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...Exercises for Day 8: Vector Fields 1. Change of Variables. Suppose that (V, ) and (V, ) are coordinate charts on the n-manifold M and that = (xi ) while = (yi ). (The indices i, j, k, etc., run from 1 to n.) Show that if a smooth vector eld X on V ...
...Exercises for Day 10: Riemannian Metrics: Examples
1. Metric Comparisons. Suppose that g and g are two Riemannian metrics on M . We say that g and g are comparable on M , if there exists a constant 1 such that 2 g(v) g (v) 2 g(v) for all v T M ...
..."Introduction to Cryptography" for Spring 2005 Brief Seminar Description: -This seminar is meant to be a first introduction to cryptography, covering both classical and modern (public-key) cryptosystems. For the first half of the semester we will dis...
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UGA >> MATH >> 1 (Fall, 2004)
Math 2200 Spring 2005 Instructor: Zubeyir Cinkir Exam 1 Date: Feb. 10, 2003 Duration: 60 min Direction: For full credit, write down your calculations as much as possible and in an organized way, so that it can be used to give a partial credit. Name...
UGA >> MATH >> 2200 (Spring, 2005)
Math 2200 Spring 2005 Instructor: Zubeyir Cinkir Exam 1 Date: Feb. 10, 2003 Duration: 60 min Direction: For full credit, write down your calculations as much as possible and in an organized way, so that it can be used to give a partial credit. Name...
UGA >> MATH >> 2 (Fall, 2004)
Math 2200 Spring 2005 Instructor: Zubeyir Cinkir Exam 2 Date: March 10, 2005 Duration: 75 min Direction: For full credit, write down your calculations as much as possible and in an organized way, so that it can be used to give a partial credit. Sepe...
UGA >> MATH >> 2200 (Spring, 2005)
Math 2200 Spring 2005 Instructor: Zubeyir Cinkir Exam 2 Date: March 10, 2005 Duration: 75 min Direction: For full credit, write down your calculations as much as possible and in an organized way, so that it can be used to give a partial credit. Sepe...
UGA >> MATH >> 2200 (Spring, 2005)
Zubeyir Cinkir, MATH 2200 Exam3 Students Name: April 14, 2005 There are 9 questions for a total of 115 points. Among these last two problems which are 15 points are bonus. Exam will last 75 minutes. For full credit, write down your calculations as...
UGA >> MATH >> 3 (Fall, 2004)
Zubeyir Cinkir, MATH 2200 Exam3 Students Name: April 14, 2005 There are 9 questions for a total of 115 points. Among these last two problems which are 15 points are bonus. Exam will last 75 minutes. For full credit, write down your calculations as...
UGA >> MATH >> 2200 (Spring, 2005)
Math 2200 Spring 2005 Instructor: Zubeyir Cinkir Final Exam Date: May 5, 2005 Duration: 3 hours Direction: For full credit, write down your calculations as much as possible and in an organized way, so that it can be used to give a partial credit. Se...
UGA >> MATH >> 2200 (Spring, 2005)
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UGA >> MATH >> 1 (Fall, 2004)
Zubeyir Cinkir Homework-1 Solutions: 1. (7 on page 62)(I solved this also in the class) Our function is f(x) = 2x2 3x + 4 so, application of the theorem on page 58 gives the slope predictor formula as m(a) = 2.2.a 3 which represents the slope of t...
UGA >> MATH >> 2 (Fall, 2004)
Zubeyir Cinkir Homework-2 Solutions: 1. (1 on page 73) limx3 (3x2 + 7x 12) = limx3 (3x2 ) + limx3 (7x) + limx3 (12) = limx3 (3). limx3 (x2 ) + limx3 (7). limx3 (x) (12) = 3.(3)2 + 7.3 12 = 36 2. (2, 3 on page 73) Similar to previous one! 3. (5 on...
