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math581_hw4

Course: MATH 581, Fall 2009
School: CSU Northridge
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581 Numerical MATH Methods for Linear Systems Spring 2008 Homework 4 Due: Tue. April 15, 2008 1. Write matlab code that implements algorithms 20.1 and 21.1. Find the LU decomposition of the matrices A= 0 1 1 1 B= 1020 1 1 1 and the matrix example in 20.3. Is the LU factorization of B by algorithm 20.1 correct? 2. Write matlab code that implements algorithm 23.1. Use the code to nd the Cholesky factorization of...

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581 Numerical MATH Methods for Linear Systems Spring 2008 Homework 4 Due: Tue. April 15, 2008 1. Write matlab code that implements algorithms 20.1 and 21.1. Find the LU decomposition of the matrices A= 0 1 1 1 B= 1020 1 1 1 and the matrix example in 20.3. Is the LU factorization of B by algorithm 20.1 correct? 2. Write matlab code that implements algorithm 23.1. Use the code to nd ...

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CSU Northridge - MATH - 715473
MATH 581Numerical Methods for Linear SystemsSpring 2008Homework 4 Due: Tue. April 15, 2008 1. Write matlab code that implements algorithms 20.1 and 21.1. Find the LU decomposition of the matrices A= 0 1 1 1 B= 1020 1 1 1and the matrix in exam
CSU Northridge - MATH - 250
MATH 250Calculus IIISpring 2008Homework 8 Due: Thurs. April. 17, 2008 Section 13.1, pg. 679: 1, 5, 9, 17, 21, 23, 29. Section 13.2, pg. 683: 1, 5, 11, 15, 17, 19, 27, 33, 34, 35. Section 13.3, pg. 689: 3, 9, 13, 15, 31, 33, 37, 41.
CSU Northridge - MATH - 715473
MATH 250Calculus IIISpring 2008Homework 8 Due: Thurs. April. 17, 2008 Section 13.1, pg. 679: 1, 5, 9, 17, 21, 23, 29. Section 13.2, pg. 683: 1, 5, 11, 15, 17, 19, 27, 33, 34, 35. Section 13.3, pg. 689: 3, 9, 13, 15, 31, 33, 37, 41.
CSU Northridge - MATH - 250
MATH 250Calculus IIISpring 2008Homework 9 Due: Thurs. April. 24, 2008 Section 13.4, pg. 695: 1, 3, 13, 19, 21, 33. Section 13.5, pg. 699: 3, 5, 7, 19. Section 13.7, pg. 711: 1, 3, 9, 11, 17.
CSU Northridge - MATH - 715473
MATH 250Calculus IIISpring 2008Homework 9 Due: Thurs. April. 24, 2008 Section 13.4, pg. 695: 1, 3, 13, 19, 21, 33. Section 13.5, pg. 699: 3, 5, 7, 19. Section 13.7, pg. 711: 1, 3, 9, 11, 17.
CSU Northridge - MATH - 250
MATH 250Calculus IIISpring 2008Homework 4 Due: Thurs. Feb. 28, 2008 Bzier Curves e Bzier Curves are often employed in computer aided design. These parametric curves are e dened by x(t) = x0 (1 t)3 + 3x1 t(1 t)2 + 3x2 t2 (1 t) + x3 t3 y(t) =
CSU Northridge - MATH - 715473
MATH 250Calculus IIISpring 2008Homework 4 Due: Thurs. Feb. 28, 2008 Bzier Curves e Bzier Curves are often employed in computer aided design. These parametric curves are e dened by x(t) = x0 (1 t)3 + 3x1 t(1 t)2 + 3x2 t2 (1 t) + x3 t3 y(t) =
CSU Northridge - MATH - 250
MATH 250Calculus IIISpring 2008Homework 11 Due: Thurs. May 15, 2008 Section 14.1, pg. 735: 1, 3, 7, 9, 13, 17, 21. Section 14.2, pg. 740: 1, 3, 5, 7, 17, 19, 21. Section 14.3, pg. 747: 1, 3, 5, 7, 13, 15, 21, 26.
CSU Northridge - MATH - 715473
MATH 250Calculus IIISpring 2008Homework 11 Due: Thurs. May 15, 2008 Section 14.1, pg. 735: 1, 3, 7, 9, 13, 17, 21. Section 14.2, pg. 740: 1, 3, 5, 7, 17, 19, 21. Section 14.3, pg. 747: 1, 3, 5, 7, 13, 15, 21, 26.
