including the problem. #1(a),(b),(c) Compute the absolute and relative error in approximations of p by p. (a) p = pi and p = 22/7; (b) p = pi and p* = 3.1416; (c) p = e and p=2.718 #2(a), (c) Find the largest interval in which p must lie to approximate p with relative error at most 10^-4 for each value of p. (a) p = pi; (c) p = square root of 2 #3 (a), (c) Suppose p* must approximate p with relative error at most 10^-3. Find the largest interval in which p* must lie for each value of p. (a) p = 150; (c) p = 1500
Fri., Jan. 20	Study/Practice Problems: pages 28 - 30 #4(c),(d), 5(e), (g), 17
Mon. Jan. 23	Study/Practice Problems: pages 29 - 30 #13(a),(d), #21
Wed., Jan. 25	Study/Practice Problems: Pages 54-55 #1, 5(b), 9
Fri., Jan. 27	Hand in:Pages 29-31 #17 (be sure to explain why the method you say is best really is), 18 (the "why" question in part (c) is important!), 24; page 39 #1(a) ("why" again!); pages 54-55 #6(a), 12, 14, 16; pages 64-65 #6 (do the following variation): - Find two different functions g such that a fixed point of g is a root of the equation given in #6. Try to pick at least one function that will probably converge (see #5 for example or the examples on page 61 or our example in class as a model for functions that may be a good choice). Perform 4 iterations of the fixed point algorithm for each of your functions starting at p0 = 1.
Wed., Feb. 1	Page 75 #1, 2, 5(a) (Find the number of iterations needed - to do this start by finding the k in fixed point iteration.)
Fri., Feb. 3	page 65 #11 Write a program for the false position method (just modify the secant method program). Click here to save these programs: Secant1.java Newton1.java Use your false position program and the secant program on page 75 #4
Mon., Feb. 6	page 86 #6, 7, 8, 10
Wed., Feb. 8	Complete the Root Finding Lab
Mon., Feb. 13	Hand-in the problems at the end of Wednesday's lab (this includes both labs).
Mon., Feb. 27	Section 7.1 pages 441-442 #1, 4, 5; Section 7.5 #1 a,d, 3 a, d
Wed., Mar. 14	Section 7.3 #1(a), 3(a)
Fri., Mar. 16	Section 7.3 #9(a), #11(a),(b), #12(a),(b)Section 9.1 #3
Wed., Mar. 28	Section 3.1 #1ab, 3ab, 5c, 7c
Fri. Mar. 30	Section 3.3, #4a, 7a, 10, 11, 16
Mon., Apr. 2	Section 3.5, #1, 3c, 5c, 7c
Wed., Apr. 4	Hand in the homework (listed above) for Sections 3.1, 3.3, and 3.5 plus: Section 4.1, #1, 3, 5a, 7a, 18a, 27 For #27 you can use the program described here.
Mon., Apr. 9	Section 4.3, page 202, #1e, 3e, 5e, 7e, 9e
Wed., Apr. 11	Section 4.3, page 202, #13, 14, 16, 18
Fri., Apr. 13	Section 4.4, pages 210-211, #1a, 3a, 5a, 13.
Fri. Apr. 20	Integration Assignment