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# Worksheet 13 - 2006 Due Thursday 20th April 9pm This worksheet gives you some more practice at problem solving using mathematica. PROBLEM 1. Make a 3-d plot of the function Sin(xy) for x [0, 3] and y [0, 3]. PROBLEM 2. Numerically find the roots to the equation x6 - 4x2 = 2. How many are real and how many are imaginary? PROBLEM 3. Solve the following equation analytically using mathematica d2 x/dt2 + 5x = 1.5sin(2t), with the initial conditions x(0) = 1, x (0) = 0. Plot the resulting solution. Give an example of a physical system which leads to this equation. In the system you have chosen what are the units of the numbers 5,1.5 and 2 appearing in the equation. PROBLEM 4. Four point charges are placed at the corners of a square, with q1 = 10-6 C at (0,1), q2 = -2 10-6 C at (1,1), q3 = -3 10-6 C at (0,0) and q4 = 2 10-6 C at (1,0), with the distances measured in centimeters. - a) Find an expression for the electrostatic potential , V , at arbitrary position (x,y). Note that the contribution of each charge to the total electrostatic potential is simply Kq/r. It is a scalar. The total electrostatic potential at any point is a sum of the electrostatic potential s for each of the point charges lying on the square). Make a 3-d plot of this potential on the interval (0.05,0.95). - b) Find the vector force on a charge q0 = 1 10-6 C placed at position (2,1). Note that the force is related to the electric field via F = q E. The electric field is related to the electrostatic potential by E = - V . 1
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Michigan State University >> PHY >> 102 (Spring, 2006)
Worksheet #4 - PHY102 (Spr. 2006) Solving equations Solving equations in Mathematica Look up how to solve algebraic equations exactly(Solve) and numerically(NSolve). If you have a transcendental equation (e.b. x = sin(x) you need to use \"FindRoot\". I...
Michigan State University >> PHY >> 410 (Spring, 2007)
1. (6 pts) Free energy of a two state system. (a) Find an expression for the free energy as a function of =kBT of a system with two states, one at energy 0 and one at energy . (b) From the free energy, find expressions for the energy and entropy of t...
Michigan State University >> PHY >> 410 (Spring, 2007)
Physics 410 Homework 9: 1. 2. 3. 4. 5. 6. (8 pts) (6 pts) (5 pts) (6pts) (4 pts) (5 pts) Problem 5.32 Problem 5.34 Problem 5.48 Problem 5.49 Problem 5.51 Problem 5.53 from Schroeder. from Schroeder. from Schroeder. from Schroeder. from Schroeder. fro...
Michigan State University >> PHY >> 410 (Spring, 2007)
Physics 410 Homework 13: 1. 2. 3. 4. 5. 5. (10 pts) (5 pts) (4 pts) (4 pts) (5 pts) (8 pts) Problem 7.28 Problem 7.31 Problem 7.37 Problem 7.39 Problem 7.45 Problem 7.46 from Schroeder. from Schroeder. from Schroeder. from Schroeder. from Schroeder. ...
Michigan State University >> PHY >> 410 (Spring, 2007)
Physics 410 Homework 6: 1. (10 pts) 2. (3 pts) 3. (12 pts) 4. (6 pts) 5. (4 pts) 6 . (7 pts) Problem 3.25 from Schroeder. Problem 3.33 from Schroeder. Problem 3.34 from Schroeder. Problem 3.37 from Schroeder. Problem 3.38 from Schroeder. Problem 3.39...
Michigan State University >> PHY >> 410 (Spring, 2007)
Physics 410 Homework 7: 1. (4 pts) 2. (8 pts) 3. (8 pts) 4. (4 pts) 5. (4 pts) 6 . (5 pts) 7 . (6 pts) 8 . (10 pts) Problem 4.4 Problem 4.6 Problem 4.14 Problem 4.17 Problem 4.19 Problem 4.20 Problem 4.30 Problem 4.33 from Schroeder. from Schroeder. ...