CSU Northridge - MATH - 250
MATH 250Calculus IIISpring 2008Homework 3 Due: Thurs. Feb. 14, 2008 Directions: For problems with multiple parts, do parts (a) and (c) only Section 11.6, pg. 592: Every odd. Section 11.7, pg. 601: 1, 5, 9, 13, 27, 33, 35, 43, 57, 61, 77.
CSU Northridge - MATH - 715473
MATH 250Calculus IIISpring 2008Homework 3 Due: Thurs. Feb. 14, 2008 Directions: For problems with multiple parts, do parts (a) and (c) only Section 11.6, pg. 592: Every odd. Section 11.7, pg. 601: 1, 5, 9, 13, 27, 33, 35, 43, 57, 61, 77.
CSU Northridge - MATH - 150
MATH 150ACalculus IFall 2007Homework 5 Due: Tue. Oct. 9, 2007 Section 3.6, pg. 169: 1, 3, 11, 15, 17, 19, 21, 29, 35, 51. Section 3.7, READ the examples in the section carefully, make sure you understand them (ask me if anything is unclear), th
CSU Northridge - MATH - 715473
MATH 150ACalculus IFall 2007Homework 5 Due: Tue. Oct. 9, 2007 Section 3.6, pg. 169: 1, 3, 11, 15, 17, 19, 21, 29, 35, 51. Section 3.7, READ the examples in the section carefully, make sure you understand them (ask me if anything is unclear), th
CSU Northridge - MATH - 255
MATH 255Applied Honors Calculus IIIWinter 2005Homework 11 Due: Wed. Apr. 20, 2005 Section 17.7, pg. 1155: 5, 9, 11, 13, 19, 24, 33. Section 17.8, pg. 1161: 3, 7, 13, 15, 17, 19. Section 17.9, pg. 1168: 3, 7, 19, 25, 27.
CSU Northridge - MATH - 715473
MATH 255Applied Honors Calculus IIIWinter 2005Homework 11 Due: Wed. Apr. 20, 2005 Section 17.7, pg. 1155: 5, 9, 11, 13, 19, 24, 33. Section 17.8, pg. 1161: 3, 7, 13, 15, 17, 19. Section 17.9, pg. 1168: 3, 7, 19, 25, 27.
CSU Northridge - MATH - 255
MATH 255Applied Honors Calculus IIIWinter 2005Homework 10 Due: Wed. Apr. 13, 2005 Section Section Section Section 17.3, 17.4, 17.5, 17.6, pg. pg. pg. pg. 1117: 1125: 1132: 1142: 3, 3, 3, 3, 9, 11, 19, 29, 33. 9, 13, 21, 25, 29. 12, 13, 31. 17,
CSU Northridge - MATH - 715473
MATH 255Applied Honors Calculus IIIWinter 2005Homework 10 Due: Wed. Apr. 13, 2005 Section Section Section Section 17.3, 17.4, 17.5, 17.6, pg. pg. pg. pg. 1117: 1125: 1132: 1142: 3, 3, 3, 3, 9, 11, 19, 29, 33. 9, 13, 21, 25, 29. 12, 13, 31. 17,
CSU Northridge - MATH - 150
MATH 150ACalculus IFall 2007Homework 1 Due: Tue. Sept. 4, 2007 Section 2.2, pg. 74: 5, 7, 9, 13, 15, 29, 40. Section 2.3, pg. 84: 2 (b), (e), and (f), 5, 11, 23, 25, 29, 37, 43.
CSU Northridge - MATH - 715473
MATH 150ACalculus IFall 2007Homework 1 Due: Tue. Sept. 4, 2007 Section 2.2, pg. 74: 5, 7, 9, 13, 15, 29, 40. Section 2.3, pg. 84: 2 (b), (e), and (f), 5, 11, 23, 25, 29, 37, 43.
CSU Northridge - MATH - 150
MATH 150ACalculus IFall 2007Homework 7 Due: Tue. Oct. 23, 2007 For each of the functions below: I. nd its domain and range II. nd its x- and y-axis intercepts III. determine whether the graph is symmetric with respect to the y-axis or the origi
CSU Northridge - MATH - 715473
MATH 150ACalculus IFall 2007Homework 7 Due: Tue. Oct. 23, 2007 For each of the functions below: I. nd its domain and range II. nd its x- and y-axis intercepts III. determine whether the graph is symmetric with respect to the y-axis or the origi
CSU Northridge - MATH - 150
MATH 150ACalculus IFall 2007Homework 4 Due: Tue. Sept. 25, 2007 Section 3.3, pg. 145: 19, 25, 31, 37, 49, 59, 63, 95. Section 3.4, pg. 154: 1 15 (odd), 23, 33, 35, 37, 39, 45, 47. Section 3.5, pg. 161: 1, 5, 13, 21, 41, 53.
