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Georgia Tech | MATH 2401
Calculus III
Professors
• Amey S. Kaloti,
• ,
• Morley,
• Steinbart,
• Belifante,
• Etnyre,
• Yongfeng Li,
• Ghomi,
• Liu,
• Liu, Yingjie,
• Yildrim Yolcu,
• Bishop,
• Pan,
• Stavros,
• Wong,
• Garoufalidis,
• Morely,
• Shannon Bishop,
• Iliev,
• Etynre

100 sample documents related to MATH 2401

• Georgia Tech MATH 2401
Math 2401 Quiz #2 Feb 25 Tom Morley 8:00 am Name: _ Problem 1 (10 points) Consider the surface : x3 y x2 y 10 z. and its contour curve corresponding to z 2. On this contour curve, find a normal to the contour curve at the point x Also Find a normal to the

• Georgia Tech MATH 2401
Math 2401 Quiz #3 March 16 Tom Morley 8:00 am Name:_ TA: _ Open Book and Notes. Carefully explain your proceedures and answers. Calculators allowed, but answers mush be exact. Don\'t evaluate integrals unless it is asked for. Problem 1 (10 points) George M

• Georgia Tech MATH 2401
Math 2401 Quiz #3 March 16 Tom Morley 8:00 am Problem 1 (10 points) George Mallory needs to know the following : Let V be the volume between the hyperboloid of two sheets x2 y2 z2 3 above the plane z 4 and below the plane z 6. Set up the volume as a tripl

• Georgia Tech MATH 2401
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• Georgia Tech MATH 2401
Math 2401 Quiz #4 April 15 Tom Morley 8:00 am Problem 1 (10 points) George Mallory needs to know the following : Find the value of the line integral y Sin x y dx x Sin x y dy C where C is the curve x ti t2 j from 0, 0 to 3, 9 . Hint : Find the potential e

• Georgia Tech MATH 2401
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• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401
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• Georgia Tech MATH 2401
Quiz 1 Review Links: Main page of calc 3: http:/tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx Basic vector valued functions, if you are a more visual person this may be valuable: http:/tutorial.math.lamar.edu/Classes/CalcIII/VectorFunctions.aspx Ba

• Georgia Tech MATH 2401
Math2401 Quiz #1 Feb 2 Tom Morley 8:00 am Problem 1 (10 points) Consider the 2 curves r1 t ti t2 j 4 t3 k, and r2 t cos t 2 i t3 2 j t 4 2 Find their intersection as curves and find the cosine of the angle between them at their intersection Ans In[64]:= t

• Georgia Tech MATH 2401
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• Georgia Tech MATH 2401
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• Georgia Tech MATH 2401
Math 2401 Quiz #3 March 16 Tom Morley 8:00 am Problem 1 (10 points) George Mallory needs to know the following : Let V be the volume between the hyperboloid of two sheets x2 y2 z2 3 above the plane z 4 and below the plane z 6. Set up the volume as a tripl

• Georgia Tech MATH 2401
Math 2401 Practice Test 2 Fall 2012 Name: GT ID Number: Calculus section (D1, D2, D3, or D4): (if you dont know your section, then put your TAs name instead) Signature: Instructions: Print your name and sign your signature to indicate that you accept the

• Georgia Tech MATH 2401
Math 2401 Practice Midterm Exam Fall 2012 Name: Calculus section (B1, B2, B3, or B4): Signature: Instructions: Print your name and sign your signature to indicate that you accept the honor code. When a box is provided for your answer you must write your a

• Georgia Tech MATH 2401
Sample test 1A Problem 1. Calculate, simplifying the answer: 3 (a) 1 1 i + ln t j + e2t k dt t t d (b) dt [(ln ti + tj) (ti + t2 j)] d2 (c) dt2 [(et i + et j) (et i et j)] Problem 2. Find the point at which the curves )j + (t2 2)k 2 r2 (u) = ui + 2j + (u2

• Georgia Tech MATH 2401
Sample test 1B Problem 1. Consider the curve r(t) = sinh ti + cosh tj + tk. Find the unit tangent, the principal normal, and write an equation in x, y , z for the osculating plane at the point on the curve corresponding to t = 0. Problem 2. An object move

• Georgia Tech MATH 2401
Sample test 2A Problem 1. Find the the directional derivatives of f (x, y, z ) = ex cos(yz ) 1 at 0, 1, 2 in the directions parallel to the line in which the planes x + y z = 5 and 4x y z = 2 intersect. Problem 2. The radius of a right circular cylinder i

• Georgia Tech MATH 2401
Sample test 2B Problem 1. Set xy (y 2 x2 ) , x2 + y 2 (x, y ) = (0, 0) 0, f (x, y ) = (x, y ) = (0, 0). (a) Is f (x, y ) continuous? (b) Compute f (0, y ) and f (x, 0). Are the rst partial derivatives of f x y continuous on R2 ? 2f 2f (c) Compute yx (0, 0