UGA >> MATH >> 3 (Fall, 2004)
Zubeyir Cinkir Homework-3 Solutions: 1. (1 on page 85) 2 lim0 sin() This is a 0 situation. This is involving trigonometric 0 function sin(). We try to connect this to the theorem 1 on page 75. = lim0 . sin() 1 = lim0 . sin() = lim0 . lim0 = 0.1 =...
UGA >> MATH >> 4 (Fall, 2004)
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UGA >> MATH >> 4 (Fall, 2004)
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UGA >> MATH >> 8 (Fall, 2004)
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UGA >> MATH >> 8 (Fall, 2004)
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UGA >> MATH >> 9 (Fall, 2004)
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UGA >> MATH >> 10 (Fall, 2004)
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UGA >> MATH >> 1 (Fall, 2004)
QUIZ-1 Name: Please show all your work! 1. Evaluate limx1 x2 1 x2 +4x5 Math 2200 Spring 2004 Zubeyir Cinkir = 2. Find the slope-predictor function for f (x) = 1 x 3. Evaluate lim0 sin() 1cos() = 1 ...
UGA >> MATH >> 2 (Fall, 2004)
QUIZ-2 Name: Please show all your work! 1. Evaluate limx1 x2 +3 x4 1 Math 2200 Spring 2004 Zubeyir Cinkir = 2. Find the equation of the tangent line to f (x) = 3x2 5x + 1 at (2, f (2) 3. Evaluate lim0+ sin(4) = 1 ...
UGA >> MATH >> 3 (Fall, 2004)
QUIZ-3 Name: Please show all your work! Math 2200 Spring 2004 Zubeyir Cinkir 1. (1 pts) Evaluate the derivative of the function f (x) = x2 3x5 2. (1 pts) let y = (x 3)(2x2 1) Find dy dx 3. (2 pts) Let the volume of the water in a container, a...
UGA >> MATH >> 4 (Fall, 2004)
QUIZ-4 solutions 2004 Name: Please show all of your work! Math 2200 Spring Zubeyir Cinkir 1. (1 pts) Evaluate the derivative of the function f (x) = 3x2 2x + 5 2. (Bonus) Let h(x) = f og(x), g (2) = 3. Suppose that h (2) = 0 2f (3) + 3h (2) Fi...
UGA >> MATH >> 5 (Fall, 2004)
QUIZ-5 Name: Please show all of your work! Math 2200 Spring 2004 Zubeyir Cinkir 1. (1 pt) Write the following formulas: a) Area of a sphere with radius r. b) Volume of a cylinder with height h and base radius r. 2. (0.5 pt) Give the precise deniti...
UGA >> MATH >> 6 (Fall, 2004)
QUIZ-6 Name: Please show all of your work! 1. Dierentiate the following functions a) (1 pnt) f (x) = (2 + sin x cos x). Math 2200 Spring 2004 Zubeyir Cinkir b)(1 pnt) f (x) = sec x + tan x. c)(1 pnt) f (x) = (sin x4 + 3)3 + 4x + tan x2 . 1 ...
UGA >> MATH >> 7 (Fall, 2004)
QUIZ-8 Name: Please show all of your work! Math 2200 Spring 2004 Zubeyir Cinkir 1. (1.5 pnt)By using linear approximation method give an approximate value of 17. Write your nal answer in digit form. 2. (1.5 pnt) Show that the equation x5 + 2x 3 ...
UGA >> MATH >> 8 (Fall, 2004)
QUIZ-8 Name: Please show all of your work! Math 2200 Spring 2004 Zubeyir Cinkir 1. (1.5 pnt)By using linear approximation method give an approximate value of 17. Write your nal answer in digit form. 2. (1.5 pnt) Show that the equation x5 + 2x 3 ...
UGA >> MATH >> 1 (Fall, 2004)
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UGA >> MATH >> 2 (Fall, 2004)
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UGA >> MATH >> 3 (Fall, 2004)
QUIZ-3 Solutions Spring 2004 Name: Please show all your work! Math 2200 Zubeyir Cinkir 1. (1 pts) Evaluate the derivative of the function f (x) = f (x) = 1.(3x5)3(x2) (3x5)2 x2 3x5 = 1 (3x5)2 2. (1 pts) let y = (x 3)(2x2 1) Find dy dx dy dx ...