Michigan State University >> PHY >> 410 (Spring, 2007)
Physics 410 Homework 5: 1. (4 pts) Problem 3.1 from Schroeder. 2. (3 pts) Problem 3.4 from Schroeder. 3. (5 pts) Problem 3.8 from Schroeder. 4. (6 pts) Problem 3.10 from Schroeder. 5. (4 pts) Problem 3.14 from Schroeder. 6. (3 pts) Problem 3.19 from ...
Michigan State University >> LIR >> 832 (Spring, 2007)
LIR 832 Qualifying Examination: Spring, 2004 This examination consists of 10 equally weighted questions which require basic knowledge of statistics. The examination lasts two hours, additional time will not be provided. Z and T tables are attached at...
Michigan State University >> PHY >> 321 (Spring, 2006)
Physics 321 Spring 2006 Homework #7, Due at beginning of class Wednesday Mar 15. 1. [8 pts] A \"triangle wave\" can be defined by F (t) = 1 - 2|t|/ for -/ < t < +/, with F (t) defined at all other values of the time t by the property of having period ...
Michigan State University >> PHY >> 321 (Spring, 2006)
PHYSICS 321 EXAM 3 April 18, 2005 NAME 1. [5 pts] Imagine a peculiar cloud of cosmic dust whose mass distribution is spherically symmetric with a density (mass per unit volume) given by (r) = k r 2 where r is the distance from the center and k is...
Michigan State University >> PHY >> 321 (Spring, 2006)
Physics 321 Spring 2006 Homework #6, Due at beginning of class Wednesday Mar 1. 1. [4 pts] A hook is at height y above the floor, where y is constant for all negative times: y = y0 for t < 0. For positive times, y oscillates: y = y0 + A sin t for t ...
Michigan State University >> PHY >> 321 (Spring, 2006)
PHYSICS 321 FINAL EXAM May 4, 2005 NAME 1. [5 pts] A particle of mass M moves in one dimension in the potential V (x) = a + bx where a and b are constants. Find all possible motions x(t). 2. [5 pts] The motion of a system with two degrees of freedom...
Michigan State University >> PHY >> 410 (Spring, 2007)
Tentative Schedule: Week 1 2 3 4 5 6 7 8 Spring 9 10 11 12 13 14 15 Finals Month Jan Jan Jan Jan/Feb Feb Feb Feb Feb/Mar Break Mar Mar Mar/Apr Apr Apr Apr Apr April 22 29 5 12 19 26 5 12 19 26 2 9 16 23 30: M 8 W 10 17 24 31 7 14 21 28 7 14 21 28 4 1...
Michigan State University >> PHY >> 410 (Spring, 2007)
Physics 410 Homework 12: 1. 2. 3. 4. 5. (6 pts) (6 pts) (12 pts) (7 pts) (14 pts) Problem 7.2 Problem 7.6 Problem 7.8 Problem 7.16 Problem 7.23 from Schroeder. from Schroeder. from Schroeder. from Schroeder. from Schroeder. ...
Michigan State University >> PHY >> 410 (Spring, 2007)
Physics 410 Homework 2: 1. 2. 3. 4. 5. 6. 7. Problem 1.36 from Schroeder. Problem 1.40 from Schroeder. Problem 1.41 from Schroeder. Problem 1.44 from Schroeder. Problem 1.50from Schroeder. Problem 1.60 from Schroeder. Problem 1.63 from Schroeder. ...
Michigan State University >> PHY >> 410 (Spring, 2007)
Physics 410 Homework 4: 1. 2. 3. 4. 5. 6. (7 pts) Problem 2.30 from Schroeder. (4 pts) Problem 2.31 from Schroeder. (4 pts) Problem 2.32 from Schroeder. (4 pts) Problem 2.34 from Schroeder. (4 pts) Problem 2.37 from Schroeder. (6 pts) Problem 2.39 fr...
Michigan State University >> PHY >> 410 (Spring, 2007)
Physics 410 Homework 1: 1. 2. 3. 4. 5. 6. 7. Problem 1.8 from Schroeder. Problem 1.16 from Schroeder. Problem 1.21 from Schroeder. Problem 1.22 from Schroeder. Problem 1.25 from Schroeder. Problem 1.26 from Schroeder. Problem 1.33 from Schroeder. ...
