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School: Oregon State
Course: Discrete Mathematics II
Mth 232 Review Problems for Exam I These are some review problems for the first midterm. They are gathered from old exams (mostly by other instructors). These questions cover the material in chapter 6, sections 1-4, and chapter 7, sections 1, 3, and 4. 1.
School: Oregon State
Course: Mth 111
COMM 218 Interpersonal Communication Instructor: Angela Cordova Exam #2 Study Guide Befamiliarwiththefollowingconceptsfromyourbookandclass.Additionally,rememberthatthisisjust a guideandis notnecessarilyallencompassing.Inotherwords,justbecauseitdoesntappea
School: Oregon State
Course: VECTOR CALCULUS I
Fall 2015: MTH 254 Vector Calculus 1 Tuesday 11/17/2015 HoeWoon Kim Practice Problems for Midterm 2 80 minutes Key and Solution Name: Student ID: Directions: 1. Bubble your last name and then your rst name on your scantron. 2. Bubble your OSU ID number on
School: Oregon State
Course: VECTOR CALCULUS I
Fall 2015: MTH 254 Vector Calculus 1 Tuesday 11/17/2015 HoeWoon Kim Practice Problems for Midterm 2 80 minutes Key and Solution Name: Student ID: Directions: 1. Bubble your last name and then your rst name on your scantron. 2. Bubble your OSU ID number on
School: Oregon State
Course: VECTOR CALCULUS I
Fall 2015: MTH 254 Vector Calculus 1 Tuesday 10/27/2015 HoeWoon Kim Practice Questions for Midterm 1 Name: 80 minutes Student ID: Directions: 1. Bubble your last name and then your rst name on your scantron. 2. Bubble your OSU ID number on your scantron.
School: Oregon State
Course: INTEGRAL CALCULUS
MTH 252 LAB 6: Areas between curves NAME: 1. Find the area of the enclosed region below: SPRING 2015 2. Determine the area of the shaded region below, which is implicitly dened by the equation x2 = y 4 (1 y 3 ). 2 2 3. Suppose 0 < a < b. In the rst quadra
School: Oregon State
Course: INTEGRAL CALCULUS
MTH 252 Midterm Review/Practice Problems Spring 2015 These are some problems to work on in preparation for the rst midterm on Tuesday, April 21, 2015 (7:00 PM - 8:20 PM, see announcement for room). You should study lecture notes, labs and homework as well
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Derivatives (Introduction) October, 2015 Derivatives Recall: Let f be dene at [a, x]. The slope of the the tangent line for f at x = a is given by f (x) f (a) mtan = lim xa xa Alternatively, f (a + h) f (a) mtan = lim h0 h f (a + h) f (a) . h If the point
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Section 3.7. The Change Rule Section 3.7. Implicit Differentiation [ Examples ] Math 251. Chain Rule F. Patricia Medina November 2, 2015 F. Patricia Medina Math 251 Notes. Part I. Section 3.7. The Change Rule Section 3.7. Implicit Differentiation [ Exampl
School: Oregon State
Course: COLLEGE ALGEBRA
Math 111 Midterm 1 Review Name: Midterm Information When is the midterm? Where will you be taking the midterm? What should you take with you to the midterm? ‘ 1. In your own words give definitions for the following two terms: a. The domain ofafunct
School: Oregon State
Course: CALCULUS FOR MANAGEMENT AND SOCIAL SCIENCE
School: Oregon State
Course: DIFFERENTIAL CALCULUS
End Behavior and Asymptotes of Rational Functions Theorem Suppose f (x) = p(x) q(x) is a rational function, where p(x) = am xm + am1 xm1 + + a2 x2 + a1 x + a0 q(x) = bn xn + bn1 xn1 + + b2 x2 + b1 x + b0 with am = 0 and bn = 0. a. If m < n, then limx f (x
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Section 3.8. Implicit Differentiation [ Examples ] Section 3.9. Derivatives of logarithmic and exponential functions Math 251 November 4, 2015 Math 251 Section 3.8. Implicit Differentiation [ Examples ] Section 3.9. Derivatives of logarithmic and exponent
School: Oregon State
Course: DIFFERENTIAL CALCULUS
More on Continuity October 9, 2015 Continuity Continuity rules Suppose that f and g are continuous at a, and that b is a constant. Then, 1 bf (x) is continuous at x = a. 2 f (x) + g(x) is continuous at x = a. 3 f (x) g(x) is continuous at x = a. f (x)g(x)
School: Oregon State
Course: Mth 111
COMM 218 Interpersonal Communication Instructor: Angela Cordova Exam #2 Study Guide Befamiliarwiththefollowingconceptsfromyourbookandclass.Additionally,rememberthatthisisjust a guideandis notnecessarilyallencompassing.Inotherwords,justbecauseitdoesntappea
School: Oregon State
Course: VECTOR CALCULUS I
Fall 2015: MTH 254 Vector Calculus 1 Tuesday 11/17/2015 HoeWoon Kim Practice Problems for Midterm 2 80 minutes Key and Solution Name: Student ID: Directions: 1. Bubble your last name and then your rst name on your scantron. 2. Bubble your OSU ID number on
School: Oregon State
Course: VECTOR CALCULUS I
Fall 2015: MTH 254 Vector Calculus 1 Tuesday 11/17/2015 HoeWoon Kim Practice Problems for Midterm 2 80 minutes Key and Solution Name: Student ID: Directions: 1. Bubble your last name and then your rst name on your scantron. 2. Bubble your OSU ID number on
School: Oregon State
Course: VECTOR CALCULUS I
Fall 2015: MTH 254 Vector Calculus 1 Tuesday 10/27/2015 HoeWoon Kim Practice Questions for Midterm 1 Name: 80 minutes Student ID: Directions: 1. Bubble your last name and then your rst name on your scantron. 2. Bubble your OSU ID number on your scantron.