UGA >> MATH >> 4 (Fall, 2004)
QUIZ-4 solutions 2004 Name: Please show all of your work! Math 2200 Spring Zubeyir Cinkir 1. (1 pts) Evaluate the derivative of the function f (x) = By chain rule, 3x2 2x + 5 6x 2 3x 1 1 .Dx (3x2 2x + 5) = = f (x) = 2 2x + 5 2 2x + 5 2 ...
UGA >> MATH >> 5 (Fall, 2004)
QUIZ-5 Solutions Spring 2004 Name: Please show all of your work! 1. (1 pt) Write the following formulas: a) Area of a sphere with radius r. A = 4r2 Math 2200 Zubeyir Cinkir b) Volume of a cylinder with height h and base radius r. V = r2 h 2. (0.5 ...
UGA >> MATH >> 6 (Fall, 2004)
QUIZ-6 Solutions Name: Please show all of your work! Math 2200 Spring 2004 Zubeyir Cinkir 1. Dierentiate the following functions a) (1 pnt) f (x) = (2 + sin x cos x). f (x) = Dx (sin x) cos x + sin xDx (cos x) = cos x cos x + sin x( sin x) = (cos x...
UGA >> MATH >> 7 (Fall, 2004)
QUIZ-7 Name: Please show all of your work! 1. Dierentiate the following functions a) (1 pnt) f (x) = ex + ln(x). 1 f (x) = ex + x Math 2200 Spring 2004 Zubeyir Cinkir b)(1 pnt) g(x) = ex +x+1 . 2 g (x) = ex +x+1 (2x + 1) 2 c)(1 pnt) h(x) = ln(x4 ...
UGA >> MATH >> 8 (Fall, 2004)
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UGA >> MATH >> 1 (Fall, 2004)
Math 2200 Spring 2004 Instructor: Zubeyir Cinkir Exam 1 Date: Feb. 3, 2003 Duration: 50 min Direction: For full credit, write down your calculations as much as possible and in an organized way, so that it can be used to give a partial credit. Name:...
UGA >> MATH >> 2 (Fall, 2004)
Math 2200 Spring 2004 Instructor: Zubeyir Cinkir Exam 2 Date: March 23, 2003 Duration: 75 min Direction: For full credit, write down your calculations as much as possible and in an organized way, so that it can be used to give a partial credit. Sepe...
UGA >> MATH >> 3 (Fall, 2004)
Math 2200 Spring 2004 Instructor: Zubeyir Cinkir Exam 3 Date: April 22, 2003 Duration: 75 min Direction: For full credit, write down your calculations as much as possible and in an organized way, so that it can be used to give a partial credit. Sepe...
UGA >> MATH >> 1 (Fall, 2004)
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UGA >> MATH >> 2 (Fall, 2004)
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UGA >> MATH >> 3 (Fall, 2004)
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UGA >> MATH >> 3 (Fall, 2004)
QUIZ-3 Name: Please show all your work! Math/CSCI 2610 Spring 2006 Zubeyir Cinkir 1. Determine whether the following is a valid argument. if x2 is irrational, then x is irrational. The number, 2 is irrational. Therefore, the number is irrational....
UGA >> MATH >> 5 (Fall, 2004)
QUIZ-5 Name: Please show all your work! Math/CSCI 2610 Spring 2006 Zubeyir Cinkir 1. Use a table to express the values of the Boolean function F (x, y, z) = x(yz + yz) 2. Find the sum-of-product expansion of the Boolean function F (x, y, z) that e...
UGA >> MATH >> 6 (Fall, 2004)
QUIZ-6 (Take home) Name: Please show all your work! Math/CSCI 2610 Spring 2006 Zubeyir Cinkir 1. Write an algorithm to nd the number of times the function f (n) = n2 n+41 has prime values for 1 n 1000. Then, implement this algorithm in your favor...
