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School: Michigan State University
Math 235 section 202 HW #1 Solution 1 dy - y = te2t , y(0) = 2 2 dt 1. (3 pts) Find the solution of the initial value problem: y - 2y = 2te2t , (t) = e e-2t y - 2e-2t y = 2t, -2dt = e-2t , (e-2t y) = 2t, e-2t y = t2 + c, c = 2, therefore y = (t2
School: Michigan State University
School: Michigan State University
School: Michigan State University
1.8: 1. g(x)=x^2+2x+3 g(2+h)-g(2)= 2. f(x)=2x^2 and g(x)=x+3 f(g(x)= f(x)+k, move graph up k f(x+k), move graph left k cf(x), stretch graph vertically (c>1) cf(x), shrink graph vertically (0<c<1) -f(x), reflect graph 1,9 y=kx^p, find k and p 1.y=3/(x
School: Michigan State University
IMMERSE 2007 Algebra Exercises 6. Supplemental Exercises Exercise 6.1. This exercise goes back to review the denition of a ring, and explore an object that is almost a ring. It should be signicantly more elementary than most of the other exercises in the
School: Michigan State University
Course: Multivariable Calculus
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School: Michigan State University
Course: Multivariable Calculus
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School: Michigan State University
Course: Multivariable Calculus
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School: Michigan State University
Course: Multivariable Calculus
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School: Michigan State University
Course: Multivariable Calculus
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School: Michigan State University
Michael Wenstrup Mrs. Ann Dunayczan Character Analysis The Crucible 19 October 2009 Wenstrup 1 A Plethora of Lies To all stories comes an antagonist, in The Crucible by Arthur Miller, Abigail Williams is definitely the antagonist behind almost all the pro
School: Michigan State University
Wenstrup 1 Michael Wenstrup Mrs. Nott English 11 May 18, 2010 At The University of _, we are committed to building an academically superb and widely diverse educational community. What would you as an individual bring to our campus community? I could say
School: Michigan State University
Universities are committed to building an academically superb and widely diverse educational community. What would I as an individual bring to the campus community? I could say I am an inner city kid, that I lost my dad at a very young age to repeated dru
School: Michigan State University
Universities are committed to building an academically superb and widely diverse educational community. What would I as an individual bring to the campus community? I could say I am an inner city kid, that I lost my dad at a very young age to repeated dru
School: Michigan State University
While I live in a predominantly a white, Christian, middle-class community so typical of those found in Southwest Michigan, one of my best friends is Ranjeet Ghorpade who we effectively just call Jeet. Jeet is a first generation American of Hindu parents
School: Michigan State University
DescribetheuniquequalitiesthatattractyoutothespecificundergraduateCollegeorSchool(includingpreferredadmission anddualdegreeprograms)towhichyouareapplyingattheUniversityofMichigan.Howwouldthatcurriculumsupportyour interests?(500wordsmaximum) Mycareerambi
School: Michigan State University
Course: Transitions
Lectures 1 and 2: Chapter 1. Sets Math 299 Denition: A set is a welldened collection of distinct objects called the elements (or members). Sets are conventionally denoted with capital letters. 1. We enclose a set with braces (curly brackets) cfw_. 2. The
School: Michigan State University
Course: Transitions
Lectures 8 and 9: Chapter 3 Math 299 0. Ch3.1 A trivial proof and a vacuous proof (Reading assignment) 1. Ch3.2 Direct proofs 2. Ch3.3 Proof by contrapositive 3. Ch3.4 Proof by cases 4. Ch3.5 Proof evaluations (Reading assignment) Ch 3.2: Direct proofs A
School: Michigan State University
Course: Transitions
Lectures 6 and 7: Sec 2.9 and Sec 2.10 Math 299 2.9: Some Fundamental Properties of Logical Equivalence Theorem: For statements P , Q, and R, the following properties hold. 1. Commutative Laws (1) P Q Q P (2) P Q Q P 2. Associate Laws (1) P (Q R) (P Q) R
School: Michigan State University
Course: Transitions
Math 299 Lecture 5: Sections 2.6 and 2.7. Biconditional, Converse, Tautologies and Contradictions Converse The statement B A is the converse of the statement A B . Give an example for each of the following cases: The statement is true and its converse is
School: Michigan State University
Course: Transitions
Math 299 Lecture 3: Chapter 2. Logic Sec 2.1: Statements Mathematics is the business of proving mathematical statements to be true or false . Logic lays the foundation for rigorous mathematical proofs. Denition: A statement is a sentence that is either tr
School: Michigan State University
Course: Transitions
Math 299Lecture 4: Chapter 2. Logic. Sections 2.4 and 2.5: Implications If ., then . Statements Denition: Statements of the form If statement A is true, then statement B is true. are called implications. Mathematically this is denoted by A B . AB If A th
School: Michigan State University
School: Michigan State University