Michigan State University >> PHY >> 410 (Spring, 2007)
Physics 410 Homework 3: 1. 2. 3. 4. 5. 6. 7. Problem 2.2 from Schroeder. Problem 2.6 from Schroeder. Problem 2.13 from Schroeder. Problem 2.17 from Schroeder. Problem 2.19 from Schroeder. Problem 2.23 from Schroeder. Problem 2.27 from Schroeder. ...
Michigan State University >> PHY >> 102 (Spring, 2006)
Worksheet #2 - PHY102 (Spr. 2006) Formats and List operations (Vectors) Formating From the toolbar do the following: \"format\" followed by \"style\", the dropdown menu offers you lots of options. \"input\" is the default, and is the \"format\" in which you ...
Michigan State University >> PHY >> 102 (Spring, 2006)
Worksheet #3 - PHY102 (Spr. 2006) Matrices and linear algebra Last week we did vector operations with lists. This week we introduce you to matrices, their representation using lists and to some of the matrix operations which Mathematica is able to do...
Michigan State University >> PHY >> 102 (Spring, 2006)
Worksheet #9 - PHY102 (Spr. 2006) Due Thursday March 23rd More on \"Do loops\", Illustrating Chaos Tools that you need You will need the following this week (look them up in the online help): Do (you can also use Table or NestList) You will also need ...
Michigan State University >> PHY >> 102 (Spring, 2006)
Worksheet #6 - PHY102 (Spr. 2006) Generating and plotting lists of numbers, \"Do\" loops and animation - due Thursday February 23rd We often ask a computer to do an operation many times. There are a large number of ways of doing these \"iterative\"tasks ...
Michigan State University >> PHY >> 102 (Spring, 2006)
Review and Examples (Spr. 2006) Due Thursday 6th April These are examples of questions with the degree of difficulty that you will encounter in the lab-exam. Make sure that you can do them! Use Mathematica to solve all parts of the problems Vectors P...
Michigan State University >> PHY >> 102 (Spring, 2006)
Worksheet #1 - PHY102 (Spr. 2006) This worksheet introduces you to the use of Mathematica. Mathematica is a programming language developed by Stephen Wolfram which has many applications,e.g., solving algebraic equations, differentiation, integration,...
Michigan State University >> PHY >> 102 (Spring, 2006)
Worksheet #10 - PHY102 (Spr. 2006) The wave and diffusion equations Due Thursday March 30th In this worksheet we will study two partial differential equations that are very important in physics. Many wave motions can be described by the linear wave e...
Michigan State University >> PHY >> 102 (Spring, 2006)
Worksheet #5 - PHY102 (Spr. 2006) Solving Equations and Differential Equations II Due Thursday February 16th Last week you learned about the following functions which are among the most important in Mathematica: Solve - solves polynomial equations a...
Michigan State University >> PHY >> 102 (Spring, 2006)
Worksheet #8 - PHY102 Motion in a potential Although you first learn about Newton\'s second law F = ma and the dynamics that results from it, much of the discussion in the more advanced physics texts is in terms of \"potentials\" V (r). A particle under...
Michigan State University >> CSE >> 422 (Spring, 2008)
CSE 422 Lab 3: Task How-To You will need to edit both the server and client In the server code: Add an member variable to the struct user object near the top of the file: sockaddr_in address; (This will be used to store the address of the client re...
Michigan State University >> CSE >> 422 (Spring, 2008)
CSE 422 Lab 3: Sending Image Files in a Chat Room Overview: As in Lab 2, the general application is that of a chat room, where clients connect to a server and can communicate with each other. Now we want you to add the ability for a client to send an...
Michigan State University >> CSE >> 422 (Spring, 2008)
CSE 422 Spring 2008 Lab 1: Simple log-in and connect client and server Objective: This lab will introduce you to socket programming using both UDP and TCP connections. You will create both a client and the server program. The client will send a usern...
Michigan State University >> CSE >> 422 (Spring, 2008)
CSE 422 Homework #1 Due at the Beginning of Class Thursday, March 13 Spring 2008 Name: Score: /100 Please write your answers CLEARLY on these sheets, which will assist the TA in grading. You must show all your work! A correct numerical answer w...