UGA >> MATH >> 7 (Fall, 2004)
QUIZ-7 (Take home, due to monday April 10) Math/CSCI 2610 Spring 2006, Zubeyir Cinkir Name: Please show all your work! 1. (1.5 pts) Find as good big-O estimate as possible to the following n (log (n + 5) n+2 + 60 log n 85)( k=1 n k2) 2. (1.5 p...
UGA >> MATH >> 8 (Fall, 2004)
QUIZ-8 (Take home, due to monday April 24) Math/CSCI 2610 Spring 2006, Zubeyir Cinkir Name: Please show all your work! 1. (1.5 pts) Show that there are no integers x , y , z that are solutions to the following equation. 7x2 21y + 5z 2 = 36 2. (1.5 ...
UGA >> MATH >> 5 (Fall, 2004)
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UGA >> MATH >> 6 (Fall, 2004)
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UGA >> MATH >> 7 (Fall, 2004)
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UGA >> MATH >> 8 (Fall, 2004)
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UGA >> MATH >> 1 (Fall, 2004)
Math/Csci 2610 Spring 2006 Instructor: Zubeyir Cinkir Exam 1 Date: Feb. 09, 2006 Duration: 60 min Direction: For full credit, write down your arguments as clearly as possible and in an organized way, (so that also it can be used to give a partial cr...
UGA >> MATH >> 3 (Fall, 2004)
Math/Csci 2610 Spring 2006 Instructor: Zubeyir Cinkir Exam 3 Date: April 13, 2003 Duration: 75 min. Direction: For full credit, write down your arguments as clearly as possible and in an organized way, (so that also it can be used to give a partial ...
UGA >> MATH >> 4 (Fall, 2004)
Math/Csci 2610 Spring 2006 Instructor: Zubeyir Cinkir Exam 4 Date: April 27, 2006 Duration: 70 min Direction: For full credit, write down your arguments as clearly as possible and in an organized way, (so that also it can be used to give a partial c...
UGA >> PUBS >> 109 (Fall, 2008)
What is NAIS? Who is developing it? Why? The National Animal Identification Systm is a national program intended to identify the animals listed on the form inside and record their movements throughout their lives. It is being developed by the U.S. De...
UGA >> MATH >> 03 (Fall, 2008)
Mathematics Department The University of Georgia Math 8100 Homework Assignment 1 Due Date: September 8 in the class Remarks on Homework The homework is an important part of this class. The homework is your best chance to learn the materials in the co...
UGA >> MATH >> 03 (Fall, 2008)
Mathematics Department The University of Georgia Math 8100 Homework Assignment 2 Due date: Sept. 24 before the lecture 4, 5, 7, 8, 9, 10, 14 in section 1.2 and 1.3 of Follands Real Analysis 1 ...
UGA >> MATH >> 03 (Fall, 2008)
Mathematics Department The University of Georgia Math 8100 Homework Assignment 3 Due date: October 1 before the lecture 18, 19, 26, 27, 30, 31 in section 1.3 and 1.4 of Follands Real Analysis 1 ...
UGA >> MATH >> 03 (Fall, 2008)
Mathematics Department The University of Georgia Math 8100 Homework Assignment 4 Due date: October 24 before the lecture 3, 8, 13, 14, 15, 16, 17 in section 2.1 and 2.2 of Follands Real Analysis 1 ...
UGA >> MATH >> 03 (Fall, 2008)
Mathematics Department The University of Georgia Math 8100 Homework Assignment 5 Due date: November 3 before the lecture 19, 20, 21, 22, 23, 25, 26, 27, 28, 32, 34, 35, 39, 44 in section 2.3 and 2.4 of Follands Real Analysis 1 ...
UGA >> MATH >> 03 (Fall, 2008)
Mathematics Department The University of Georgia Math 8100 Homework Assignment 6 Due date: November 17 before the lecture 48,50,55,56,57,58,59,60,61 in the section 2.5 and 2.6. 2,4,6 in the section 3.1 of Follands Real Analysis 1 ...
