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...M454 - Boundary Value Problems - Winter 2008 Assignment # 5. Due: Thursday, February 14, 2008. Fourier Series 1. The integration-by-parts formula
b a b b
u(x)v (x) dx = u(x)v(x)
a a
u (x)v(x) dx
is valid for functions u(x) and v(x) are continous...
...M454 - Boundary Value Problems - Winter 2008 Assignment # 3. Due: Thursday, January 31, 2008. 1. Compute the following integrals where m and n are non-negative integers. Look out for special cases. (a) (b) (c)
L 0 cos(nx/L) cos(mx/L) dx L 0 cos(nx/L)...
...Math 605, Fall Term, 2005 Homework #2. To be handed in on Monday, October 3. 1. Let u be a locally bounded function on a set E Rn that takes values in [, +). The upper semicontinuous regularization of u is the function u dened by u (x) = lim sup u(y...
...MATH 451 FIRST MIDTERM EXAM
Solutions. Instructor: B. A. Taylor, Section 2 Fall 2005
1 (1)n n , n = 1, 2, 3, . . . . n
1. ( 30 pts.) Let {sn } be the sequence of real numbers, sn = (a) Write the rst 6 terms of the sequence.
2 1 4 3 6 5 , , , , , ...
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Problems Cooling T (t ) = Temperature of a body at time t unit= T (t ) = rate of change of temperature of the body at time t unit= t H (t ) = rate of increase/decrease in temperature in the body at time t due to internal sources. unit= t unit= M (t ) = Temperature the of outside bath at time t Conductivity constant describes how a material conducts heat energy. Positive, if you heat something it doesn't get cooler. Similar to heat capacity. Difference between body and bath temperature k= T = k (M - T ) + H
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JMU >> M >> 266 (Fall, 2009)
Math/Phys 266E Introduction to Solid Mechanics Tu,Th 11:00 - 12:15, Roop 212 W 8:00 - 8:50, Roop 212 Required Text: Continuum Mechanics, A.J.M. Spencer, Dover. Suggested Text: Continuum Mechanics: Concise Theory and Problems, P. Chadwick, Dover. Prer...
JMU >> M >> 235 (Fall, 2009)
M235 Calculus I (Section 0005) MWF 10:10 - 11:00, Roop 0327 Tu 9:30 - 10:45, Burruss 0139 Text: Calculus by Anton (Special Edition, Volume One) Wiley, 2007. Prerequisite: Sufficient score on the Mathematics Placement Exam. Instructor: Dr. Debra Polig...
JMU >> M >> 266 (Fall, 2009)
Math/Phys 266E Introduction to Solid Mechanics MWF 12:20 - 1:10, Burruss 0130 Th 3:30 - 4:45, Burruss 0032 Text: Continuum Mechanics, A.J.M. Spencer, Longman Scientific and Technical and Wiley, 1988. Available as a JMU Academic Coursepack. Prerequisi...
Oklahoma State >> NSCI >> 2114 (Fall, 2008)
Digestion #1 Find the hidden words within the grid of letters. K P F K A M O H J R H E E Y S V S M A J C P Q I I V E L V D O X Y M O S S F F B V Q I S Q R C M P T O I O D A F H P Z A O I V M L T J M G F S T Z J O J E X M F B K S R P S A M O U T H...
Oklahoma State >> NSCI >> 2114 (Fall, 2008)
Osteoporosis Terms #4 Find the hidden words within the grid of letters. J R C P Z T P A Z I D A D L D T G M W H G U L A X J Q B H N Z X X Y B K I E FW L X J I R K E Q N A V R X T O X O Z B F O N Y U I E K V N Y T H Y C MS Z Q N L O J DWP B Z B N C ...
Oklahoma State >> NSCI >> 2114 (Fall, 2008)
Vitamin Word Search #1 Find the hidden words within the grid of letters. P A N T O T H E N I C A I N P antivitamin apoenzyme ascorbicacid beriberi calciferol carotenes C S N H A P O E N Z Y M E A E O F C O I L T N C I OM L A L I A H G T EW N T N E...
Oklahoma State >> NSCI >> 2114 (Fall, 2008)
Osteoporosis Risk Factors #2 Find the hidden words within the grid of letters. G V A T G L G K M U R R E D N E G X C K L D X V A A O W C F O G Q C W H G R E Z G L C K J D S U R J V A D W T N T X H R K I W Q G Q H O R M O N E K E S U R V I I Q O F...