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Tentative Calendar. Math 251. Fall 2015 Week 0 Material (sections from book) Syllabus 2.1, 2.1 Evaluations None Week 1 2.2 (cont.), 2.3, 2.4 Quiz 1 (Friday 01/02) Week 2 2.5, 2.6, 3.1 Quiz 2 (Friday 10/09) Week 3 3.2, 3.3 Review for Midterm 1 3.4, 3.5 Qui
School: Oregon State
Course: CALCULUS FOR MANAGEMENT AND SOCIAL SCIENCE
OSU Mth 241 Midterm I 1. Find the slope of the line tangent to the curve P(x) 2 1 — 4t — 2x3 at the point where x = —2 . 'L. a) Not enough infomation is given to answer the question I?! “a -_ - L\ , {1} y b) the slope is: —g -’ Ll ~ to >5 2 ’L @mesiopejs;
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Lab 3 MATH 251 The lab is based on your participation. We must have a total of ve groups in class. Each group will be choosing one of the problems listed below. After discussing the problem, the group will select one representative to solve the problem on
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Lab 2 MATH 251. More limits (and continuity). The lab is based on your participation. We must have a total of ve groups in class. Each group will be choosing one of the problems listed below. After discussing the problem, the group will select one represe
School: Oregon State
Course: VECTOR CALCULUS I
Worksheet on Polar, Cylindrical and Spherical Coordinates 1. (a) 2. (a) Plot the following polar points. 2, 6 (b) 5 3, 6 (c) 2, 3 (d) 2, 3 (d) 1, 3 Convert the following rectangular points to polar coordinates. 1, 3 (b) 1, 3 (c) 1, 3 3.
School: Oregon State
Course: ADVANCED CALCULUS
2.4 # 8 If cfw_an is monotone and has a convergent subsequence, then cfw_an converges. Assume that cfw_an is monotonically increasing (if decreasing, similar argument). It suces to show that cfw_an is bounded above, by the Monotone Convergence Theorem
School: Oregon State
Course: ADVANCED CALCULUS
I I ) é P/IOUC (:3 (940/? 6L /7W1 thtqjja M4,-imm, ' M 31 6! 714/344 7 (/13 . / VIA/Jr MIN-6014. Maw/(m {/JIMK W3 (1) 3 m Wollwum ,aém/f me 0% rm aim/VS 0M_ W MM: 5442/ M Mm 504% Wm WM Wkwé beytee/ rm MM Mom 30 1:1 Ana M W 1/»: MM m 2- b; My. éwmh m aMé
School: Oregon State
Course: INTEGRAL CALCULUS
MTH 252 LAB 6: Areas between curves NAME: 1. Find the area of the enclosed region below: SPRING 2015 2. Determine the area of the shaded region below, which is implicitly dened by the equation x2 = y 4 (1 y 3 ). 2 2 3. Suppose 0 < a < b. In the rst quadra
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Mth 251 Limits Sections 2.1 2.4 The purpose of this lab is to review the limit concepts covered in sections 2.1 2.4. You will revisit limits from the left, limits from the right, and infinite limits (which are tied to vertical asymptotes). You will revisi
School: Oregon State
Course: VECTOR CALCULUS I
Math 254, Fly in the Lab Lab This lab is designed to be done as a group project with each group having 3 to 4 students. Please use a separate sheet of paper to record the groups work and answers. An OSU scientist has constructed an enclosed study room tha
School: Oregon State
Course: VECTOR CALCULUS I
Summary Prime notation Below are the most important dierentiation rules, written with primes. (f and g are functions; c is a constant.) f (x) = xn f (x) = ex f () = sin f () = cos = = = = f (x) = ln x = f () = tan = g(p) = sin1 p = g(p) = tan1 p = f (x)
School: Oregon State
Course: VECTOR CALCULUS I
Here are a few familiar dierentiation rules expressed as indenite integrals: d un+1 = (n + 1)un du d u e = eu du d sin u = cos u du d cos u = sin u du 1 d ln u = du u un+1 +C n+1 (n = 1) un du = eu du = eu + C cos u du = sin u + C sin u du = cos u + C 1 d
School: Oregon State
Course: VECTOR CALCULUS I
Math 254 project An engineering firm wants to place a bid on dredging a waterway to make it navigable for ocean going craft. Depth soundings were made every 100 feet across the 700 foot channel with the first sounding take at the 50 ft mark into the chann
School: Oregon State
Course: VECTOR CALCULUS I
Mth 254 Lab Partial Derivatives and Chain Rule 1. The following is a map with curves of the same elevation of a region in Orangerock National Park. We define the altitude function A(x, y), as the altitude at a point x meters east and y meters north of the
School: Oregon State
Course: VECTOR CALCULUS I
Mth 254 Lagrange Multiplier Practice 1. Use Lagrange multipliers to find the maximum and minimum values of f ( x, y ) xy subject to 4 x y 8. Dont forget to find the interior points using a previous technique from section 13.8. 2 2. 3. 4. 2 Now, sketch the
School: Oregon State
Course: VECTOR CALCULUS I
MTH 254 STUDY GUIDE Summary of Topics Lesson 1 (p. 3): Coordinate Systems, 10.2, 13.5 Lesson 2 (p. 9): Vectors in the Plane and in 3-Space, 11.1, 11.2 Lesson 3 (p. 16): Dot Products, 11.3 Lesson 4 (p. 20): Cross Products, 11.4 Lesson 5 (p. 22): Lines & Cu
School: Oregon State
Course: COLLEGE ALGEBRA
‘MATH 111 Winter 2014 INSTRUCTOR: Linda Mummy Ofﬁce: Snell 342 E-mail: mummylﬁnlajth.oregonstate.edﬁg Ofﬁce Hours: M 11-12, W 1-2, R 2-250 and by appointment Sectio 1 A: Naveen Somasunderam Office: TBA E-mail: " Office Hours: TBA MLC Hours: TBA Section
School: Oregon State
Course: ADVANCED CALCULUS
AdvancedCalculus ThisisMTH311,Sec1. Timeandplace: MWRF10:0010:50,MWRF:WNGR287. Instructor: PatrickDeLeenheer Office:296KidderHall OfficeHours:MWF12:0012:50orbyappointment. Email:deleenhp@math.oregonstate.edu URL:www.math.oregonstate.edu/~deleenhp Prerequi
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Syllabus Introduction to Mathematical Software Math 321, 3 credits Spring Quarter, 2015 Prerequisite: MTH 252 and either MTH 341 or 306. Course Content: This course is designed to familiarize students with the
School: Oregon State
Course: Discrete Mathematics II
Mth 232 Review Problems for Exam I These are some review problems for the first midterm. They are gathered from old exams (mostly by other instructors). These questions cover the material in chapter 6, sections 1-4, and chapter 7, sections 1, 3, and 4. 1.