CSU Northridge - MATH - 715473
MATH 150ACalculus IFall 2007Homework 4 Due: Tue. Sept. 25, 2007 Section 3.3, pg. 145: 19, 25, 31, 37, 49, 59, 63, 95. Section 3.4, pg. 154: 1 15 (odd), 23, 33, 35, 37, 39, 45, 47. Section 3.5, pg. 161: 1, 5, 13, 21, 41, 53.
CSU Northridge - MATH - 150
MATH 150ACalculus IFall 2007Homework 6 Due: Tue. Oct. 16, 2007 Section 3.9, pg. 193: 1, 3, 11, 17, 21, 31, 33, 35, 37. Section 4.1, pg. 211: 3, 5, 11, 17, 21, 25, 31, 35, 47, 53, 69. Section 4.2, pg. 219: 1, 5, 11, 19, 29, 33.
CSU Northridge - MATH - 715473
MATH 150ACalculus IFall 2007Homework 6 Due: Tue. Oct. 16, 2007 Section 3.9, pg. 193: 1, 3, 11, 17, 21, 31, 33, 35, 37. Section 4.1, pg. 211: 3, 5, 11, 17, 21, 25, 31, 35, 47, 53, 69. Section 4.2, pg. 219: 1, 5, 11, 19, 29, 33.
CSU Northridge - MATH - 150
MATH 150ACalculus IFall 2007Homework 3 Due: Tue. Sept. 18, 2007 Section 3.1, pg. 119: 1, 3, 5, 7, 11, 17, 27, 43. Section 3.2, pg. 131: 3, 5, 7, 17, 23, 39, 51. Section 3.3, pg. 145: 1 11 every odd.
CSU Northridge - MATH - 715473
MATH 150ACalculus IFall 2007Homework 3 Due: Tue. Sept. 18, 2007 Section 3.1, pg. 119: 1, 3, 5, 7, 11, 17, 27, 43. Section 3.2, pg. 131: 3, 5, 7, 17, 23, 39, 51. Section 3.3, pg. 145: 1 11 every odd.
CSU Northridge - MATH - 250
MATH 250Calculus IIISpring 2008Homework 6 Due: Thurs. Mar. 13, 2008 Section 12.4, pg. 640: 1, 3, 7, 11, 15, 17, 19, 21. Section 12.5, pg. 646: 5, 7, 9, 11, 13, 19, 21, 25. Section 12.6, pg. 651: 1, 3, 5, 9, 13, 19, 21, 31.
CSU Northridge - MATH - 715473
MATH 250Calculus IIISpring 2008Homework 6 Due: Thurs. Mar. 13, 2008 Section 12.4, pg. 640: 1, 3, 7, 11, 15, 17, 19, 21. Section 12.5, pg. 646: 5, 7, 9, 11, 13, 19, 21, 25. Section 12.6, pg. 651: 1, 3, 5, 9, 13, 19, 21, 31.
CSU Northridge - MATH - 150
MATH 150ACalculus IFall 2007Homework 9 Due: Thurs. Nov. 15, 2007 Section 5.1, pg. 299: 3, 17, 20, 21. Section 5.2, pg. 310: 3, 11, 17, 21, 29, 35, 53. Section 5.3, pg. 321: 5, 7, 19 25 (odds), 35. Additional Problems: 1. Prove:n n n(ai + bi
CSU Northridge - MATH - 715473
MATH 150ACalculus IFall 2007Homework 9 Due: Thurs. Nov. 15, 2007 Section 5.1, pg. 299: 3, 17, 20, 21. Section 5.2, pg. 310: 3, 11, 17, 21, 29, 35, 53. Section 5.3, pg. 321: 5, 7, 19 25 (odds), 35. Additional Problems: 1. Prove:n n n(ai + bi
CSU Northridge - MATH - 250
MATH 250Calculus IIISpring 2008Homework 5 Due: Thurs. Mar. 6, 2008 Section 12.1, pg. 622: 5, 21, 23, 25, 27, 33. Section 12.2, pg. 628: 1, 3, 5, 9, 27, 29, 33, 41. Section 12.3, pg. 634: 3, 15, 17, 19, 25, 27, 35.
