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Oregon State | MTH 255
Vector Calculus II4
34 sample documents related to MTH 255
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Oregon State MTH 255
MTH 255 1. HW #1 a Fall 2005 The figure at the right shows a rectangular box containing several vectors. Are the following statements true or false? Explain. b (a) c = f (b) a = d (c) a = -b (d) g = f + a (e) e = a - b (f) d = g - c Compute the -
Oregon State MTH 255
MTH 255 1. 2. HW #6 Fall 2005 Find the ux of F = z 2 k through the upper hemisphere of the sphere x2 + y 2 + z 2 = 25, oriented away from the origin. Let H = (exy + 3z + 5) + (exy + 5z + 3) + (3z + exy ) k. Calculate the ux of H through the -
Oregon State MTH 255
DIFFERENTIALS 1. The voltage V (in volts) across a circuit is given by Ohms law: V = IR, where I is the current (in amps) owing through the circuit and R is the resistance (in ohms). If we place two circuits, with resistance R1 and R2 , in parallel, -
Oregon State MTH 255
MTH 255 1. HW #8 Spring 2004 Decide whether the vector elds below have a nonzero curl at the center of the region shown. In each case, the vector eld is shown in the xy-plane; assume it has no z-component and is independent of z. 2. A smooth vec -
Oregon State MTH 255
OSU Dot Product Proof Winter 2004 Reference: Tevian Dray Dot Product Proof Jason Siefken February 7, 2004 If v w = u w for all w, show that v = u Let w1 = v |v| v w = u w = v w1 = u w1 By the denition fo the dot product, we know: v w1 = |u|w1 | co -
Oregon State MTH 255
OSU mth255H Winter 2004 Lab 6 Writeup Recorder: Jason Siefken Task Master: Dan Cynic: Seth February 16, 2004 In order to nd the total amount of chocolate on the cone, we rst convert the equations we were given for the cone (z 2 = 9(x2 +y 2 ) : z [ -
Oregon State MTH 255
MTH 255 Skills check (not to turn in): (a) 16.1: 3, 11, 13, 15, 17 (b) 16.2: 3, 17 Assigned: 1. HW #3 Spring 2003 y x Consider a valley whose height h in meters is given by h = 10 + 10 , with x and y (and 10!) in meters. Suppose you are hiking thr -
Oregon State MTH 255
MTH 255 1. HW #8 Winter 2009 Water in a bathtub has velocity vector field near the drain given by y + xz yz - x 1 ^ ^- 2 ^ F =- 2 i - 2 k 2 2 (z + 1) (z + 1) z +1 with x, y, z in cm, and F in cm sec . (a) Rewriting F as follows, describe in words -
Oregon State MTH 255
MTH 255 Suppose F = xyz 2 . (a) Find F at the point (1, 2, 1). Note: You are given F , not F ! HW #7 Winter 2009 (b) Using your answer to part (a), but no other information about the vector eld F , estimate the ux out of a small box of side -
Oregon State MTH 255
Calculating Line Elements in Cylindrical and Spherical Coordinates by Corinne Manogue and Katherine Meyer c 1997 Corinne A. Manogue Rectangular Coordinates: The arbitrary innitesimal displacement vector in Cartesian coordinates is: dr = dx + dy + -
Oregon State MTH 255
MTH 255 Skills check (not to turn in): (a) 14.5: 34 HW #3 Winter 2003 (b) The voltage V (in volts) across a circuit is given by Ohm\'s law: V = IR, where I is the current (in amps) flowing through the circuit and R is the resistance (in ohms). If w -
Oregon State MTH 255
MTH 255 Skills check (not to turn in): (a) 16.1: 3, 11, 13, 15, 17 (b) 16.2: 3, 17 HW #4 Winter 2003 (c) Let C be the ellipse parameterized by x = 3 cos , y = 4 sin , [0, 2]. Evaluate the line integral F dr, where F = y + x . C Assigned: 1. -
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Oregon State MTH 255
Flux is the total amount of electric field through a given area. Perpendicular Component Normal Vector = E da E da E da over all rectangles -
Oregon State MTH 255
MTH 255 Final Review 1. Each part of this problem concerns the parametric curve r(t) = (t2 2) + (2t 1) + ln(t) k, t > 0. (a) Find the velocity, v, the speed, , and the acceleration, a, at every t > 0. (b) Find the length of the parametric curve -
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Oregon State MTH 255
MTH 255 SUMMER 2003 INFORMATION FOR STUDENTS Instructor: Juha Pohjanpelto Office/Phone: Kidder Hall 312, 737-5156 Office hours: Monday 12:001:00, Thursday 1:00-2:00, or by appointment Email: juha@math.orst.edu Homepage: www.onid.orst.edu/~pohjanpp Te -
Oregon State MTH 255
