Math 343 Fall 99
Homework Assignments
Homework 01: due Wed. Sept. 1 Read Section 1.1 and 1.2 Page 48, #5, 6
Homework 02: due wed. Sept. 8 Page 48: #8, 12, 14 Page 57: #1, 2
Homework 03 Page 70, #2, 3, 6
Homework 04, due Monday, 09/20/99 Page 72, #8: set up the linear programming problem and solve by Maple Page 96, #13, #14, solve the linear systems using "gaussjord" command in Maple
Homework 05, due Wed. 09/22 Using the finite-difference method, find the simplified general i-th equation of the boundary value problem of ordinary differential equation y"-y'/x-3y/(x^2)=ln(x)/x - 1, x in [1, 2] y(1)=y(2)=0
Homework 06, due Mon. 09/27 Solve the BVP in Homework 05 with Maple using the finite-difference method and plot the solution (Note: There is no apparent exact solution to compare with)
Homework 07, due Mon. 09/27 Page 366: Use the data corresponding to #6-10, formulate a linear system Ax=b where the matrix has more rows than columns. Then formulate the normal equation transpose(A)Ax=transpose(A)b
Homework 08, due Mon. 10/04/99 Find the cubic polynomial y=a*x^3+b*x^2+c*x+d that is the least squares fit to the data: x 1 2 3 4 5 6 -------------------------------------------- y -2.2 -1.8 0.4 3 1.2 2.3 Requirements: (1) construct a linear system Ax=b with more equations than variables (2) derive the normal equation from (1) (3) find the cubic polynomial (4) using Maple, plot the data points and the cubic polynomial together to visualize the results
Homework 09, due Mon. 10/04/99 P301, Section 6.1: #2, 6, 9(a,b), 10(a,b)
Homework 10, due Mon. 10/11/99 P308, #2, #4
Homework 11, due Mon. 10/11/99 P308, for matrices in problem #2 and #4, find the probability eigenvectors.
Homework 12, due Wed. 10/20/99 P320, #8
Homework 13, due Mon. 10/25/99 P321, #16
Homework 14, due Mon. 11/01/99 Find the closed form solution to the sequence: G[0]=1, G[1]=2, G[k]=0.5*(G[k-1]+G[k-2]), for k=2,3,... Use your solution to find the limit of G[k] when k goes to infinity
Homework 15, due Mon. 11/01/99 Solve system of ODE: x' = x + 2y + 3z y' = y z' =2x + y + 2z
Homework 16, due Mon. 11/08/99 Find the substitutions and the standard forms of (1) 9*x[1]^2+ x[2]^2+6*x[1]*x[2]-10*sqrt(10)*x[1]+10*sqrt(10)*x[2]+90=0 (2) 5*x[1]^2+5*x[2]^2-6*x[1]*x[2]-30*sqrt(2)*x[1]+18*sqrt(2)*x[2]+82=0
Homework 17, due Mon. 11/08/99 For the quadratic form 5*x[1]^2+12*x[1]*x[2]-12*sqrt(13)*x[1],-36=0 (1) find the substitutions and the standard form; (2) use the substitutions to plot the graph with Maple
Homework 18, due Mon. 11/15/99 Identify the standard quadratic form of (1) -x[1]^2-x[2]^2-x[3]^2+4*x[1]*x[2]+4*x[1]*x[3]+4*x[2]*x[3]=3; (2) 2*x[1]*x[3]-2*x[1]-4*x[2]-4*x[3]+8=0
Homework 19, due Mon. 11/15/99 Problem 1: Section 7.1, #4 Problem 2: Let u, v, w be n-vectors with u orthogonal to both v and w. Prove that u is orthogonal to every linear combination of v and w. (A linear combination of v and w can be written as a*v+b*w for real numbers a and b)
Homework 20, due Mon. 11/22/99 Section 7.1, #8, 9, 10, extra credit for #11
Homework 21, due Mon. 11/22/99 Section 7.2, #2, 3, 5
Homework 22, due Mon. 11/29/99 Problem 1. Find an orthonomal basis for the subspace V of R^4 consisting of all vectors of the form (a, a+b, c, b+c) Problem 2. Find an orthonomal basis for the subspace W of R^4 consisiting of all vectors (a,b,c,d) such that a-b-2c+d=0
Homework 23, due Mon 12/06/99 1. Use the matrix on page 414 #9 to perform QR decomposition in detail 2. Use the QR decomposition you got and the vector b in problem 11 to solve Ax=b
Homework 24, due Mon 12/06/99 P414, #10, 12
Homework 25, due Mon 12/13/99 For A = matrix(3,3,[1,2,3,4,5,6,2,0,2]) and b = vector([1,1,1]), use Maple to get SVD of A and solve Ax=b with the decomposition.