Michigan State University >> CSE >> 422 (Spring, 2008)
1 CSE 422 Name: Practice Problems Spring 2008 1. (22 points total) Consider a checkout lane in the supermarket. Customer arrivals are Poisson with a mean arrival rate of one customer every four minutes. The service times are exponen tially distri...
Michigan State University >> LIR >> 832 (Spring, 2007)
LIR 832 Qualifying Examination: Spring, 2004 This examination consists of 10 equally weighted questions which require basic knowledge of statistics. The examination lasts two hours, additional time will not be provided. Z and T tables are attached at...
Michigan State University >> LIR >> 832 (Spring, 2007)
LIR 832 Qualifying Examination: Summer 2004 This examination consists of 10 equally weighted questions which require basic knowledge of statistics. The examination lasts two hours, additional time will not be provided. Z and T tables are attached at ...
Michigan State University >> LIR >> 832 (Spring, 2007)
LIR 832 Qualifying Examination: Summer 2004 This examination consists of 10 equally weighted questions which require basic knowledge of statistics. The examination lasts two hours, additional time will not be provided. Z and T tables are attached at...
Michigan State University >> CE >> 421 (Spring, 2005)
CE 321 Lab # 3 Bernoulli\'s Equation General Info: - Hand in Pre-lab Questions - Worksheet and Spreadsheets (sent by email) due Thursday by 5 pm - Lab Reports due Tuesday by 5 pm (both Hardcopy and Electronic) - www.egr.msu.edu/cee/techcomm Experim...
Michigan State University >> CE >> 421 (Spring, 2005)
CE 321 Lab # 2 Flow Rate Measurement General Info: - Hand in Pre-lab Questions - Worksheet and Spreadsheets due Thursday by 5 pm - Lab Reports due Tuesday by 5 pm (both Hardcopy and Electronic) - www.egr.msu.edu/cee/techcomm Experiment Objectives:...
Michigan State University >> CE >> 421 (Spring, 2005)
CE 321 Lab # 4 Momentum Flux Make sure you write down anything you see during the experiment that may help you answer the questions asked in the memo. Experiment Theory: How do forces exerted by a liquid jet impacting targets of different shapes...
Michigan State University >> CE >> 421 (Spring, 2005)
CEE 321 Fluid Mechanics Laboratory Writing Seminar COPE Clarity Organization Precision Economy Plagiarism: ZERO TOLERANCE If a group or person is caught submitting someone else\'s work as their own; that group or person will be given a 0.0 for the ...
Michigan State University >> PHY >> 321 (Spring, 2006)
PHYSICS 321 EXAM 1 Feb 16, 2005 NAME 1. [3 pts] The location of a particle of mass M is given by ^ r = C1 cos( t) ^ + C2 eB t ^ + C3 t3 k i j as a function of the time t, where C1 , C2 , C3 , B, and are constants. Find the component of force in ...
hw6
Michigan State University >> MATH >> 421 (Fall, 2007)
M421 HW 6 Due Friday Nov. 30 From Wade Section 11.4 11.5 11.6 Page Number 350-351 357-358 368 Problems 2, 3, 8 1, 5a, 7 3 Non-book Exercises 1) Let be a curve in R3 , = (t) = (1 (t), 2 (t), 3 (t) t [0, 1] , where C 2 ([0, 1], R3 ) satisfies (...
UGA >> POLS >> 1101 (Summer, 2008)
Hill Committees o Democratic Congressional Campaign Committee DCCC, D Triple-C, D-Trip o National Republican Congressional Committee NRCC o Raise money to get/keep members of their party into Congress 3 types of candidates o Incumbent o Challenger ...
UGA >> POLS >> 1101 (Summer, 2008)
Politicians look for ways to connect with people o Candidates become extremely capable of targeting people Find out when and how they vote If you\'re a democrat, get as many blacks to the polls as possible o Walkin Lawton Mainor Chiles walked acros...
UGA >> POLS >> 1101 (Summer, 2008)
1. Legislature 1. Govern 2. Create Laws 3. Executive Oversight i. Impeach 1. Treason 2. Misdemeanor 3. High Crimes 4. Senate has power to approve Presidential Appointment 5. 25 years old for House, 30 for Senate 6. 16 women Senators, 70 total i. Firs...