UGA >> MATH >> 03 (Fall, 2008)
Mathematics Department The University of Georgia Math 8100 Midterm October 16 1. If the set E R has measure zero, then the set {x2 : x E} has measure zero. Prove the statement. Hint: Let S = {x2 , x E}. Show that Sn = S (0, n2 ) has measure zero....
UGA >> MATH >> 03 (Fall, 2008)
Real Analysis: Final Exam Dec. 10, 2003 Print Your Name: Problem Points Score 1 20 2 20 3 10 4 10 5 20 6 20 Total 100 1 1. Let f (x) = sin x . Prove the following statements: x (a) 0 |f (x)|dx = . by repeated integrating exy sin x with respect...
UGA >> MATH >> 03 (Fall, 2008)
Mathematics Department The University of Georgia Math 8100 Homework Assignment 1 Due Date: September 8 in the class Riemann Integrals 1. Let f : [a, b] R be a bounded function. A nite set of points P = {x0 , x1 , , xn } is a partition of [a, b]. ...
UGA >> MATH >> 03 (Fall, 2008)
Mathematics Department The University of Georgia Math 8100 Homework Assignment 2 Due Date: September 24 in the class 4, 5, 7, 8, 9, 10, 14 in section 1.2 and 1.3 of Follands Real Analysis (4). This follows since any countable union can be written as ...
UGA >> MATH >> 03 (Fall, 2008)
Mathematics Department The University of Georgia Math 8100 Homework Assignment 3 Due date: October 1 before the lecture 18, 19, 26, 27, 30, 31 in section 1.3 and 1.4 of Follands Real Analysis (18) (a) By denition, given > 0, there exist Aj A for j =...
UGA >> MATH >> 03 (Fall, 2008)
Mathematics Department The University of Georgia Math 8100 Homework Assignment 4 Due date: October 24 before the lecture 3. By Proposition 2.7, g3 (x) = lim sup fn (x) and g4 (x) = lim inf fn (x) are measurable, and hence so is g3 g4 . The set{x : l...
UGA >> MATH >> 03 (Fall, 2008)
Mathematics Department The University of Georgia Math 8100 Homework Assignment 5 Due date: November 3 before the lecture Here is the solutions of some of the homework problems. Please try to the problems yourself rst. If you really dont know how to s...
UGA >> MATH >> 03 (Fall, 2008)
Mathematics Department The University of Georgia Math 8100 Midterm October 16 1. If the set E R has measure zero, then the set {x2 : x E} has measure zero. Prove the statement. Hint: Let S = {x2 , x E}. Show that Sn = S (0, n2 ) has measure zero....
UGA >> MATH >> 03 (Fall, 2008)
Real Analysis: Final Exam Dec. 10, 2003 1. Let f (x) = sin x . Prove the following statements: x (a) 0 |f (x)|dx = . by repeated integrating exy sin x with respect to x and y. b 0 2 eau Hint: you may need the formula eau sin budu = 2 (a sin bu ...
UGA >> PUBS >> 440 (Fall, 2008)
NUTRITIONAL RESPONSE MODELS Dmitry Vedenov Gene Pesti A workbook to fit data from nutritional experiments to several mo Department of Agricultural and Applied Econ Department of Poultry Science The University of Georgia Athens, Georgia 30602 *IN V...
UGA >> MATH >> 06 (Fall, 2008)
PRINT NAME: Student ID#: Mathematics 4720/6720 - Final Examinations Friday, May 4, 2001 Problem # Points Score 1 25 2 25 3 15 4 15 5 20 bonus 20 Total 120 1 2 1 1.1 (10) Using the method of separation of variables to nd the bounded solution of the...
UGA >> GLY >> 3030 (Fall, 2008)
1 GEOL 3030 (92-416) University of Georgia Spring Semester, 2009 12:20 - 1:10 pm MWF Room 200A GG Professor: Dr. L. Bruce Railsback Phone: 542-3453 Office: 133 GG Lab: 201 GG email: rlsbk@gly.uga.edu Elementary Oceanography: Syllabus Office Hours: ...
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