• Georgia Tech MATH 2401
Sample Final Exam A Problem 1. Find the unit tangent, the principal normal and write an equation in x, y, z for the osculating plane at the point (2, 0, 1) on the curve r(t) = 2t i + ln t j t2 k. Problem 2. Find the intersecting points of the curves r1 (t

• Georgia Tech MATH 2401
Sample Final Exam B 2 Problem 1. Set r(t) = cos t i + sin t j + 3 t3/2 k. (a) Determine the arc length s from r(0) to r(t). (b) Find the parametrization R( s) of the curve by arc length. (c) Show that |R ( s)| = 1. Problem 2. Let S be the surface 2 x2 + 3

• Georgia Tech MATH 2401
Final exam, Math 2401, Spring 2011 Name: GTID#: The exam consists of eight problems. You need to show all your work, including all intermediate steps! Problem No. Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Total Points

• Georgia Tech MATH 2401
Answers to the nal exam, Math 2401, Spring 2011 Problem 1. The unit tangent at (1, 1, 2) is T = 1 i 1 j 2 2 1 1 1 The principal normal at (1, 1, 2) is N = 2 i 2 j + k. 2 An equation for the osculating plane is x y = 0. 1 k. 2 Problem 2. (a) The line l1

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401
Practice Test 2 Math 2401 B1 & B2 June 25, 2009 Name: by writing my name I agree to uphold the honor code Read all of the following information before starting the exam: This test has 5 problems worth 100 points. You have 70 minutes to complete the test

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401
Practice Test 3 Math 2401 B1 & B2 July 16, 2009 Name: by writing my name I agree to uphold the honor code Read all of the following information before starting the exam: This test has 5 problems worth 100 points. You have 70 minutes to complete the test

• Georgia Tech MATH 2401
Practice Final Exam Math 2401 B1 & B2 July 29, 2009 Name: by writing my name I agree to uphold the honor code Read all of the following information before starting the exam: This test has 8 problems worth 100 points. You must complete problems 1-6. Choos

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401
Chapter 18 Line Integrals and Surface Integrals Line Integral To find the line integral over a pathway given the indices, parametrize using the equation: To find the line integral with respect to arc length (look for notation with dx and dy): Length of a

• Georgia Tech MATH 2401
Calculus III Midterm I Study Guide Chapters 14.1 16.4 Chapter 14 Vector Calculus Tangent Vector Unit Tangent Unit Normal The plane determined by the unit tangent and unit normal is called the osculating plane, given by Arc Length Parametrize a Curve by Ar

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401
Finding Stationary Points and Local Extreme Values - Find the gradient of the function then set it equal to zero. Solving for x and y gives the critical points of the function. Use the second partials test to classify the points as a local min/max or sadd

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401
P1: PBU/OVY JWDD027-16 P2: PBU/OVY JWDD027-Salas-v1 QC: PBU/OVY T1: PBU December 7, 2006 16:36 788 SECTION 16.1 CHAPTER 16 SECTION 16.1 1. f = (6x y ) i + (1 x) j 3. f = exy [ (xy + 1) i + x2 j] 4. f = (x2 1 [(y 2 x2 + 2xy )i + (y 2 x2 2xy )j] + y 2 )2 2.

• Georgia Tech MATH 2401
P1: PBU/OVY JWDD027-17 P2: PBU/OVY JWDD027-Salas-v1 QC: PBU/OVY T1: PBU December 7, 2006 16:38 866 SECTION 17.1 CHAPTER 17 SECTION 17.1 3 3 1. i=1 j =1 2i1 3j +1 = 3 i=1 2i1 3 j =1 3j +1 = (1 + 2 + 4)(9 + 27 + 81) = 819 2. 2 + 22 + 3 + 32 + 4 + 42 + 5

• Georgia Tech MATH 2401
P1: PBU/OVY JWDD027-18 P2: PBU/OVY JWDD027-Salas-v1 QC: PBU/OVY T1: PBU January 4, 2007 18:12 918 SECTION 18.1 CHAPTER 18 SECTION 18.1 1. (a) h(x, y ) = y i + x j; r(u) = u i + u2 j, u [ 0, 1 ] x (u) = 1, y (u) = 2u x(u) = u, y (u) = u2 ; 1 0 h(r(u) r (u)

• Georgia Tech MATH 2401
P1: PBU/OVY JWDD027-19 P2: PBU/OVY JWDD027-Salas-v1 QC: PBU/OVY T1: PBU January 4, 2007 19:13 984 SECTION 19.1 CHAPTER 19 SECTION 19.1 1. y + xy = xy 3 = y 3 y + xy 2 = x. Let v = y 2 , v = 2y 3 y . 1 v + xv = x 2 v 2xv = 2x ex v 2xex v = 2xex 2 2 2 2 2 e