School: Oregon State
Course: Mth 111
COMM 218 Interpersonal Communication Instructor: Angela Cordova Exam #2 Study Guide Befamiliarwiththefollowingconceptsfromyourbookandclass.Additionally,rememberthatthisisjust a guideandis notnecessarilyallencompassing.Inotherwords,justbecauseitdoesntappea
School: Oregon State
Course: VECTOR CALCULUS I
Fall 2015: MTH 254 Vector Calculus 1 Tuesday 11/17/2015 HoeWoon Kim Practice Problems for Midterm 2 80 minutes Key and Solution Name: Student ID: Directions: 1. Bubble your last name and then your rst name on your scantron. 2. Bubble your OSU ID number on
School: Oregon State
Course: VECTOR CALCULUS I
Fall 2015: MTH 254 Vector Calculus 1 Tuesday 11/17/2015 HoeWoon Kim Practice Problems for Midterm 2 80 minutes Key and Solution Name: Student ID: Directions: 1. Bubble your last name and then your rst name on your scantron. 2. Bubble your OSU ID number on
School: Oregon State
Course: VECTOR CALCULUS I
Fall 2015: MTH 254 Vector Calculus 1 Tuesday 10/27/2015 HoeWoon Kim Practice Questions for Midterm 1 Name: 80 minutes Student ID: Directions: 1. Bubble your last name and then your rst name on your scantron. 2. Bubble your OSU ID number on your scantron.
School: Oregon State
Course: INTEGRAL CALCULUS
MTH 252 LAB 6: Areas between curves NAME: 1. Find the area of the enclosed region below: SPRING 2015 2. Determine the area of the shaded region below, which is implicitly dened by the equation x2 = y 4 (1 y 3 ). 2 2 3. Suppose 0 < a < b. In the rst quadra
School: Oregon State
Course: INTEGRAL CALCULUS
MTH 252 Midterm Review/Practice Problems Spring 2015 These are some problems to work on in preparation for the rst midterm on Tuesday, April 21, 2015 (7:00 PM - 8:20 PM, see announcement for room). You should study lecture notes, labs and homework as well
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Tentative Calendar. Math 251. Fall 2015 Week 0 Material (sections from book) Syllabus 2.1, 2.1 Evaluations None Week 1 2.2 (cont.), 2.3, 2.4 Quiz 1 (Friday 01/02) Week 2 2.5, 2.6, 3.1 Quiz 2 (Friday 10/09) Week 3 3.2, 3.3 Review for Midterm 1 3.4, 3.5 Qui
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Mth 251 Limits Sections 2.1 2.4 The purpose of this lab is to review the limit concepts covered in sections 2.1 2.4. You will revisit limits from the left, limits from the right, and infinite limits (which are tied to vertical asymptotes). You will revisi
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Lab 3 MATH 251 The lab is based on your participation. We must have a total of ve groups in class. Each group will be choosing one of the problems listed below. After discussing the problem, the group will select one representative to solve the problem on
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Section 3.8. Implicit Differentiation [ Examples ] Section 3.9. Derivatives of logarithmic and exponential functions Math 251 November 4, 2015 Math 251 Section 3.8. Implicit Differentiation [ Examples ] Section 3.9. Derivatives of logarithmic and exponent
School: Oregon State
Course: DIFFERENTIAL CALCULUS
More on Continuity October 9, 2015 Continuity Continuity rules Suppose that f and g are continuous at a, and that b is a constant. Then, 1 bf (x) is continuous at x = a. 2 f (x) + g(x) is continuous at x = a. 3 f (x) g(x) is continuous at x = a. f (x)g(x)
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Derivatives (Introduction) October, 2015 Derivatives Recall: Let f be dene at [a, x]. The slope of the the tangent line for f at x = a is given by f (x) f (a) mtan = lim xa xa Alternatively, f (a + h) f (a) mtan = lim h0 h f (a + h) f (a) . h If the point
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Lab 2 MATH 251. More limits (and continuity). The lab is based on your participation. We must have a total of ve groups in class. Each group will be choosing one of the problems listed below. After discussing the problem, the group will select one represe
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Section 3.7. The Change Rule Section 3.7. Implicit Differentiation [ Examples ] Math 251. Chain Rule F. Patricia Medina November 2, 2015 F. Patricia Medina Math 251 Notes. Part I. Section 3.7. The Change Rule Section 3.7. Implicit Differentiation [ Exampl
School: Oregon State
Course: DIFFERENTIAL CALCULUS
End Behavior and Asymptotes of Rational Functions Theorem Suppose f (x) = p(x) q(x) is a rational function, where p(x) = am xm + am1 xm1 + + a2 x2 + a1 x + a0 q(x) = bn xn + bn1 xn1 + + b2 x2 + b1 x + b0 with am = 0 and bn = 0. a. If m < n, then limx f (x
School: Oregon State
Course: VECTOR CALCULUS I
Summary Prime notation Below are the most important dierentiation rules, written with primes. (f and g are functions; c is a constant.) f (x) = xn f (x) = ex f () = sin f () = cos = = = = f (x) = ln x = f () = tan = g(p) = sin1 p = g(p) = tan1 p = f (x)
School: Oregon State
Course: VECTOR CALCULUS I
Here are a few familiar dierentiation rules expressed as indenite integrals: d un+1 = (n + 1)un du d u e = eu du d sin u = cos u du d cos u = sin u du 1 d ln u = du u un+1 +C n+1 (n = 1) un du = eu du = eu + C cos u du = sin u + C sin u du = cos u + C 1 d
School: Oregon State
Course: VECTOR CALCULUS I
Math 254 project An engineering firm wants to place a bid on dredging a waterway to make it navigable for ocean going craft. Depth soundings were made every 100 feet across the 700 foot channel with the first sounding take at the 50 ft mark into the chann
School: Oregon State
Course: VECTOR CALCULUS I
Mth 254 Lab Partial Derivatives and Chain Rule 1. The following is a map with curves of the same elevation of a region in Orangerock National Park. We define the altitude function A(x, y), as the altitude at a point x meters east and y meters north of the
School: Oregon State
Course: VECTOR CALCULUS I