UGA >> POLS >> 1101 (Summer, 2008)
I. Legislature A. State House 1. Speaker of the Georgia House Glenn Richardson a) Republican b) Does not get along with governer c) Potential challenge for Speaker (1) 2. David Ralston Speaker Protemp a) Mark Burkholter 3. Run for Governer a) Jer...
UGA >> POLS >> 1101 (Summer, 2008)
I. II. III. IV. V. Bill through the Senate A. 100 Senators vs. 435 House members B. Senate, hearings happen in committee; house happens in sub-committee C. Senate does not have committee with same function as Rules Committee D. UCA Unanimous Co...
UGA >> POLS >> 1101 (Summer, 2008)
I. II. III. IV. V. Incumbency\'s Power A. How they keep their position 1. Send newsletters to households a) Costs a lot of money b) Paul Brown (1) Sent out 10 mass mailings (2) Spent office in one year (3) Spent the bulk of his budget on newslett...
UGA >> POLS >> 1101 (Summer, 2008)
I. II. III. IV. V. VI. VII. VIII. IX. X. Georgia Governor A. OPB Office of Planning a Budget 1. Fiscal year begins in July 2. Has line item veto B. Sets the state revenue estimate to keep state out of debt C. Supplemental Budget 1. When the...
UGA >> POLS >> 1101 (Summer, 2008)
I. Getting Involved 1. To get involved in politics, you could Help in a campaign Lobby Protest Turn to protest if you have a grievance but not much power Need the media; no media, no one may see you Controversy Try to be innovative 2. Get people t...
UGA >> UNIV >> 1113 (Summer, 2008)
Billy Cook Identity Map Pretty much everything on my identity map stems from being a Methodist, except for being a Fraternity Member; I couldn\'t link that to anything, really. I think this is because I draw my morals from my religious values. My pare...
UGA >> UNIV >> 1113 (Summer, 2008)
Billy Cook Why I Am Here I think my main motivation for being here at the University of Georgia would be to better my education so I can be a better and more prepared worker later in life. If I am better and more prepared as a worker, I would be able...
UCSB >> PHYS >> 115b (Spring, 2008)
PHYS 115B Homework 7 Solutions Spring 2008 Problem 1 (a) Since (z )2 = I, we have: If n is even, then (z )n = I. (Write even n = 0, 2, 4, 6, . . . as n = 2j where j = 0, 1, 2, 3, 4, . . .) If n is odd, then (z )n = z . (Write odd n = 1, 3, 5, 7, . ....
UCSB >> PHYS >> 115b (Spring, 2008)
...
UCSB >> MATH >> 100 (Winter, 2007)
18,100BC final exam December 18, 2007 NAME: 1. (20 points) If S R, show that the set of isolated points of S is at most countable (use that the set of rational numbers is countable). Solution: Let I be the set of isolated points of S. If s I, let d...
Michigan State University >> CSE >> 460 (Fall, 2007)
Module 18 NFA\'s nondeterministic transition functions computations are trees, not paths L(M) and LNFA LFSA subset of LNFA 1 Nondeterministic Finite State Automata NFA\'s 2 Change: is a relation For an FSA M, (q,a) results in one and only o...
Michigan State University >> CSE >> 460 (Fall, 2007)
Module 30 EQUAL language Designing a CFG Thinking recursively 1 EQUAL language Designing a CFG 2 EQUAL EQUAL is the set of strings over {a,b} with an equal number of a\'s and b\'s Strings in EQUAL include aabbab bbbaaa abba Strings in {a,...
Michigan State University >> STT >> 200 (Summer, 2008)
Chapter 11 Random Numbers ActivStats: 11-1 to 11-4 Read: Chapter 11 Pick a number at random 1 2 3 4 Table of random digits - Appendix E: A-97. Random digits are used to: 1. select a sample at random 2. simulate independent repetition of a rand...
Michigan State University >> CSE >> 460 (Fall, 2007)
CSE 460 - Computability and Formal Language Theory Homework 7 Due: 3PM, Thursday, October 25, 2007 This homework is based on material from Modules 14-17. 1. Describe the set of strings that end up in each state of the following FSA. Think binary. [2,...