• Georgia Tech MATH 2401
MATH 2401 Sections F4 & F5 September 16, 2009 PRACTICE EXAM 1 Name: Note: gtID#: There are ve problems in this exam, each worth 20 points. Write out your solutions neatly and explain your work. Calculators are not allowed. Basic formulas: Unit tangent and

• Georgia Tech MATH 2401
MATH 2401 Sections F4 & F5 October 19, 2009 PRACTICE EXAM 2 Name: Note: gtID#: There are ve problems in this exam, each worth 20 points. Write out your solutions neatly and explain your work. Calculators are not allowed. Basic formulas: f (x) = f f f (x)i

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401
MATH 2401 Sections F4 & F5 PRACTICE FINAL EXAM gtID#: December 10, 2009 11:30-14:20 Name: Note: There are eight problems in this exam, each worth 20 points. Write out your solutions neatly and explain your work. Calculators are not allowed. Problem number

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401
MATH 2401A1-B1 TEST1 (01/25/02) Name: SOLUTION Please read questions carefully and show all your work. You are allowed 50 minutes on this exam. 1. (20 pts) Find d (f dt g), d (f dt g), d (uf ), dt and d (f dt u) for the functions 1 i + t3

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401
Math 2411 Honors Calculus III Spring 2006, Georgia Tech Feb 15, 2006 Midterm 1 the parallelogram is a rectangle. Time: 50min 1. Show that if the diagonals of a parallelogram have the same length then 2. Find the distance between the point (3, 4,

• Georgia Tech MATH 2401
Math 2401 M1 M2 M3 Final Total: 40 points Section: Name: Student Number: (1) (a) Parametrize the curve C: x2 + 4y 2 = 36 with a vector valued function r. (2 points). (b) Find the tangent and normal vectors of curve C. (2 points). (c) Find the curva

• Georgia Tech MATH 2401
Math 2401 M1 M2 M3 Test 2. Total: 20 points Section: Name: Student Number: 1. Find (cos2 r), where r = 2 x + y 2 + z 2 . (4 points). 2. Suppose u = u(x, y) has continuous second partial derivatives. Let ux (1, 0) = 1, uy (1, 0) = 0, uxx (1, 0) = 1,

• Georgia Tech MATH 2401
Math 2401 M1 M2 M3 Test 3 Total: 20 points Section: Name: Student Number: 1. Determine whether or not the following vector function is the gradient of a function f that is everywhere dened. If so, nd all the functions with that gradient. (A) (z + y s

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401
MATH 2401, Fall 2009 Practice Exam 2, Solutions Problem 1. Calculations. (a) Find the directional derivative of f (x, y, z ) = xy + yz + zx at P (1, 1, 1) in the direction of i + 2j + k Solution: f = (y + z )i + (x + z )j + (y + x)k, f (1, 1, 1) = 2j. u =

• Georgia Tech MATH 2401
MATH 2401, Fall 2009 Practice Exam 1, Solutions Problem 1. Calculations. (a) d [(2ti dt + tj) (ti 3j)] 3 solution: 4t 2 t1/2 . (b) d [(costi dt + sintj + tk) (3i + 4j + 5k)] solution: (5cost 4)i + (5sint + 3)j (4sint + 3cost)k (c) d cos2t [e i dt + ln(1 +

• Georgia Tech MATH 2401
MATH 2401, FAll 2009 Midterm I, September 23, Solutions Problem 1(30 points). Calculations. (a)(6 pt) dt [(e i + tj) (et i 3 tj)]. dt Solution: 3 d2 [(t i + j) (t2 i 3tj)]. dt Solution: (9t2 2t)k. (b)(7 pt) (c)(9 pt) Let h(r, , t) = r2 e2t sin( t), calcul

• Georgia Tech MATH 2401
MATH 2401, FAll 2009 Midterm II, Solutions Problem 1.(40 pt) Calculations. (a)(10 pt) Find the directional derivative of f (x, y, z ) = x2 + 2xyz yz 2 at P (1, 1, 2) in the direction of 2i + j 3k Solution: f = (2x + 2yz )i + (2xz z 2 )j + (2xy 2yz )k, f (

• Georgia Tech MATH 2401
2401 Practice Final: Fall 2005 Written by Adam Tart 1) Given an ellipse in the form: x2 + 25y2 = 25 a) Parameterize the ellipse b) Find the unit tangent and principal normal vectors at the point (3, 4/5) c) Find the curvature at the point (3, 4/5) d)

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401

• Georgia Tech MATH 2401
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• Georgia Tech MATH 2401
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