Mth 254 Lagrange Multiplier Practice 1. Use Lagrange multipliers to find the maximum and minimum values of f ( x, y ) xy subject to 4 x y 8. Dont forget to find the interior points using a previous technique from section 13.8. 2 2. 3. 4. 2 Now, sketch the
School: Oregon State
Course: VECTOR CALCULUS I
MTH 254 STUDY GUIDE Summary of Topics Lesson 1 (p. 3): Coordinate Systems, 10.2, 13.5 Lesson 2 (p. 9): Vectors in the Plane and in 3-Space, 11.1, 11.2 Lesson 3 (p. 16): Dot Products, 11.3 Lesson 4 (p. 20): Cross Products, 11.4 Lesson 5 (p. 22): Lines & Cu
School: Oregon State
Course: VECTOR CALCULUS I
Math 254, Fly in the Lab Lab This lab is designed to be done as a group project with each group having 3 to 4 students. Please use a separate sheet of paper to record the groups work and answers. An OSU scientist has constructed an enclosed study room tha
School: Oregon State
Course: VECTOR CALCULUS I
Mth 254 Lab Visualizing Partial Derivatives Our goal for this activity is to visualize the partial derivatives f x ( x, y ) and f y ( x, y ) at the point ( / 4, / 3,1 / 2) if f ( x, y ) sin(2 x y ) using the 2-D graphing features on our calculators. A gra
School: Oregon State
Course: VECTOR CALCULUS I
Mth 254 LabDirectional Derivatives, Gradient and More Suppose you are climbing a hill whose shape is given by the equation z 1000 0.01x 0.02 y , where x, y, and z are measured in meters, and you are standing at a point with coordinates (50, 80, 847). The
School: Oregon State
Course: VECTOR CALCULUS I
Mth 254 Lab Parameterized Curves Sections 12.6 and 12.7 1. a. b. c. d. e. f. g. Let r (t ) t cos t i t sin t represent the position vector of a moving particle in the plane. (Hint. Find the j derivatives below in terms of t before evaluating at t = 4.) Ro
School: Oregon State
Course: VECTOR CALCULUS I
Manager: Research: Secretary: Reporter: HANGING BY A THREAD Working in groups of four, decide on your roles rst. Try to resolve questions within the group before asking for help. The Secretary is responsible for producing a nal report and all parties are
School: Oregon State
Course: VECTOR CALCULUS I
Parallelepiped Lab Math 254 This lab is designed to be done as a group project where each group should have 3 to 4 students. In this lab we will explore a parallelepiped. U V T W S R P Q The drawing above is for reference only and is not to scale or even
School: Oregon State
Course: INTEGRAL CALCULUS
MTH 252 Midterm Review/Practice Problems Spring 2015 These are some problems to work on in preparation for the rst midterm on Tuesday, April 21, 2015 (7:00 PM - 8:20 PM, see announcement for room). You should study lecture notes, labs and homework as well
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Derivatives (Introduction) October, 2015 Derivatives Recall: Let f be dene at [a, x]. The slope of the the tangent line for f at x = a is given by f (x) f (a) mtan = lim xa xa Alternatively, f (a + h) f (a) mtan = lim h0 h f (a + h) f (a) . h If the point
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Section 3.7. The Change Rule Section 3.7. Implicit Differentiation [ Examples ] Math 251. Chain Rule F. Patricia Medina November 2, 2015 F. Patricia Medina Math 251 Notes. Part I. Section 3.7. The Change Rule Section 3.7. Implicit Differentiation [ Exampl
School: Oregon State
Course: COLLEGE ALGEBRA
Math 111 Midterm 1 Review Name: Midterm Information When is the midterm? Where will you be taking the midterm? What should you take with you to the midterm? ‘ 1. In your own words give definitions for the following two terms: a. The domain ofafunct
School: Oregon State
Course: CALCULUS FOR MANAGEMENT AND SOCIAL SCIENCE
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Chapter 3 A L TEX A LTEX is a markup language. It is essentially an upgrade of Donald Knuths landmark typesetting language called TEX [3]. In the late 1970s Knuth realized that printing technology had neared a point at which very sophisticated typesetting
School: Oregon State
Course: Introductory Applications Of Mathematical Software
IntroductiontoMATLAB DavidKoslicki OregonStateUniversity 3/20/2015 Contents Preliminary Basics HomeworkExercises Vectors HomeworkExercises Plotting HomeworkExercises Matrices HomeworkExercises Matrix/VectorandMatrix/MatrixOperations HomeworkExercises Flow
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Latex Lecture 1 \documentclass[12pt]cfw_article \usepackagecfw_amsmath,amsfonts,amsthm,amssymb \authorcfw_Author \titlecfw_Title \begincfw_document \maketitle Hello world! $\mathbbcfw_N$ \sectioncfw_My section \subsectioncfw_My subsection \subsubsectioncf
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Title Author March 21, 2015 Hello world! N 1 My section 1.1 1.1.1 My subsection My subsubsection My unumbered subsubsection These are centered formulas f (x) = x + 2 f (x) = x + 2 f (x) = x + 2 f (x) = x + 2 f (x) = x + 2 This is an inline formula f (x) =
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Latex Lecture 2: \documentclass[12pt]cfw_article \usepackagecfw_amsmath,amsfonts,amsthm,amssymb \authorcfw_Author \titlecfw_Title \usepackagecfw_graphicx \newtheoremcfw_definitioncfw_Definition[section] \newtheoremcfw_theoremcfw_Theorem[section] %\theorem
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Title Author March 21, 2015 1 Alignment f (x) = (x 1)(x + 1) = x2 1. A= u(x) = 2 1 2 0 4 0 x<0 1 x 0. Lists 1. item1 2. item2 3. item3 1. Enumerate (a) Lettered items (b) Lettered items 2. Itemize Bulleted items Bulleted items 1 (1) This is a test yup i
School: Oregon State
Course: INTRODUCTION TO MODERN ALGEBRA
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
Homework 3 Solutions 1) A metric on a set X is a function d : X X R such that For all x, y, z R, (a) d (x, y) 0, with d (x, y) = 0 if and only if x = y (b) d (x, y) = d (y, x) (c) d (x, z) d (x, y) + d (y, z) 2) If x = (x1 , . . . , xn ) and y = (y1 , . .