Michigan State University >> STT >> 200 (Summer, 2008)
Intro Stats Classwork Chapter 8 Year (x) 1965 1970 1975 1980 1985 1990 1995 1999 Rate (y) 19.4 18.4 14.8 15.9 15.6 16.4 14.8 14.5 y^ Residual Mean of x Mean of y SD of x SD of y r R-squared 1982.38 16.23 12.05 1.79 -0.78 0.61 a) Scatterplot: 2...
Michigan State University >> CSE >> 460 (Fall, 2007)
Simulating 2 FSA\'s with 1 FSA Why the algorithm works! Purpose This presentation attempts to give the reader some intuition as to why the algorithm which takes as input two FSA\'s and produces as output an FSA which \"simulates\" both input FSA\'s on a...
Michigan State University >> STT >> 200 (Summer, 2008)
Intro Stats Classwork A white and colored dice are tossed 1. Identify the events: A =\"sum equals 6\", B = \"sum is at most 5\" , C= \"same number on each die\", D =\"at least one shows 4\" and find their probabilities Chapter 14 A 2. Find the probability...
Michigan State University >> CSE >> 460 (Fall, 2007)
Module 9 Closure Properties Definition Language class definition set of languages Closure properties and first-order logic statements For all, there exists 1 Closure Properties A set is closed under an operation if applying the operation to...
Michigan State University >> CSE >> 460 (Fall, 2007)
Module 3 Worksheet In Class Questions 1) (S9) Which of the following two problems is a function problem? Problem 1 Problem 2 Input: Integer n Input: Integers m and n Output: An integer smaller than n Output: Answer to \"Is m < n?\" 2) (S9) Convert the ...
Michigan State University >> CSE >> 460 (Fall, 2007)
Module 8 Worksheet In Class Questions 1) (S5) A universal Turing machine is able to execute any program on any input. Which of the two following people is most like a universal Turing machine and why? Brilliant scientist Obedient soldier Take home r...
Michigan State University >> STT >> 200 (Summer, 2008)
Chapter 7 Scatterplot, Association and Correlation ActivStats: 7-1 to 7-4 Read: Chapter 7 A scatterplot displays a relationship between two quantitative variables. In a scatterplot a variable assigned to x-axis is called explanatory (or predictor),...
Michigan State University >> STT >> 200 (Summer, 2008)
Intro Stats Classwork 200 adults shopping at a supermarket were asked about the highest level of education they had completed and whether or not they smoke cigarettes. Results are summarized in the table. 1. Identify the variables. Smoker High schoo...
Michigan State University >> STT >> 200 (Summer, 2008)
Intro Stats Classwork 1. Given data: 0 2 6 3 4 8 1 7 13 5 7 2 find Five number summary Outliers (if any) Make a boxplot NOTE: First sort ! Chapter 5 2. Given data: 0 2 6 3 4 8 1 7 5 7 find Five number summary Mean Variance and standard deviation b...
Michigan State University >> STT >> 200 (Summer, 2008)
Intro Stats Classwork Chapter 6 A 1. Given data: 206 177 175 167 162 186 162 206 166 163 a) Compute the mean and the standard deviation (use calculator) b) Compute z-scores c) Compute the mean and the standard deviation of the z-scores Data 206 1...
Michigan State University >> GLG >> 411 (Fall, 2006)
Date _ Grader _ Name _ Grade _ - GLG 411 - Problem Set 10 MASS TRANSPORT OF SOLUTES: ONEDIMENSIONAL ATTENUATION PURPOSE: The purpose of this problem set is to introduce the student to the concept of solute transport and attenuation using a simple ...
Michigan State University >> GLG >> 411 (Fall, 2006)
Date _ Grader _ Name _ Grade _ - GLG 411 - Problem Set 12 MASS TRANSPORT OF SOLUTES: VISUAL SOLUTE TRANSPORT (VST) PURPOSE: This week\'s problem set will again use Visual Solute Transport (VST) (Thorbjamarson et al. 2002) to simulate in one dimensi...
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