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math255_hw10

Course: MATH 255, Fall 2009
School: CSU Northridge
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255 Applied MATH Honors Calculus III Winter 2005 Homework 10 Due: Wed. Apr. 13, 2005 Section Section Section Section 17.3, 17.4, 17.6, 17.5, 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, 21, 35, 45.

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255 Applied MATH Honors Calculus III Winter 2005 Homework 10 Due: Wed. Apr. 13, 2005 Section Section Section Section 17.3, 17.4, 17.6, 17.5, 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, 21, 35, 45.
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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
CSU Northridge - MATH - 53971
Math 550. Homework 5. Due 10/15/03Problem 1. Let : [a, b] R2 \ {0} be a continuous path. Prove that there are continuous functions r : [a, b] R+ (the positive real numbers) and : [a, b] R, so that (t) = (r(t) cos (t), r(t) sin (t), a t b.P
CSU Northridge - MATH - 550
Math 550. Homework 5. Due 10/15/03Problem 1. Let : [a, b] R2 \ {0} be a continuous path. Prove that there are continuous functions r : [a, b] R+ (the positive real numbers) and : [a, b] R, so that (t) = (r(t) cos (t), r(t) sin (t), a t b.P
CSU Northridge - MATH - 53971
Math 550. Homework 4. Due 10/01/2003Problem 1 Given a 1-form on an open set U, prove that the following are equivalent (i) d = 0; (ii)R R = 0 for all closed rectangles R contained in U; (iii) every point in U has a neighborhood such that = 0 f
CSU Northridge - MATH - 550
Math 550. Homework 4. Due 10/01/2003Problem 1 Given a 1-form on an open set U, prove that the following are equivalent (i) d = 0; (ii)R R = 0 for all closed rectangles R contained in U; (iii) every point in U has a neighborhood such that = 0 f
CSU Northridge - MATH - 53971
Math 550. Homework 3. Due 9/24/2003You have two options to choose from. Option A Generalize (that is, state and prove) the last lemma proved in class today (9/10) to an open set of the form U = R2 \ {P1 , , Pn }. Option B Prepare a set of lectur
CSU Northridge - MATH - 550
Math 550. Homework 3. Due 9/24/2003You have two options to choose from. Option A Generalize (that is, state and prove) the last lemma proved in class today (9/10) to an open set of the form U = R2 \ {P1 , , Pn }. Option B Prepare a set of lectur
CSU Northridge - MATH - 512
Math 512B. Homework 1. Due 1/30/08(Revised 1/27)Problem 1. In class we dened cos x and sin x for x in [0, ]. The values of cos x and sin x for x not in [0, ] are dened in two steps as follows: (1) If x 2, then set cos x sin x = cos(2 x), = sin
CSU Northridge - MATH - 53971
Math 512B. Homework 1. Due 1/30/08(Revised 1/27)Problem 1. In class we dened cos x and sin x for x in [0, ]. The values of cos x and sin x for x not in [0, ] are dened in two steps as follows: (1) If x 2, then set cos x sin x = cos(2 x), = sin
CSU Northridge - MATH - 512
Math 512B. Homework 3. Due 2/13/08The symbol lim f (x) means the limit of f (x) as x approaches . We say that lim f (x) = L if for every x x > 0 there is a number M such that, for all x, if x > M , then |f (x) L| < . A similar denition applies t
CSU Northridge - MATH - 53971
Math 512B. Homework 3. Due 2/13/08The symbol lim f (x) means the limit of f (x) as x approaches . We say that lim f (x) = L if for every x x > 0 there is a number M such that, for all x, if x > M , then |f (x) L| < . A similar denition applies t
CSU Northridge - MATH - 512
Math 512B. Homework 4. Due 2/20/08(Revised 2/18)Problem 1. (i) Prove that the remainder R2n+1,0,arctan (x) of degree 2n + 1 of the function arctan satises |R2n+1,0,arctan (x)| for |x| 1. (ii) Use the relation arctan x + arctan y = arctan x+y 1 x
CSU Northridge - MATH - 53971
Math 512B. Homework 4. Due 2/20/08(Revised 2/18)Problem 1. (i) Prove that the remainder R2n+1,0,arctan (x) of degree 2n + 1 of the function arctan satises |R2n+1,0,arctan (x)| for |x| 1. (ii) Use the relation arctan x + arctan y = arctan x+y 1 x
CSU Northridge - MATH - 512
Math 512B. Homework 9. Due 4/37/08Problem 1. Let z1 , z2 , z3 be three distinct nonzero complex numbers. Prove that the following are equivalent: (i) The points z1 , z2 , and z3 are the vertices of an equilateral triangle. (ii) The center of mass o
CSU Northridge - MATH - 53971
Math 512B. Homework 9. Due 4/37/08Problem 1. Let z1 , z2 , z3 be three distinct nonzero complex numbers. Prove that the following are equivalent: (i) The points z1 , z2 , and z3 are the vertices of an equilateral triangle. (ii) The center of mass o
CSU Northridge - MATH - 512
Math 512B. Homework 8. Due 4/16/08Problem 1. (i) Find the Fourier series of the following functions (they are 2-periodic, so only the values on (, ] are given). (a) f (x) = 0 if < x 0 and f (x) = sin x if 0 < x . (b) g(x) = x2 if < x . (ii) Di
CSU Northridge - MATH - 53971
Math 512B. Homework 8. Due 4/16/08Problem 1. (i) Find the Fourier series of the following functions (they are 2-periodic, so only the values on (, ] are given). (a) f (x) = 0 if < x 0 and f (x) = sin x if 0 < x . (b) g(x) = x2 if < x . (ii) Di