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
NAME: HW 3 and Midterm Review: Due Tuesday May 5 For this combined review and HW assignment, you may work with your classmates. For the exam, you may bring a 3x5 note card, but no calculator or wi device, and you will work individually. The Midterm Exam t
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
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School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
NOTES FOR MATH 4510, FALL 2010 DOMINGO TOLEDO 1. Metric Spaces The following denition introduces the most central concept in the course. Think of the plane with its usual distance function as you read the denition. Denition 1.1. A metric space (X, d) is a
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
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School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
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School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
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School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
Notes on Introductory Point-Set Topology Allen Hatcher Chapter 1. Basic Point-Set Topology . 1 Topological Spaces 1, Interior, Closure, and Boundary 5, Basis for a Topology 7, Metric Spaces 9, Subspaces 10, Continuity and Homeomorphisms 12, Product Spaces
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
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School: Oregon State
Course: DIFFERENTIAL CALCULUS
End Behavior and Asymptotes of Rational Functions Theorem Suppose f (x) = p(x) q(x) is a rational function, where p(x) = am xm + am1 xm1 + + a2 x2 + a1 x + a0 q(x) = bn xn + bn1 xn1 + + b2 x2 + b1 x + b0 with am = 0 and bn = 0. a. If m < n, then limx f (x
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Section 3.8. Implicit Differentiation [ Examples ] Section 3.9. Derivatives of logarithmic and exponential functions Math 251 November 4, 2015 Math 251 Section 3.8. Implicit Differentiation [ Examples ] Section 3.9. Derivatives of logarithmic and exponent
School: Oregon State
Course: DIFFERENTIAL CALCULUS
More on Continuity October 9, 2015 Continuity Continuity rules Suppose that f and g are continuous at a, and that b is a constant. Then, 1 bf (x) is continuous at x = a. 2 f (x) + g(x) is continuous at x = a. 3 f (x) g(x) is continuous at x = a. f (x)g(x)
School: Oregon State
Course: Mth 111
COMM 218 Interpersonal Communication Instructor: Angela Cordova Exam #2 Study Guide Befamiliarwiththefollowingconceptsfromyourbookandclass.Additionally,rememberthatthisisjust a guideandis notnecessarilyallencompassing.Inotherwords,justbecauseitdoesntappea
School: Oregon State
Course: VECTOR CALCULUS I
Fall 2015: MTH 254 Vector Calculus 1 Tuesday 11/17/2015 HoeWoon Kim Practice Problems for Midterm 2 80 minutes Key and Solution Name: Student ID: Directions: 1. Bubble your last name and then your rst name on your scantron. 2. Bubble your OSU ID number on
School: Oregon State
Course: VECTOR CALCULUS I
Fall 2015: MTH 254 Vector Calculus 1 Tuesday 11/17/2015 HoeWoon Kim Practice Problems for Midterm 2 80 minutes Key and Solution Name: Student ID: Directions: 1. Bubble your last name and then your rst name on your scantron. 2. Bubble your OSU ID number on
School: Oregon State
Course: VECTOR CALCULUS I
Fall 2015: MTH 254 Vector Calculus 1 Tuesday 10/27/2015 HoeWoon Kim Practice Questions for Midterm 1 Name: 80 minutes Student ID: Directions: 1. Bubble your last name and then your rst name on your scantron. 2. Bubble your OSU ID number on your scantron.
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Tentative Calendar. Math 251. Fall 2015 Week 0 Material (sections from book) Syllabus 2.1, 2.1 Evaluations None Week 1 2.2 (cont.), 2.3, 2.4 Quiz 1 (Friday 01/02) Week 2 2.5, 2.6, 3.1 Quiz 2 (Friday 10/09) Week 3 3.2, 3.3 Review for Midterm 1 3.4, 3.5 Qui
School: Oregon State
Course: CALCULUS FOR MANAGEMENT AND SOCIAL SCIENCE
OSU Mth 241 Midterm I 1. Find the slope of the line tangent to the curve P(x) 2 1 — 4t — 2x3 at the point where x = —2 . 'L. a) Not enough infomation is given to answer the question I?! “a -_ - L\ , {1} y b) the slope is: —g -’ Ll ~ to >5 2 ’L @mesiopejs;
School: Oregon State
Course: CALCULUS FOR MANAGEMENT AND SOCIAL SCIENCE
OSU Mth 241 Midterm 2 a _ 91. For all x in the interval ( 2, 5 ) the ﬁmction f has a positive ﬁrst derivative and O K, W" h; I negative second derivative. _ L L} 0‘9"“ f ' [ﬂ ? -~ .\<’l5 ,2” X , Which of the follow'ﬁjould be a table of values for f?
