MATH 128A, SUMMER 2010, HOMEWORK 6 SOLUTION
BENJAMIN JOHNSON
Homework 6: Due Wednesday, July 14 4.1; 2b, 4b 4.2; 9 4.3; 2a, 4a, 6a, 14 section 4.1 2. Use the forward-dierence and backward dierence formulas to determine each missing entry in the following
MATH 128A, SUMMER 2010, HOMEWORK 3 SOLUTION
BENJAMIN JOHNSON
Homework 3: Due Tuesday, July 6 2.3; 2, 12a, 19 2.4; 1b, 6b, 10 2.5; 1d, 6, 9 section 2.3 2. Let f (x) = x3 cos x and p0 = 1. Use Newtons method to nd p2 . Could p0 = 0 be used? solution: We hav
MATH 128A, SUMMER 2010, HOMEWORK 13 SOLUTION
BENJAMIN JOHNSON
Homework 13: Due Monday, August 9 6.5; 5a, 9a 6.6; 1ab 7.1; 1b, 4a section 6.5 5. Factor the following matrices into the LU decomposition using the LU Factorization Algorithm with lii = 1for al
MATH 128A, SUMMER 2010, HOMEWORK 12 SOLUTION
BENJAMIN JOHNSON
Homework 12: Due Wednesday, August 4 6.1; 1a, 3b 6.2; 1a, 3a, 7a 6.3; 1b, 5c, 6c 6.4; 1b, 12a section 6.1 1. For each of the following linear systems, obtain a solution by graphical methods, if
MATH 128A, SUMMER 2010, HOMEWORK 11 SOLUTION
BENJAMIN JOHNSON
Homework 11: Due Monday, August 2 5.9; 4a 5.10; 1, 2a 5.11; 1a section 5.9 4. Use the Runge-Kutta for Systems Algorithm to approximate the solutions of the following higher-order dierential equ
MATH 128A, SUMMER 2010, HOMEWORK 10 SOLUTION
BENJAMIN JOHNSON
Homework 10: Due Wednesday, July 28 5.6; 1c, 14 5.7; 3a 5.8; 3a section 5.6 1. Use all the Adams-Bashforth methods to approximate the solutions to the following initialvalue problems. In each c
MATH 128A, SUMMER 2010, HOMEWORK 9 SOLUTION
BENJAMIN JOHNSON
Homework 9: Due Monday, July 26 5.3; 2a, 5b 5.4; 1b, 5b 5.5; 1d section 5.3 1. [Not Assigned included in the solution for your benet because I did it by accident :)] Use Taylors method of order
MATH 128A, SUMMER 2010, HOMEWORK 8 SOLUTION
BENJAMIN JOHNSON
Homework 8: Due Wednesday, July 21 4.8; 1d, 5d 4.9; 1a, 8 5.1; 4b, 8a 5.2; 2b section 4.8 1 Use Algorithm 4.4 with n = m = 4 to approximate the following double integrals, and compare the result
MATH 128A, SUMMER 2010, HOMEWORK 7 SOLUTION
BENJAMIN JOHNSON
Homework 7: Due Monday, July 19 4.4; 1d, 3d 4.5; 2a 4.6; 1d, 9 4.7; 1f, 8 section 4.4 1. Use the composite Trapezoid rule with the indicated values of n to approximate the following integrals. x
MATH 128A, SUMMER 2010, HOMEWORK 5 SOLUTION
BENJAMIN JOHNSON
Homework 5: Due Monday, July 12 3.2; 4a, 9a, 16 3.3; 2a, 4a 3.4; 4b, 6b, 19 section 3.2 4. Use the Newton forward-dierence formula to construct interpolating polynomials of degree one, two, and
MATH 128A, SUMMER 2010, HOMEWORK 4 SOLUTION
BENJAMIN JOHNSON
Homework 4: Due Wednesday, July 7 2.6; 1c, 4h 3.1; 1c, 3c, 12 section 2.6 1. Find the approximations to within 104 of all the real zeros of the following polynomials using Newtons method. c. f (
The Harmonic Series Diverges Again and Again
Steven J. Kifowit Prairie State College
The harmonic series, 1 1111 = 1 + + + + + , n 2345 n=1 is one of the most celebrated innite series of mathematics. As a counterexample, few series more clearly illustrate