Oklahoma State >> NSCI >> 2114 (Fall, 2008)
Vitamin Word Search #2 Find the hidden words within the grid of letters. L L E C D O O L B D E R A X D antivitamin apoenzyme ariboflavinosis beriberi calciferol carotene F H Y E S S E N T I A L R E I M E H B E R I B E R I E I R C A N T I V I T A ...
Oklahoma State >> NSCI >> 2114 (Fall, 2008)
Fat Soluble Vitamin Puzzle #1 Find the hidden words within the grid of letters. Can you define each term or associate it with a particular vitamin? O L S A T I E L O E MH A T L I A P C E I T AW WH J N A L anemia anti-hemorrhagic anti-oxidant beta car...
Oklahoma State >> NSCI >> 2114 (Fall, 2008)
Vitamin Word Search #4 Find the hidden words within the grid of letters. T O C O P H E R O L Q T B C S antivitamin apoenzyme ascorbicacid beriberi biotin A P O E N Z Y M E B I O T I N B E R I B E R I R E T I N O L R I B O F L A V I N X H I J I P...
Oklahoma State >> NSCI >> 2114 (Fall, 2008)
Osteoporosis Risk Factors #5 Find the hidden words within the grid of letters. A P L T E B XWG G H Y WT P WB P U FW B K J E M I B QO D MS S L C Q P X T HG A T M NO I T D T HQ J A L C V GO H C U H R R Y H U D P S J G B Activity Age Alcohol P T F P K...
Oklahoma State >> NSCI >> 2114 (Fall, 2008)
Cardiovascular Disease Risk Factors #2 Find the hidden words within the grid of letters. Q N W W K P L X S G D R E O F N B D P H Q E N N S L E X I Y O N T A R E L A P M N I C X K H O O O M S O Y B H Z R Z B K B N U W N Q G I A R U Y I E B J S R O...
Oklahoma State >> NSCI >> 2114 (Fall, 2008)
Cardiovascular Disease Risk Factors #1 Find the hidden words within the grid of letters. V C I A P N J N H G R F Y J M O I I M C U B H E J E K J L M P O A I N A X P O X J J G G Q I M I L N N R O X R H A I N R J D D D U Q E T J Y I M O B U B K V L...
Oklahoma State >> NSCI >> 2114 (Fall, 2008)
Cardiovascular Disease Risk Factors #4 Find the hidden words within the grid of letters. S X X S P P V Z A H D B J E K R G U K Y F V Z Z WO U I HO K D CW L X X L R A T R I U U A MB U H Alcohol Cholesterol Diabetes J L E G F H R T S K B Y K U G I I ...
Oklahoma State >> OKLAHOMA >> 4 (Fall, 2009)
Name _ Find Your Way on the Farm Study the map grid of the farm. Use the grid to complete the questions below. 1 A Pear Tree Lane B Market Street 2 3 4 5 6 7 Farm Road C Tractor Trail D Crop Avenue Key: fence tractor cow wheat field milk truck ba...
Oklahoma State >> OKLAHOMA >> 4 (Fall, 2009)
Skills: Language Arts Background tats. Objective: Students research, interview experts and design pollinator habiPollination is the transfer of pollen grains from the anther to the stigma of the same or another flower. Pollination is required to pro...
Oklahoma State >> OKLAHOMA >> 4 (Fall, 2009)
How Reliable Are Your Sources? well-researched sources. When conducting research, make sure you use reliable information from legitimate sources. Reliable information is well-researched from sources that are well-respected and as objective, or neutr...
Oklahoma State >> OKLAHOMA >> 4 (Fall, 2009)
By the Pound Objective: The student will estimate the weight and cost of produce and calculate the actual price. Background Whether you are a student buying an apple for lunch or a farmer selling wheat, you have to have a way to measure whatever it i...