School: Oregon State
Course: CALCULUS FOR MANAGEMENT AND SOCIAL SCIENCE
/ f’/,.- Review guestionsﬁom the text Pg 194-196 Supplementary exercises chapter 2: #1, 7-20, 22, 35, 3'7, 41, 43, 45, 46, 47, 52, 53, 54, 55, 60, 61 Questions ﬁ'om 01d mth 241 exams listed by chapter. Chapter 2 {The demand function for a particular commo
School: Oregon State
Course: LINEAR ALGEBRA II
Quiz #3 r. . You 11:11! 20 111111111135. . L ff: .1' " '1 {r ,5. :- P102150 explain 111111 11(1): the answers. Kenna: 1. [5 1111-1) Find the eigenvalues and 1:1111'05111'11111i11g eigcuvectors 0f 1 11 {- A:[1 J 1 a _ _ a I _ r . -' F11 2 - 1 I - 1- a
School: Oregon State
Course: PROBABILITY I
Midterm for Math 463/563 Theory of Probability \ \ l l \ Bob Burton \I * 7 November, 2014 /-/: -~ /" I I, There are a total of problems of varying length. /; -_#_'_/ l 2 2 3 3' .a (D 6 5 8 g Ul B 6 5" \. 2/ '"'-.\ 6 /M .H q \ "/5 Ac- <3 U D l l\ 2/ Z
School: Oregon State
Course: ADVANCED CALCULUS
1'1 Math 312, Section 003 -~ Second midterm exam March 2, 2015 Show you: work on all problems. 1. Assume D C R and f1 : D > R for all integers n 21. (8.) Dene what it means for the sequence {fn 3:1 of functions to converge uniformly to a. function f on
School: Oregon State
Course: ADVANCED CALCULUS
Name blues; News; Math 312, Section 003 First midterm exam February 9, 2015 Show your work on all problems. 1. Assume F(;r) = si11(:1:2) for all real 1, and also assume F(}) = 2. Use ideas developed in class to find an expression for F(:1:) that is valid
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
NAME: MIdterm Exam100 pointsMay 7, 2015 You may use a 3x5 note card, but no calculator or wi device, and you will work individually. Each problem is worth 10 points. The exam will end promptly at 9:50am. Problem 1 Let (X, d) be a metric space. Let A X and
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
NAME: (athm ? Midterm Exam100 pointsuuMay 7, 2015 You may use a 3x5 note card, but no calculator or wi device, and you will work individually. Each problem is worth 10 points. The exam will end promptly at 9:50am. Problem 1 Let (X, d) be a metric space. L
School: Oregon State
Course: Introduction To Probability
MIDTERM II MATH 361, SPRING 2013 PROFESSOR OSSIANDER SHOW YOUR WORK COMPLETELY, COHERENTLY, AND LEGIBLY There are 6 problems on this exam, each with multiple parts. Each part of each problem is worth 4 points. ' Show your work completely to receive full
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Lab 3 MATH 251 The lab is based on your participation. We must have a total of ve groups in class. Each group will be choosing one of the problems listed below. After discussing the problem, the group will select one representative to solve the problem on
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Lab 2 MATH 251. More limits (and continuity). The lab is based on your participation. We must have a total of ve groups in class. Each group will be choosing one of the problems listed below. After discussing the problem, the group will select one represe
School: Oregon State
Course: VECTOR CALCULUS I
Worksheet on Polar, Cylindrical and Spherical Coordinates 1. (a) 2. (a) Plot the following polar points. 2, 6 (b) 5 3, 6 (c) 2, 3 (d) 2, 3 (d) 1, 3 Convert the following rectangular points to polar coordinates. 1, 3 (b) 1, 3 (c) 1, 3 3.
School: Oregon State
Course: ADVANCED CALCULUS
2.4 # 8 If cfw_an is monotone and has a convergent subsequence, then cfw_an converges. Assume that cfw_an is monotonically increasing (if decreasing, similar argument). It suces to show that cfw_an is bounded above, by the Monotone Convergence Theorem
School: Oregon State
Course: ADVANCED CALCULUS
I I ) é P/IOUC (:3 (940/? 6L /7W1 thtqjja M4,-imm, ' M 31 6! 714/344 7 (/13 . / VIA/Jr MIN-6014. Maw/(m {/JIMK W3 (1) 3 m Wollwum ,aém/f me 0% rm aim/VS 0M_ W MM: 5442/ M Mm 504% Wm WM Wkwé beytee/ rm MM Mom 30 1:1 Ana M W 1/»: MM m 2- b; My. éwmh m aMé
School: Oregon State
Course: ADVANCED CALCULUS
3.5 # 7 a. Prove that f (x) = x, x [0, 1] is continuous, i.e. if cfw_xn is a sequence in [0, 1], and xn x0 in [0, 1] as n , then xn x0 . 2 cases: If x0 = 0, then: xn x0 1 | xn x0 | = | | |xn x0 | xn + x0 x0 By the comparison lemma, the result follows.