CSU Northridge - MATH - 715473
MATH 250Calculus IIISpring 2008Homework 5 Due: Thurs. Mar. 6, 2008 Section 12.1, pg. 622: 5, 21, 23, 25, 27, 33. Section 12.2, pg. 628: 1, 3, 5, 9, 27, 29, 33, 41. Section 12.3, pg. 634: 3, 15, 17, 19, 25, 27, 35.
CSU Northridge - MATH - 150
MATH 150ACalculus IFall 2007Homework 2 Due: Tue. Sept. 11, 2007 Section 2.3, pg. 84: 47, 55. Section 2.4, pg. 95: 1, 11, 13, 15, 17 read section before attempting problems! Section 2.5, pg. 105: 1, 5, 7, 9, 13, 37, 41, 61, 62.
CSU Northridge - MATH - 715473
MATH 150ACalculus IFall 2007Homework 2 Due: Tue. Sept. 11, 2007 Section 2.3, pg. 84: 47, 55. Section 2.4, pg. 95: 1, 11, 13, 15, 17 read section before attempting problems! Section 2.5, pg. 105: 1, 5, 7, 9, 13, 37, 41, 61, 62.
CSU Northridge - MATH - 581
MATH 581Numerical Methods for Linear SystemsSpring 2008Homework 1 Due: Thurs. Feb. 7, 2008 Lecture Lecture Lecture Lecture 1, 2, 3, 4, pg. pg. pg. pg. 9: 1.1, 1.3 16: 2.1, 2.5, 2.6 24: 3.2, 3.3, 3.5 31: 4.1, 4.3Additional Problem 1. Let A be
CSU Northridge - MATH - 715473
MATH 581Numerical Methods for Linear SystemsSpring 2008Homework 1 Due: Thurs. Feb. 7, 2008 Lecture Lecture Lecture Lecture 1, 2, 3, 4, pg. pg. pg. pg. 9: 1.1, 1.3 16: 2.1, 2.5, 2.6 24: 3.2, 3.3, 3.5 31: 4.1, 4.3Additional Problem 1. Let A be
CSU Northridge - MATH - 53971
Math 550. Homework 8. Due 11/10/03Problem 1. Let U, V be open subsets of R2 . Prove that the coboundary map : H 0 (U V ) H 1 (U V ) is a homomorphism of vector spaces. Problem 2. Let F : U V be a smooth map from the open set U R2 into the open
CSU Northridge - MATH - 550
Math 550. Homework 8. Due 11/10/03Problem 1. Let U, V be open subsets of R2 . Prove that the coboundary map : H 0 (U V ) H 1 (U V ) is a homomorphism of vector spaces. Problem 2. Let F : U V be a smooth map from the open set U R2 into the open
CSU Northridge - MATH - 311
Math 311. Quiz 5 Due: Monday, October 20, 2008Name:Construction a Golden Triangle We have proved that an isosceles triangle with long side equal to 1 and short of 51 side equal to is a golden triangle. Problem 1 uses this information in order to
CSU Northridge - MATH - 53971
Math 311. Quiz 5 Due: Monday, October 20, 2008Name:Construction a Golden Triangle We have proved that an isosceles triangle with long side equal to 1 and short of 51 side equal to is a golden triangle. Problem 1 uses this information in order to
CSU Northridge - MATH - 53971
Math 550. Homework 9. Due 12/03/03Problem 1. Suppose that U = R2 \ {P1 , , Pn } is the complement of n points in the plane. Prove that the mapping that takes a closed 1-chain to W (, P1 ), , W (, Pn ) determines an isomorphism of H1 U with t
CSU Northridge - MATH - 550
Math 550. Homework 9. Due 12/03/03Problem 1. Suppose that U = R2 \ {P1 , , Pn } is the complement of n points in the plane. Prove that the mapping that takes a closed 1-chain to W (, P1 ), , W (, Pn ) determines an isomorphism of H1 U with t
CSU Northridge - MATH - 53971
Math 550. Homework 7. Due 10/29/03Problem 1. A vector X in Rn is called a probability vector if its coordinates are all nonnegative and add up to 1. An n n matrix is an stochastic matrix if its columns are probability vectors. Use the Brouwer xed
CSU Northridge - MATH - 550
Math 550. Homework 7. Due 10/29/03Problem 1. A vector X in Rn is called a probability vector if its coordinates are all nonnegative and add up to 1. An n n matrix is an stochastic matrix if its columns are probability vectors. Use the Brouwer xed
CSU Northridge - MATH - 53971
Math 623. Homework 5. Due 04/21/04Problem 1. Show that the hyperbolic distance d(z, w) between points z and w in the unit disk satises the following identity 1 zw Tanh d(z, w) = . 2 1 zw Problem 2. A circle in H2 centered at p with radius r is the