Oklahoma State >> OKLAHOMA >> 4 (Fall, 2009)
Barnyard Bingo Skills: Language Arts, Mathematics Objective: sounds and mark farm animal bingo cards as they recognize the correct sounds. Talking animals are the subject for many popular books and movies. Although farmers can\'t exactly talk to their...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Final exam (1) Find the interval of convergence of of the interval. 0 1 0 (2) Calculate eigenvalues and eigenvectors of matrix A = 6 1 0 . 0 0 0 (3) Calculate the triple scalar product (ABC) if A = i - 2j, B = j - 2k, C = k - 2i. (4)...
Oklahoma State >> HEP >> 0 (Fall, 2009)
Alexander Khanov Department of Physics Oklahoma State University 145 Physical Sciences Building Stillwater, OK 74078-3072 Phone: (405) 744 2404 Fax: (405) 744 6811 e-mail: alexander.khanov@okstate.edu Education Ph.D. in Physics, University of Roche...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Homework #3 (due 9/12) The numbers in parentheses after the problem number indicate points for each problem. 2x + 3y P1(10) (Boas 2.7) Solve x x = 1 + 2y = 2 + 3y = 5 P2(10) (Boas 2.10) Solve x + 2y - z = 1 2x + 3y - 2z = ...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Homework #8 (due 10/24) The numbers in parentheses after the problem number indicate points for each problem. P1(10) (Boas 2.5) Solve by separating variables: xy - xy = y, y(1) = 1 P2(10) (Boas 3.8) Solve (x ln x)y + y = ln x P3(10) (Bo...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Homework #12 (due 11/21) The numbers in parentheses after the problem number indicate points for each problem. P1(10) (Boas 1.1) Solve by series and by an elementary method and verify that the two solutions agree: xy = xy + y. P2(10) (B...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Homework #5 (due 9/26) The numbers in parentheses after the problem number indicate points for each problem. P1(10) (Boas 1.6) For u = ex cos y, verify that (a) 2u 2u 2u 2u = ; (b) + 2 = 0. xy yx x2 y P2(10) (Boas 2.6) Find the two-var...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Homework #2 (due 9/5) The numbers in parentheses after the problem number indicate points for each problem. P1(10) (Boas 5.6) Calculate 1+i 1-i 2 P2(10) (Boas 5.47) Solve z 3 = -1 P3(10) Solve z + |z| = 0 P4(10) (Boas 5.59) Find and dr...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Homework #7 (due 10/13) The numbers in parentheses after the problem number indicate points for each problem. P1(10) (from Boas 3.1) If A = (2, -1, -1), B = (2, -3, 1), C = (0, 1, 1), find (A B) C, A (B C), (A B) C, A (B C). P2(...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Midterm II: solutions (1) The result is 8 times the mass of a pyramid inclosed by the coordinate planes and the 1 1 1 z (1 z)2 dz. Answer: . plane x + y + z = 1 (Boas Ch.5, Problem 3.9c), or 8 2 3 0 (2) F = (x x)i + (y y)j + (z z)k...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Homework #1 (due 8/29) The numbers in parentheses after the problem number indicate points for each problem. P1(10) (Boas 6.7) Test for convergence using the integral test: 1 n ln n n=2 P2(10) (Boas 6.24) Test for convergence using t...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Homework #10 (due 11/7) The numbers in parentheses after the problem number indicate points for each problem. P1(20) (Boas 5.7, 6.14) (a) Expand in a Fourier series: f (x) = (b) Using the previous result, find 0, - < x < 0, x, 0 < x < ....
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Homework #9 (due 10/31) The numbers in parentheses after the problem number indicate points for each problem. P1(10) (Boas 1.21) Find the real and imaginary parts u(x, y) and v(x, y) of f (z) = e iz P2(10) (Boas 3.7) Evaluate dz along t...