MTH 255 - Summer 2003 Monday June 23 Lesson 1 Classes Begin Tuesday 24 Wednesday 25 Lesson 2 Thursday 26 Lesson 3 Friday 27 30 Lesson 4 July 1 Lesson 45 2 Lesson 5 3 4 July Lesson 6 7 8 Lesson 7 9 Lesson 78 10 11 14 Lesson 8 15 Lesso -
Oregon State MTH 255
VECTOR DERIVATIVES Rectangular coordinates ^ dr = dx ^ + dy + dz k i ^ ^ F = Fx ^ + Fy + Fz k i ^ f f f ^ ^+ i + ^ k x y z Fx Fy Fz + + F = x y z Fz Fy Fx Fz Fy Fx ^ F = k ^+ i + ^ - - - y z z x x y f = Cylindrical coordinates ^ dr = dr r + r d + -
Oregon State MTH 255
MTH 255 Skills check (not to turn in): 16.8: 3, 5, 13 Assigned: 1. HW #10 Spring 2003 Water in a bathtub has velocity vector field near the drain given, for x, y, z in cm, by yz - x 1 ^ y + xz ^- 2 ^ i - 2 k F =- 2 2 2 (z + 1) (z + 1) z +1 (a) Re -
Oregon State MTH 255
MTH 255 HW #9 Spring 2003 Skills check (not to turn in): Compute the curl of each vector field below. Without doing any further computation, decide whether each vector field is conservative. Use the Murder Mystery Method to check your work! ^ (a) -
Oregon State MTH 255
MTH 255 Skills check (not to turn in): 16.9: 14 Assigned: 1. Suppose F = xyz 2 . HW #8 Spring 2003 (a) Find F at the point (1, 2, 1). Note: You are given F , not F ! (b) Using your answer to part (a), but no other information about the vector f -
Oregon State MTH 255
MTH 255 Skills check (not to turn in): 16.6: 11, 13, 22 Assigned: 1. Parameterization (a) 16.6: 12 HW #6 Spring 2003 (b) Write a sentence or two comparing the answers to 11, 12, 13. 2. Flux (a) What do you think will be the flux through the cylin -
Oregon State MTH 255
MTH 255 1. HW #9 Spring 2004 Water in a bathtub has velocity vector field near the drain given by y + xz yz - x 1 ^ ^- 2 ^ F =- 2 i - 2 k 2 2 (z + 1) (z + 1) z +1 with x, y, z in cm, and F in cm sec . (a) Rewriting F as follows, describe in words -
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Oregon State MTH 255
MTH 255H 1. THE PUDDLE Winter 2009 The depth of a puddle in millimeters is given by 1 (1 + sin(xy) h= 10 Your path through the puddle is given by x = 3t y = 4t and your current position is x = 3, y = 4, with x and y also in millimeters, and t in s -
Oregon State MTH 255
THE GEOMETRY OF CONSERVATIVE VECTOR FIELDS THE GEOMETRY OF CONSERVATIVE VECTOR FIELDS THE GEOMETRY OF CONSERVATIVE VECTOR FIELDS -
Oregon State MTH 255
MTH 255 1. HW #8 Fall 2005 Water in a bathtub has velocity vector field near the drain given by y + xz yz - x 1 ^ ^- 2 ^ F =- 2 i - 2 k 2 2 (z + 1) (z + 1) z +1 with x, y, z in cm, and F in cm sec . (a) Rewriting F as follows, describe in words h -
Oregon State MTH 255
MTH 255 1. Flux HW #5 Fall 2005 (a) What do you think will be the flux through the cylindrical surface that is placed as shown in the constant vector field in the figure on the left? (b) What if the cylinder is placed upright, as shown in the figu -
Oregon State MTH 255
MTH 255 HW #4 2 Fall 2005 1. For each of the problems below, say whether you expect the given vector field to have positive, negative, or zero circulation counterclockwise around the closed curve C in the figure shown at the right. Two of the seg -
Oregon State MTH 255
OSU mth255H Winter 2004 Lab 6 Writeup Recorder: Jason Siefken Task Master: Kim Cynic: Alicia March 5, 2004 1. Loop 1 is a small circle in the upper right corner of F = y + x i j. (a) The circulation is posotive. (b) A paddlewheel will spin if place -
Oregon State MTH 255
Math 255, Spring 2009 Scarborough Midterm NAME (print) _ NAME (sign) _ Student Number _ Recitation Time (Circle One) This exam is closed book. 12:00 2:00 4:00 Calculators are not allowed or needed. You may use one side of a 4 inch by 6 inch no -
Oregon State MTH 255
Math 255, Spring 2009 Scarborough Midterm KEY NAME (print) _KEY _ NAME (sign) _ Student Number _ Recitation Time (Circle One) This exam is closed book. 12:00 2:00 4:00 Calculators are not allowed or needed. You may use one side of a 4 inch by -
Oregon State MTH 255
Homework: Selected Comments and Hints References to Stewart, such as Sec. 12.5 should be read to include looking at corresponding material in your class notes and in the MTH 255 Study Guide. HW #1: 1. (a) Stewart Sec. 12.5. (b) Is there a time t for
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