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CSU Northridge - VER - 9
capug.book Page 1 Tuesday, May 23, 2000 12:08 PMOrcad CaptureUsers Guidecapug.book Page 2 Tuesday, May 23, 2000 12:08 PMCopyright 1985-2000 Cadence Design Systems, Inc. All rights reserved. Trademarks Allegro, Ambit, BuildGates, Cadence, Cad
CSU Northridge - WS - 20500
ANNOUNCEMENT OF ANTICIPATED PART-TIME FACULTY POSITION OPENINGS18111 Nordhoff Street Northridge, California 91330 Department: Gender & Womens Studies 2009 Effective Date of Appointment: Fall 2008 and/or SpringAll part-time faculty appointments ar
CSU Northridge - VCGEO - 005
ARTICLETime to Accumulate Chloride Ions in the Worlds OceansCreationisms Young Earth Not SupportedINTRODUCTION Some creation scientists claim that the earth is only about 6000 years old, but this assertion is not based on science.They also object
CSU Northridge - KFS - 103
Math 103 Section 3.1, 3.2: Math of Finance: solving for timeThree ways to compute future valueSimple interest Compound interest Continuous compounded interest A = P (1 + rt) A = P (1 + i)n A = P ertThese formulas can also be used to compute the
CSU Northridge - KFS - 4816
Math 103 Section 3.1, 3.2: Math of Finance: solving for timeThree ways to compute future valueSimple interest Compound interest Continuous compounded interest A = P (1 + rt) A = P (1 + i)n A = P ertThese formulas can also be used to compute the
CSU Northridge - KFS - 4816
Katherine F. StevensonDepartment of Mathematics California State University, Northridge, CA 91330 Telephone: (818)677-6446; Email: Katherine.Stevenson@csun.edu Web: http:/www.csun.edu/kfs4816/Education: B.S., Mount Holyoke College, June 1989. Cum
CSU Northridge - KFS - 4816
NAME: CALCULUS II (Math 150B): Final. General Instructions 1. You are allowed your cheatsheat (one page, front and back allowed). 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. You may use the tables in
CSU Northridge - KFS - 4816
Practice Test 3 1. In each of the following determine whether the series converges or diverges. Circle your answer. You do not need to show all your work. (a)(1)k k=0 k2 +3 .Converges (b) 1 k=2 (ln n)2 n .DivergesConverges (c) k=1 (k1/3 1)
CSU Northridge - KFS - 4816
Homework: Vectors Math 150B. 1. Let a = 2j + 3j, b = 2j 3j and c = 5j. Compute the following: (a) 2a 4b; (b) a b; (c) a (b + c; (d) (2a 4b) 5c; (e) b b |b|; 2. Find the cosine of the angle between the vectors a and b below. (a) a = j 3j and
CSU Northridge - KFS - 4816
CALCULUS II (Math 150B): Practice Midterm II.1. Suppose that Alice computed the Left, Right, Trapezoidal, and Midpoint approximations with 10 partitions to 01 f (x)dx, where f (x) is as shown below. She wrote them on cards, but forgot to label whic
CSU Northridge - KFS - 103
4.2 Systems of Linear equations and Augmented Matrices1. 2.3.It is impractical to solve more complicated linear systems by hand. Computers and calculators now have built in routines to solve larger and more complex systems. Matrices, in conjunct
CSU Northridge - KFS - 4816
4.2 Systems of Linear equations and Augmented Matrices1. 2.3.It is impractical to solve more complicated linear systems by hand. Computers and calculators now have built in routines to solve larger and more complex systems. Matrices, in conjunct
CSU Northridge - KFS - 320
Course Notes for Math 320: Fundamentals of Mathematics Analysis.May 4, 20061Completeness Property1. A is bounded above if there is a real number b R such that a b for all a A. 2. A is bounded below if there is a real number l R such that a
CSU Northridge - KFS - 4816
Course Notes for Math 320: Fundamentals of Mathematics Analysis.May 4, 20061Completeness Property1. A is bounded above if there is a real number b R such that a b for all a A. 2. A is bounded below if there is a real number l R such that a
CSU Northridge - KFS - 103
WARM UP EXERCISEThe ozone level (in parts per billion) on a summer day at R University is given by P(x) = 80 + 12t t 2 Where t is hours after 9 am. 1. P (x). 2. Find P (3) and P (3). 3. Write an interpretation.Given y = f (x) then the derivativ