Oklahoma State >> HEP >> 0 (Fall, 2009)
Syllabus: Mathematical Physics, PHYS 3513 Instructor: Alexander Khanov, office PS 208B, phone 744-2404 e-mail: alexander.khanov@okstate.edu course web site: http:/hep0.okstate.edu/khanov/phys3513.html Time and location: MWF 12:301:20, PS 121 Text: ...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Midterm II (1) Find the mass of the octahedron with vertices (1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 0, 0), (0, 1, 0), (0, 0, 1) (see sketch), if the density is proportional to |z|. z 1 -1 1 y 1 -1 x -1 (2) Verify that the function F ...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Homework #11 (due 11/14) The numbers in parentheses after the problem number indicate points for each problem. 1 3 P1(20) (Boas 5.1,5.7) Given = , (a) find ; (b) find the Laplace transform of 2 2 1/ t (use the table on p. 469 of the...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Homework #6 (due 10/3) The numbers in parentheses after the problem number indicate points for each problem. P1(10) Find the area: y 1 sin(x) cos(x) 0 /4 x P2(20) (Boas 2.42,44) Find (a) the volume, and (b) the mass of the solid betwe...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Midterm I (1) Find the interval of convergence, including end-point tests, for xn n2 . 5n (n2 + 1) n=1 (2) Show that |z|2 = cz + c (c is an arbitrary complex constant) describes a circle, and z find its center and radius. (3) Calcula...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Midterm I: solutions (1) lim |x| an+1 , so the series converges if |x| < 5 and diverges if |x| > 5. At |x| = 5, = an 5 an does not tend to zero, so the series diverges. Answer: |x| < 5. n (2) Let z = x+iy, c = a+ib, then |z|2 = x2 +y ...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Homework #4 (due 9/19) The numbers in parentheses after the problem number indicate points for each problem. P1(10) (Boas 5.10) Find symmetric and parametric equations of a line through (3, 4, -1) and parallel to 2i - 3j + 6k. P2(10) (B...
Oklahoma State >> PHYS >> 3513 (Fall, 2008)
Physics 3513, Final exam: solutions (1) The series converges if lim |x - 1| an+1 < 1, or -1 < x < 3, and diverges if = an 2 1 1 x < -1 or x > 3. At x = -1, the series -1 + - + . . . converges, and at x = 3, the 2 3 1 1 series 1 + + + . . . diverges. ...
Oklahoma State >> CALC >> 3 (Fall, 2009)
Math 2163 Calculus 3 Fall 08 Sample Final 1 (1) Find the distance from the origin to the line given by x = 1 + t, y = 2 - t and z = -1 + 2t. (2) Find the tangent plane and normal vector to the surface xy 2 z 3 = 2 at the point (2, 1, 1). (3) Find the...
Oklahoma State >> CALC >> 3 (Fall, 2009)
Math 2163 Calculus 3 Fall 08 Sample Midterm 3 1. Evalate 1 0 1 x3 sin(y 3 )dydx x2 by reversing the order of integration. 2. Use polar coordinates to nd the volume of the solid bounded by z = 3x2 + 3y 2 and z = 4 x2 y 2 . 3. Find the center of ma...
Oklahoma State >> CALC >> 3 (Fall, 2009)
Math 2163 Calculus 3 Fall 08 Sample Midterm 1 (1) Use the gradient vector to find the tangent plane to the surface described by 2ex+y =1 x+z at the point (1, -1, 1). (2) Find the local maxima, local minima and saddle points of the function 1 f (x, y...
Oklahoma State >> CALC >> 3 (Fall, 2009)
Math 2163 Calculus 3 Fall 08 Sample Final 2 (1) Find a vector perpendicular to the plane through the points (1, 0, 0), (2, 0, 1) and (1, 4, 3), and nd the area of the triangle whose vertices are those three points. (2) Find all rst and second order p...
Oklahoma State >> CALC >> 3 (Fall, 2009)
...
Oklahoma State >> MATH >> 2233 (Fall, 2008)
Quiz # 7 Math 2233, Differential Equations Oct. 23, 2008 1. Find the general solution to y (4) + 3y - 4y = 0 Solution. The characteristic equation is r4 + 3r2 - 4 = 0 (r2 + 4)(r2 - 1) = 0 (r - 2i)(r + 2i)(r - 1)(r + 1) = 0 r1 = 2i, Hence the gen...
Oklahoma State >> MATH >> 2163 (Fall, 2008)
Math 2163, Practice Final Exam 1. Please read through previous practice exams. Problem types that have appeared in previous practice exams will not be repeated here! 2. Find the three angles of the triangle with given vertices A(1, 0), B(3, 6), C(-1,...
Oklahoma State >> MATH >> 2153 (Fall, 2008)
Trigonometry csc = tan = cot = 1 sin sin cos 1 tan sec = cot = 1 cos cos sin sin2 + cos2 = 1 1 + cot2 = csc2 cos() = cos sin(/2 ) = cos tan(/2 ) = cot cos(x + y) = cos x cos y sin x sin y cos(x y) = cos x cos y + sin x sin y t...