CSU Northridge - MATH - 623
Math 623. Homework 5. Due 04/21/04Problem 1. Show that the hyperbolic distance d(z, w) between points z and w in the unit disk satises the following identity 1 zw Tanh d(z, w) = . 2 1 zw Problem 2. A circle in H2 centered at p with radius r is the
CSU Northridge - MATH - 53971
Math 655. Homework 3. Due 2/26/03Problem 1 Let f be an analytic function on a connected open set U C. (1) Show that if f is real valued, then f is constant on U . (2) Show that if f has constant absolute value, then f is constant on U . Problem 2
CSU Northridge - MATH - 655
Math 655. Homework 3. Due 2/26/03Problem 1 Let f be an analytic function on a connected open set U C. (1) Show that if f is real valued, then f is constant on U . (2) Show that if f has constant absolute value, then f is constant on U . Problem 2
CSU Northridge - MATH - 53971
Math 655. Homework 1. Due 2/5/03Problem 1 Prove thatab <1 1 abif |a| < 1 and |b| < 1. Prove also thatab =1 1 abif either |a| = 1 or |b| = 1. What exception must be made if |a| = |b| = 1? Problem 2 Show that the functions f (z) and f (z) a
CSU Northridge - MATH - 655
Math 655. Homework 1. Due 2/5/03Problem 1 Prove thatab <1 1 abif |a| < 1 and |b| < 1. Prove also thatab =1 1 abif either |a| = 1 or |b| = 1. What exception must be made if |a| = |b| = 1? Problem 2 Show that the functions f (z) and f (z) a
CSU Northridge - MATH - 53971
Math 592D. Homework 4. Due: 4/28/051. Problem 5.3.2 2. Problem 5.4.2
CSU Northridge - MATH - 592
Math 592D. Homework 4. Due: 4/28/051. Problem 5.3.2 2. Problem 5.4.2
CSU Northridge - MATH - 53971
Math 592D. Homework 3. Due: 3/10/05Do at least 2, 3, 4 (not 4(e). Then 1 if possible. 5 and 6 are suggestions. 1. The approach to modeling age-structured populations in continuous time is similar to what we have done in discrete time. If u(a, t) is
CSU Northridge - MATH - 592
Math 592D. Homework 3. Due: 3/10/05Do at least 2, 3, 4 (not 4(e). Then 1 if possible. 5 and 6 are suggestions. 1. The approach to modeling age-structured populations in continuous time is similar to what we have done in discrete time. If u(a, t) is
CSU Northridge - MATH - 53971
Math 550. Homework 2 (Revised). Due 9/22/2003Problem 1 Let U be the union of two open sets U1 ,U2 , i.e., U = U1 U2 . Let f j be a smooth functions on U j , j = 1, 2, such that f1 (x) = f2 (x) for every x in U1 U2 . Prove that f (x) = is a smooth f
CSU Northridge - MATH - 550
Math 550. Homework 2 (Revised). Due 9/22/2003Problem 1 Let U be the union of two open sets U1 ,U2 , i.e., U = U1 U2 . Let f j be a smooth functions on U j , j = 1, 2, such that f1 (x) = f2 (x) for every x in U1 U2 . Prove that f (x) = is a smooth f
CSU Northridge - MATH - 53971
Math 550. Homework 1. Due 9/3/2003Problem 1 Let U be an open subset of the plane. Prove that U is connected if and only if every locally constant function on U is constant on U . Problem 2 Let = ydx xdy and let be the line segment from (0, 0) to
CSU Northridge - MATH - 550
Math 550. Homework 1. Due 9/3/2003Problem 1 Let U be an open subset of the plane. Prove that U is connected if and only if every locally constant function on U is constant on U . Problem 2 Let = ydx xdy and let be the line segment from (0, 0) to
CSU Northridge - MATH - 53971
Math 550. Homework 6. Due 10/22/03Denition 1. Two continuous mappings f , g : X Y are homotopic if there is a continuous mapping H : X [0, 1] Y such that H(x, 0) = f (x) and H(x, 1) = g(x) for all x in X. Problem 1. Let C and C be circles. (i) P
CSU Northridge - MATH - 550
Math 550. Homework 6. Due 10/22/03Denition 1. Two continuous mappings f , g : X Y are homotopic if there is a continuous mapping H : X [0, 1] Y such that H(x, 0) = f (x) and H(x, 1) = g(x) for all x in X. Problem 1. Let C and C be circles. (i) P