School: Oregon State
Course: ADVANCED CALCULUS
Homework assignments: HW assignments (collected): HWI: 1.1: #5 (Use Example 1.1) and #16; 1.2: #4a (use suggested problems 1.1#15 and 1.2 #3, but don't turn in the proofs of these) (due Mon Jan 13). Note the typo on p.1: a square is missing in the very la
School: Oregon State
Course: ADVANCED CALCULUS
6.1 # 1 Let P = cfw_0, 1/4, 1/2, 1. For the following functions f : [0, 1] R, nd L(f, P ) and U (f, P ): a.f (x) = x. L(f, P ) U (f, P ) 1 1 1 1 1 5 0. + . + . = 4 4 4 2 2 16 1 1 1 1 1 11 . + . + 1. = 4 4 2 4 2 16 = = b.f (x) = 10. L(f, P ) = 10. 1 1 1 +
School: Oregon State
Course: PROBABILITY I
_ r Slw/(' I; oil-.312. 1 3' "jl;r(_'qd>¢ -JL,.'5.,K PICK, {gli'H-!rr\l'! (/Fian'hf'vl'r INLC nag-{L} bol;~s_glt;)i I,( 74(57r'igqrf; +L / l/pgkilyookj - r+H_.;'1 bi +0; (Hf- II-Eff 1'wa wdtbwkj a? Hnw'ooru mde 96 I" a {H.(Irp vfgq a 5 f " _;.'A rsgc jk
School: Oregon State
Course: ADVANCED CALCULUS
Math 312, Section 003 Lab session for Wednesday, February 11, 2015 Turn in your write-up at the beginning of class on Friday, February 13. 1. Let f(a:) = e for all real a. (a) Let n be a. positive integer, and let 1),; be the Taylor polynomial of f of deg
School: Oregon State
Course: ADVANCED CALCULUS
[It Mf g, Math 312, Section 003 /l 7( Lab session for Wednesday, January 14, 2015 [ a L / Turn in your writeup at the beginning of class on Friday, January 16. 1. Let [(1,1)] be a closed bounded interval. Assume that f : [(1, b] > R is continuous on [(1,
School: Oregon State
Course: ADVANCED CALCULUS
r_ o L - lllw 00 (L3 Math 312, Section 003 Lab session for Wednesday, January 7, 2015 Turn in your write-up at the beginning of class on Friday, January 9. 1. (Problem 11, page 150.) For a partition P = {3:0, . . . , 23,1} of the interval [(1,1)], Show th
School: Oregon State
Course: ADVANCED CALCULUS
Math 312, Section 003 Lab session for Wednesday, January 28, 2015 Turn in your writeup at the beginning of class on Hiday, January 30. 1. Let u(:c,t) = %[f(r+ct)+f(:r-ct)] + (£3 for all real 3: and all t 2 0, where c is a positive constant, and f and g ar
School: Oregon State
Course: ADVANCED CALCULUS
.xi / l. 3c .R-J Math 312, Section 003 Lab session for Wednesday, February 18, 2015 Turn in your writeup at the beginning of class on Friday, February 20. 1. For every positive integer 71, let " 1 l 1 S: =1 e+. - n g k + 2 + n - 1 (61) Find a positive con
School: Oregon State
Course: ADVANCED CALCULUS
Math 312, Section 003 Lab session for Wednesday, March 4, 2015 Turn in your writeup at the beginning of class on Friday, March 6. 1. Prove the following theorem, which is known as the Weierstrass Mtest. Theorem. Assume D C R, fk : D ) R for all k 2 1, a
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
p. 13-14: 1bdefg, 3, 4, 6 1b) The interval on the x-axis 0 x 1 1d) The whole x-axis 1e) The whole plane 1f) The graph of the equation xy = 1 1g) The points in the plane with integer coordinates 3) The statement in the problem is logically equivalent to th
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
HW 2, MTH 430, Due Thursday April 23 Problem 1 The purpose this (geometry) problem is to show that midpoints are unique in the Euclidean metric on Rn . We use the Euclidean metric, norm, and scalar (dot) product: d2 (x, y) = |x y| = (x y) (x y). 1 Given x
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
Homework 4 Solutions p. 16: 2ab, 4ab, 5ab 2a) Proof: Let U be an open subset of X and which lies inside a set A. Let x U . Then U is an open subset of A containing x, hence x int (A). Therefore, U int (A). 2b) Proof: Let C be a closed subset of X, and let
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
Homework 2 Solutions 1) Let Rn be equipped with the Euclidean metric. Let x, y Rn , and dene m = (Recall that a point M Rn is a midpoint of x and y if x M = y M = 1 2 1 2 (x + y). x y .) Observe that m is a midpoint of x and y (verication is left to the r
School: Oregon State
Course: INTRODUCTION TO CONTEMPORARY MATHEMATICS
ID NUMBER:_ NAME: _ SECTION:_ ASSIGNMENT Answer the questions for each exercise. If there is a need for computed answers, solve and write the correct answers from your computed values in the blanks provided. Exercise 1. Select the correct answer and write
School: Oregon State
Course: INTEGRAL CALCULUS
MTH 252 LAB 6: Areas between curves NAME: 1. Find the area of the enclosed region below: SPRING 2015 2. Determine the area of the shaded region below, which is implicitly dened by the equation x2 = y 4 (1 y 3 ). 2 2 3. Suppose 0 < a < b. In the rst quadra
School: Oregon State
Course: DIFFERENTIAL CALCULUS
Mth 251 Limits Sections 2.1 2.4 The purpose of this lab is to review the limit concepts covered in sections 2.1 2.4. You will revisit limits from the left, limits from the right, and infinite limits (which are tied to vertical asymptotes). You will revisi
School: Oregon State
Course: VECTOR CALCULUS I
Math 254, Fly in the Lab Lab This lab is designed to be done as a group project with each group having 3 to 4 students. Please use a separate sheet of paper to record the groups work and answers. An OSU scientist has constructed an enclosed study room tha
School: Oregon State
Course: Multiple Variable Calculus
21141'12 Lab %231, Winter 2012 Insmlctor: Dr. Scarborough / -r_._._.._._v-f"/ GTA: (circle One) Veronika Vasylkivska Shers'oHV \ . . {/d') h Class Tlme: (Clrcle One) 1:00 Recitation Tirm:(CirCie One) 8:00 9.00 1000 1100 1:00 NAME (Print) E12 -; 5
School: Oregon State
Course: Applied Discrete Math
MLC Lab Visit - Lab 07 - Maple Mth 355 (a.k.a. Mth 399) Feb 19, 2003 Maple 7 Bent E. Petersen petersen@math.orst.edu There are 5 problems below. Problem solutions are due Feb 26, 2003. Email your solutions to me as Maple worksheet attachments. Your worksh