Oklahoma State >> MATH >> 5543 (Fall, 2008)
Programming assignment 3 1. Consider the following problem: ut + ux = uxx for x [0, 1], t 0, u(0, x) = 1 - x for x [0, 1], u(t, 0) = 1, u(t, 1) = 0. (a) Set = 1, solve the problem using the forward-time central-space scheme with h = 1/20, = ...
Oklahoma State >> MATH >> 2163 (Fall, 2008)
Math 2163, Exam I, Sept. 21, 2007 Name: Score: 1. (12 points) Calculate the following (please write your final answer on the line): (a) 3 < 2, 1, -1 > -2 < 0, 4, 2 >= < 6, -5, -7 > (b) | < -1, 4, 3 > | = (-1)2 + 42 + 32 = 26 (c) (i - j + k) ...
Oklahoma State >> MATH >> 2163 (Fall, 2008)
Math 2163, Practice Exam I, Solution 1. 14, 3a + 4b =< 15, 7, 34 >, a b = 3,a b =< 5, 33, 9 >; (b) |a| = 6, 3a + 4b =< 3, 2, 11 >, a b = 0,a b =< 5, 2, 1 >. (a) |a| = 5 j. 13 12 i 13 5 (a) = arccos 21 , skew; 2. 3. (b) = arccos 3 , skew; ...
Oklahoma State >> MATH >> 2153 (Fall, 2008)
Math 2153, Exam I, Feb. 7, 2008 Name: Score: Each problem is worth 5 points. The total is 50 points. 1. Solve the equation for x. 2 ln x = ln 2 + ln(3x - 4) Solution Using the property of logarithmic functions, we have ln x2 = ln[2(3x - 4)] x2 = 2(...
Oklahoma State >> MATH >> 2233 (Fall, 2008)
Math 2233, Exam I, Sept. 16, 2008 Name: Score: Part 1: Multiple choice. Each question is worth 4 points. 1. ( e ) Consider the autonomous differential equation y = f (y). The graph of f (y) is given in below. Then, about the equilibrium solution...
Oklahoma State >> MATH >> 2163 (Fall, 2008)
Quiz # 4 Math 2163, Calculus III Sept. 14, 2007 Show all your work neatly and concisely, and indicate your nal answer clearly. 1. Given f (x, y) = ln(3x + 5y), nd all the rst and second order partial derivatives. Solution: fx = fy = fxx = fyy = fxy...
Oklahoma State >> MATH >> 2233 (Fall, 2008)
...
Oklahoma State >> MATH >> 2233 (Fall, 2008)
Quiz # 6 Math 2233, Dierential Equations Oct. 8, 2008 1. Find the general solution to y + 4y + 4 = t2 e2t , Formula for variation of parameters: t t>0 t t0 Y = y1 (t) t0 y2 (s)g(s) ds + y2 (t) W (s) y1 (s)g(s) ds W (s) Solution: Step 1: Compu...
Oklahoma State >> MATH >> 2233 (Fall, 2008)
Quiz # 5 Math 2233, Differential Equations Oct. 2, 2008 1. Find the general solution to y - y - 2y = 4t + sin t - 3 cos t Solution: We solve the problem in following steps: Step 1. Compute y1 , y2 which are solutions to the associated homogeneous ...
Oklahoma State >> MATH >> 2233 (Fall, 2008)
MATH 2233 - SPRING 2009 - QUIZ 0 SOLUTIONS 1. Factor x2 - 7x + 10. Solution: We need to find a and b such that x2 -7x+10 = (x-a)(x-b). Since (x - a)(x - b) = x2 - (a + b)x + ab, we need a + b = 7 and ab = 10. Examining the factors 1, 2, 5, and 10 of ...
Oklahoma State >> MATH >> 3013 (Fall, 2008)
SUPPLEMENTARY PROBLEMS FOR SECTION 5.1 Find the characteristic polynomial and the real eigenvalues of the given matrix. (These problems involve cases where the characteristic polynomial does not have an obvious factor you can bring out early in its c...