Name: ID Number: TA: Section Time: Math 20D. Exam 2 May 19, 2008 No calculators or any other devices are allowed on this exam. Read each question carefully. If any question is not clear, ask for clarication. Write your solutions clearly and legibly; no cr
School: Michigan State University
Name: ID Number: TA: Section Time: Math 20D. Exam 1 April 23, 2008 No calculators or any other devices are allowed on this exam. Read each question carefully. If any question is not clear, ask for clarication. Write your solutions clearly and legibly; no
School: Michigan State University
Name: Sect. Number: TA: Sect. Time: Math 20D. Quiz 2 April 18, 2008 Answer each question completely, and show your work. If you use extra paper, write your name on each extra page, and staple the question page and your own added pages together. 1. (30 poi
School: Michigan State University
Name: ID Number: TA: Section Time: Math 20D Exam 2. May 19, 2008 No calculators or any other devices are allowed on this exam. Read each question carefully. If any question is not clear, ask for clarication. Write your solutions clearly and legibly; no cr
School: Michigan State University
Name: Sect. Number: TA: Sect. Time: Math 20D. Quiz 3 May 2, 2008 Answer each question completely, and show your work. If you use extra paper, write your name on each extra page, and staple the question page and your own added pages together. 1. (30 points
School: Michigan State University
Math 235 section 202 HW #1 Solution 1 dy - y = te2t , y(0) = 2 2 dt 1. (3 pts) Find the solution of the initial value problem: y - 2y = 2te2t , (t) = e e-2t y - 2e-2t y = 2t, -2dt = e-2t , (e-2t y) = 2t, e-2t y = t2 + c, c = 2, therefore y = (t2
School: Michigan State University
School: Michigan State University
MAT 4200, eksamen 12.12.13, solutions Oppgave 1 La p1 , p2 , p3 vre forskjellige primtall, og la n = p1 p2 p3 . 2 3 1a. Hva er de maksimale idealene i Z/nZ? Hva er nilradikalet? Gi et eksempel p et a primrt ideal i Z/nZ som ikke er et primideal. (2pt) Sol
School: Michigan State University
Homework 1 (due: 10-7-11). All rings are commutative with identity! (1) [4pts] Let R be a nite ring. Show that R = NZD(R). (2) [8pts] Suppose that R is a subring of a ring S and that R is a direct summand of S as an R-module (i.e. S = R N as an R-module).
School: Michigan State University
Solutions Ark 1 From the book: Number 8, 9, 10 and 12 on page 11. Number 8 : Show that the set of prime ideals of A has a minimal element with respect to inclusion. Solution: By Zorns lemma it sucies to show that any descending chain of prime ideals conta
School: Michigan State University
Solutions Ark2 From the book: Number 10, 11 and 12 on page 32. Number 10 : Let A be a ring, a an ideal contained in the Jacobson radical of A; let M be an A-module and N a nitely generated A-module, and let u : M N be homomorphism. If the induced homomorp
School: Michigan State University
PNHSPhysics IBPhysicsDensityComparisonofDensityCubes MichaelWenstrup Date: 9/29/09 Codes: 1.2.11 Hours: 1 Evaluating: DPP & CE Discussion: Your task is to calculate the density of three different density cubes. One cube must be the wood block. You may use
School: Michigan State University
IBPhysicsHorizontalProjectileMotionNameMichaelWenstrup Codes: 9.1.1 Date: Materials: steel ball ramp Meter stick Carbon paper Hours: 1.5 Evaluating: DCP plumb line unlined white paper Procedure: Set up the apparatus as shown in the diagram. Use the appara
School: Michigan State University
PLANNINGLAB:HELICOPTERMOTION IBCRITERIA:TOPIC2MECHANICSHOURS:3 MICHAELWENSTRUP EVALUATING:DESIGN,DCP,CEDATE: _9/14/10_ ABSTRACT RESEARCHQUESTION Asthelength(independentvariable)ofthehelicoptersrotorsincrease,howistheamountoftime(dependent)the helicopterr
School: Michigan State University
PLANNINGLAB:HELICOPTERMOTION IBCRITERIA:TOPIC2MECHANICSHOURS:3 MICHAELWENSTRUP EVALUATING:DESIGN,DCP,CEDATE: _9/14/10_ ABSTRACT Theaimofthislabwastoinvestigateonefactorthataffectsthemotionofthepaperhelicopter.SoIdesignedthelabto measurehowthechangeinroto
School: Michigan State University
School: Michigan State University
1.8: 1. g(x)=x^2+2x+3 g(2+h)-g(2)= 2. f(x)=2x^2 and g(x)=x+3 f(g(x)= f(x)+k, move graph up k f(x+k), move graph left k cf(x), stretch graph vertically (c>1) cf(x), shrink graph vertically (0<c<1) -f(x), reflect graph 1,9 y=kx^p, find k and p 1.y=3/(x
School: Michigan State University
Course: Transition To Formal Mathematics
SYLLABUS TRANSITIONS: MATH 299, SECTION 6 SPRING 2014 Instructors Name: David Duncan Instructors Email: duncan42[at]math.msu.edu Instructors Oce: Wells Hall C-315 Oce Hours: TBD TAs Name: Alex A. Chandler Lecture Times and Location: M, W 5-6:20, Wells Hal
School: Michigan State University
Course: Intro To Algebra
Math 110. Finite Mathematics and Elements of College Algebra Fall 2007 Syllabus Students who do not satisfy the prerequisites for Math 110 will be dropped from this course by the Registrar's office. Course supervisor: Irina Kadyrova, Ph.D. Office Loc
School: Michigan State University
Course: Calc I
1 MTH 132 Calculus I SYLLABUS Spring 2008 Section: 18 TIME: MWF 3:00-3:50pm Room: C110 Wells Hall Instructor: Tsung-Lin Lee (Jules) Email: leetsung@msu.edu Office: D-316 Wells Hall Office Hours: M W F 13:50pm 14:50pm and by appointment Homepage