School: Oregon State
Course: Applied Discrete Math
MLC Lab Visit - Lab 06 - Maple Mth 355 (a.k.a. Mth 399) Feb 12, 2003 Maple 7 Bent E. Petersen petersen@math.orst.edu There are 3 problems below. Problem solutions are due Feb 19, 2003. Email your solutions to me as Maple worksheet attachments. Your worksh
School: Oregon State
Course: Applied Discrete Math
MLC Lab Visit - Lab 05 - Maple Mth 355 (a.k.a. Mth 399) Feb 05, 2003 Maple 7 Bent E. Petersen petersen@math.orst.edu There are 6 problems below. Problem solutions are due Feb 12, 2003. Email your solutions to me as Maple worksheet attachments. Your worksh
School: Oregon State
Course: Linear Algebra
Mth 341 Linear Algebra Spring 2000 MLC Computer Lab Visit 1 Bent Petersen Login Press the Ctrl-Alt-Delete keys simultaneously. You should get a login prompt. Enter your ORST user name and press the Tab key. Then enter your ORST password and press the Ente
School: Oregon State
Course: VECTOR CALCULUS I
Summary Prime notation Below are the most important dierentiation rules, written with primes. (f and g are functions; c is a constant.) f (x) = xn f (x) = ex f () = sin f () = cos = = = = f (x) = ln x = f () = tan = g(p) = sin1 p = g(p) = tan1 p = f (x)
School: Oregon State
Course: VECTOR CALCULUS I
Here are a few familiar dierentiation rules expressed as indenite integrals: d un+1 = (n + 1)un du d u e = eu du d sin u = cos u du d cos u = sin u du 1 d ln u = du u un+1 +C n+1 (n = 1) un du = eu du = eu + C cos u du = sin u + C sin u du = cos u + C 1 d
School: Oregon State
Course: VECTOR CALCULUS I
Math 254 project An engineering firm wants to place a bid on dredging a waterway to make it navigable for ocean going craft. Depth soundings were made every 100 feet across the 700 foot channel with the first sounding take at the 50 ft mark into the chann
School: Oregon State
Course: VECTOR CALCULUS I
Mth 254 Lab Partial Derivatives and Chain Rule 1. The following is a map with curves of the same elevation of a region in Orangerock National Park. We define the altitude function A(x, y), as the altitude at a point x meters east and y meters north of the
School: Oregon State
Course: VECTOR CALCULUS I
Mth 254 Lagrange Multiplier Practice 1. Use Lagrange multipliers to find the maximum and minimum values of f ( x, y ) xy subject to 4 x y 8. Dont forget to find the interior points using a previous technique from section 13.8. 2 2. 3. 4. 2 Now, sketch the
School: Oregon State
Course: VECTOR CALCULUS I
MTH 254 STUDY GUIDE Summary of Topics Lesson 1 (p. 3): Coordinate Systems, 10.2, 13.5 Lesson 2 (p. 9): Vectors in the Plane and in 3-Space, 11.1, 11.2 Lesson 3 (p. 16): Dot Products, 11.3 Lesson 4 (p. 20): Cross Products, 11.4 Lesson 5 (p. 22): Lines & Cu
School: Oregon State
Course: VECTOR CALCULUS I
Mth 254 Lab Visualizing Partial Derivatives Our goal for this activity is to visualize the partial derivatives f x ( x, y ) and f y ( x, y ) at the point ( / 4, / 3,1 / 2) if f ( x, y ) sin(2 x y ) using the 2-D graphing features on our calculators. A gra
School: Oregon State
Course: VECTOR CALCULUS I
Mth 254 LabDirectional Derivatives, Gradient and More Suppose you are climbing a hill whose shape is given by the equation z 1000 0.01x 0.02 y , where x, y, and z are measured in meters, and you are standing at a point with coordinates (50, 80, 847). The
School: Oregon State
Course: VECTOR CALCULUS I
Mth 254 Lab Parameterized Curves Sections 12.6 and 12.7 1. a. b. c. d. e. f. g. Let r (t ) t cos t i t sin t represent the position vector of a moving particle in the plane. (Hint. Find the j derivatives below in terms of t before evaluating at t = 4.) Ro
School: Oregon State
Course: VECTOR CALCULUS I
Manager: Research: Secretary: Reporter: HANGING BY A THREAD Working in groups of four, decide on your roles rst. Try to resolve questions within the group before asking for help. The Secretary is responsible for producing a nal report and all parties are
School: Oregon State
Course: VECTOR CALCULUS I
Parallelepiped Lab Math 254 This lab is designed to be done as a group project where each group should have 3 to 4 students. In this lab we will explore a parallelepiped. U V T W S R P Q The drawing above is for reference only and is not to scale or even
School: Oregon State
Course: VECTOR CALCULUS I
Math 254 - Dot and Cross Product Lab For each part below, you will need to think about what it means to find the shortest distance between a point and a plane, a line and a plane, etc. in space. Work #1 - #3 and #5. Then work #4 if you have time. 1. Using
School: Oregon State
Course: VECTOR CALCULUS I
Worksheet on Polar, Cylindrical and Spherical Coordinates 1. (a) 2. (a) Plot the following polar points. 2, 6 (b) 5 3, 6 (c) 2, 3 (d) 2, 3 (d) 1, 3 Convert the following rectangular points to polar coordinates. 1, 3 (b) 1, 3 (c) 1, 3 3.
School: Oregon State
Course: COLLEGE ALGEBRA
‘MATH 111 Winter 2014 INSTRUCTOR: Linda Mummy Ofﬁce: Snell 342 E-mail: mummylﬁnlajth.oregonstate.edﬁg Ofﬁce Hours: M 11-12, W 1-2, R 2-250 and by appointment Sectio 1 A: Naveen Somasunderam Office: TBA E-mail: " Office Hours: TBA MLC Hours: TBA Section
School: Oregon State
Course: ADVANCED CALCULUS
AdvancedCalculus ThisisMTH311,Sec1. Timeandplace: MWRF10:0010:50,MWRF:WNGR287. Instructor: PatrickDeLeenheer Office:296KidderHall OfficeHours:MWF12:0012:50orbyappointment. Email:deleenhp@math.oregonstate.edu URL:www.math.oregonstate.edu/~deleenhp Prerequi
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Syllabus Introduction to Mathematical Software Math 321, 3 credits Spring Quarter, 2015 Prerequisite: MTH 252 and either MTH 341 or 306. Course Content: This course is designed to familiarize students with the