Oklahoma State >> MATH >> 3013 (Fall, 2008)
MATH 3013 - SUMMER 2008 - EXAM I, VERSION 1 Do all of your work in your blue book. Show all your work. Justify your answers. Write down all of the algebraic steps and numerical calculations involved in getting the answer. If a problem specifies a par...
Oklahoma State >> MATH >> 3013 (Fall, 2008)
SUPPLEMENTARY PROBLEMS FOR SECTION 5.3 A. Use diagonalization to compute Ak and A10 , where A = 1 0 . 1 2 (1 ) 0 , so we get that 1 (2 ) p() = (1 )(2 ), and hence 1 = 1 and 2 = 2. 0 0 1 1 For = 1 we have AI = which has REF . Setting x2 = t, 1 1...
Oklahoma State >> MATH >> 3013 (Fall, 2008)
MATH 3013 - SUMMER 2008 - EXAM II, VERSION 2 SOLUTIONS Do all of your work in your blue book. Show all your work. Justify your answers. Write down all of the algebraic steps and numerical calculations involved in getting the answer. If a problem spec...
Oklahoma State >> MATH >> 3013 (Fall, 2008)
MATH 3013 - SUMMER 2008 - EXAM I, VERSION 2 SOLUTIONS Do all of your work in your blue book. Show all your work. Justify your answers. Write down all of the algebraic steps and numerical calculations involved in getting the answer. If a problem speci...
Oklahoma State >> MATH >> 3013 (Fall, 2008)
MATH 3013 - SUMMER 2008 - EXAM II, VERSION 2 Do all of your work in your blue book. Show all your work. Justify your answers. Write down all of the algebraic steps and numerical calculations involved in getting the answer. If a problem specifies a pa...
Oklahoma State >> MATH >> 3013 (Fall, 2008)
MATH 3013 - SUMMER 2008 - EXAM II, VERSION 1 Do all of your work in your blue book. Show all your work. Justify your answers. Write down all of the algebraic steps and numerical calculations involved in getting the answer. If a problem specifies a pa...
Oklahoma State >> MATH >> 3013 (Fall, 2008)
QUIZ #2 - SUMMER 2008 1. Find all solutions (x1 , x2 , x3 , x4 ) of the system with augmented matrix 0 1 -2 0 1 0 0 1 -5 4 . 0 0 0 0 0 Solution: We have pivots in the second and third columns, so our bound variables are x2 and x3 . The remainin...
Oklahoma State >> MATH >> 3013 (Fall, 2008)
QUIZ #3 - SUMMER 2008 1. V = R2 with [a, b] [c, d] = [b, c] and r a vector space. [a, b] = [ra, rb]. Show that V is NOT Solution: Remember, to show that something is NOT a vector space you just have to nd ONE example of ONE of the eight laws being ...
Oklahoma State >> MATH >> 3013 (Fall, 2008)
MATH 3013 - SUMMER 2008 - EXAM I, VERSION 1 SOLUTIONS Do all of your work in your blue book. Show all your work. Justify your answers. Write down all of the algebraic steps and numerical calculations involved in getting the answer. If a problem speci...
Oklahoma State >> MATH >> 3013 (Fall, 2008)
MATH 3013 - SUMMER 2008 - EXAM I, VERSION 2 Do all of your work in your blue book. Show all your work. Justify your answers. Write down all of the algebraic steps and numerical calculations involved in getting the answer. If a problem species a parti...
Oklahoma State >> MATH >> 3013 (Fall, 2008)
SUPPLEMENTARY PROBLEMS FOR SECTION 6.3 Orthogonally diagonalize the given matrix. 0 A. A = 1 0 1 p() = 0 1 0 0 0 . 0 1 1 0 0 = (2 1)(1 ) = ( + 1)( 1)2 . 0 (1 ) So the eigenvalues are 1 = 1 and 2 = 1. 1 1 For 1 = 1 we have A + I = 1 1 ...
Oklahoma State >> MATH >> 3013 (Fall, 2008)
QUIZ #4 - SUMMER 2008 1. Find the 5 0 A= 0 characteristic polynomial (in factored form) and all the eigenvalues of 1 2 1 -3 . 2 6 (5 - ) 1 2 0 (1 - ) -3 0 2 (6 - ) = (5 - ) (1 - ) -3 2 (6 - ) = Solution: p() = (5 - )[(1 - )(6 - ) - -6] = (5 - )[...
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