CSU Northridge - KFS - 4816
WARM UP EXERCISEThe ozone level (in parts per billion) on a summer day at R University is given by P(x) = 80 + 12t t 2 Where t is hours after 9 am. 1. P (x). 2. Find P (3) and P (3). 3. Write an interpretation.Given y = f (x) then the derivativ
CSU Northridge - KFS - 320
Math 320 Project Equivalence of 2-by-2 integral matricesSeptember 8, 20051An equivalence relation on integral matricesThis project is about an equivalence relation on 2-by-2 integral matrices. Our notation for these matrices is: M2 (Z) = a b
CSU Northridge - KFS - 4816
Math 320 Project Equivalence of 2-by-2 integral matricesSeptember 8, 20051An equivalence relation on integral matricesThis project is about an equivalence relation on 2-by-2 integral matrices. Our notation for these matrices is: M2 (Z) = a b
CSU Northridge - KFS - 320
Course Notes for Math 320: Fundamentals of Mathematics Chapter 2: Sets.September 15, 20041Introdction to SetsDenition 1.1. A set A is a well dened collection of objects. If a is an element of A then we write a A. Remark 1.2. Well dened means
CSU Northridge - KFS - 4816
Course Notes for Math 320: Fundamentals of Mathematics Chapter 2: Sets.September 15, 20041Introdction to SetsDenition 1.1. A set A is a well dened collection of objects. If a is an element of A then we write a A. Remark 1.2. Well dened means
CSU Northridge - KFS - 103
4.5 Inverse of a Square MatrixIn this section, we will learn how to find an inverse of a square matrix (if it exists) and learn the definition of the identity matrix.Identity Matrix for Multiplication:The number 1 is called the multiplicative ide
CSU Northridge - KFS - 4816
4.5 Inverse of a Square MatrixIn this section, we will learn how to find an inverse of a square matrix (if it exists) and learn the definition of the identity matrix.Identity Matrix for Multiplication:The number 1 is called the multiplicative ide
CSU Northridge - KFS - 103
4.4 Matrices: Basic OperationsAddition and subtraction of matrices Product of a number k and a matrix M Matrix Product.Addition and Subtraction of matrices! !To add or subtract matrices, they must be of the same size mxn. To add matrices of th
CSU Northridge - KFS - 4816
4.4 Matrices: Basic OperationsAddition and subtraction of matrices Product of a number k and a matrix M Matrix Product.Addition and Subtraction of matrices! !To add or subtract matrices, they must be of the same size mxn. To add matrices of th
CSU Northridge - KFS - 320
NAME: FINAL: Fundamentals of Mathematics (Math 320) Stevenson General Instructions 1. You are allowed your cheatsheat. 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. Please ask if you are not sure of an
CSU Northridge - KFS - 4816
NAME: FINAL: Fundamentals of Mathematics (Math 320) Stevenson General Instructions 1. You are allowed your cheatsheat. 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. Please ask if you are not sure of an
CSU Northridge - KFS - 103
Math 103 Section 3.1, 3.2: Math of Finance simple interest compound interestSimple Interest:A = P (1 + rt) A: amount, or future value P : principal, or present value r: annual simple interest rate (decimal form) t time in years.1Example
CSU Northridge - KFS - 4816
Math 103 Section 3.1, 3.2: Math of Finance simple interest compound interestSimple Interest:A = P (1 + rt) A: amount, or future value P : principal, or present value r: annual simple interest rate (decimal form) t time in years.1Example
CSU Northridge - KFS - 320
Project Notes for Math 320: Fundamentals of Mathematics Recurrence Relations.August 17, 20051Silly examplePlease complete the following: 1. Consider the table below: n 0 1 2 3 4 5 6 k 3 XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX
CSU Northridge - KFS - 4816
Project Notes for Math 320: Fundamentals of Mathematics Recurrence Relations.August 17, 20051Silly examplePlease complete the following: 1. Consider the table below: n 0 1 2 3 4 5 6 k 3 XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX
CSU Northridge - KFS - 320
Course Notes for Math 320: Fundamentals of Mathematics Homework Hints for Number Theory.October 5, 200588 Let r1 , r2 , r3 , . be an innite sequence of nonnegative integers such that r1 > r2 > r3 > . Prove that for some number k N, rk = 0. Hint: (
CSU Northridge - KFS - 4816
Course Notes for Math 320: Fundamentals of Mathematics Homework Hints for Number Theory.October 5, 200588 Let r1 , r2 , r3 , . be an innite sequence of nonnegative integers such that r1 > r2 > r3 > . Prove that for some number k N, rk = 0. Hint: (
CSU Northridge - KFS - 103
WARM UP EXERCSEA cable company has found that the total number N (in thousands) of subscribers t months after the installation of the system is given by N( t ) = 200t / (t + 5) Find N (15) and N (15). Write an interpretation of these results.11
CSU Northridge - KFS - 4816
WARM UP EXERCSEA cable company has found that the total number N (in thousands) of subscribers t months after the installation of the system is given by N( t ) = 200t / (t + 5) Find N (15) and N (15). Write an interpretation of these results.11
CSU Northridge - KFS - 103
Math 103 Section 2.2: Elementary Functions and Transformations1. A beginning library of elementary functions2. Graphs of elementary functions3. Shifts and stretches4. Piecewise -dened functions1Beginning Library identity function f (x) =
CSU Northridge - KFS - 4816
Math 103 Section 2.2: Elementary Functions and Transformations1. A beginning library of elementary functions2. Graphs of elementary functions3. Shifts and stretches4. Piecewise -dened functions1Beginning Library identity function f (x) =
CSU Northridge - KFS - 103
103 Section 3.1, 3.2: Math of Finance continued simple interest compound interest continuous compounded interestThree ways to compute future valueSimple interest Compound interest Continuous compounded interest A = P (1 + rt) A = P (1 + i)n A =
CSU Northridge - KFS - 4816
103 Section 3.1, 3.2: Math of Finance continued simple interest compound interest continuous compounded interestThree ways to compute future valueSimple interest Compound interest Continuous compounded interest A = P (1 + rt) A = P (1 + i)n A =
CSU Northridge - KFS - 320
Course Notes for Math 320: Fundamentals of Mathematics Chapter 4: Relations, Equivalence Relations and Congruence.March 14, 20061RelationsDenition 1.1. (Kazimierz Kuratowski) Let S be a set and let a and b be members of S. The ordered pair (a,
CSU Northridge - KFS - 4816
Course Notes for Math 320: Fundamentals of Mathematics Chapter 4: Relations, Equivalence Relations and Congruence.March 14, 20061RelationsDenition 1.1. (Kazimierz Kuratowski) Let S be a set and let a and b be members of S. The ordered pair (a,
CSU Northridge - KFS - 103
Practice Math 103 Spring 2007: Midterm III. You are allowed your cheatsheat 1/4 of a page. 1. Find the derivatives of the following functions and simplify. (a) q(x) = 4x5 + 3x2 (b) n(x) = (c) m(x) =4x+3 (7x1)2 4x+3 (7x1)2 1/32. Use the denition of
CSU Northridge - KFS - 4816
Practice Math 103 Spring 2007: Midterm III. You are allowed your cheatsheat 1/4 of a page. 1. Find the derivatives of the following functions and simplify. (a) q(x) = 4x5 + 3x2 (b) n(x) = (c) m(x) =4x+3 (7x1)2 4x+3 (7x1)2 1/32. Use the denition of
CSU Northridge - KFS - 320
Project Notes for Math 320: Fundamentals of Mathematics Partitions ARE Equivalence Relations.August 31, 20051Introduction to Partitions and CountingS = {1, 2, 3, 4, 5, 6, 7}Example 1.1. Let Consider the following three subsets of the power s
CSU Northridge - KFS - 4816
Project Notes for Math 320: Fundamentals of Mathematics Partitions ARE Equivalence Relations.August 31, 20051Introduction to Partitions and CountingS = {1, 2, 3, 4, 5, 6, 7}Example 1.1. Let Consider the following three subsets of the power s
CSU Northridge - KFS - 103
WARM UP EXERCSERoots, zeros, and x-intercepts.f (x) = x 2 ! 25 f (x) = x 2 + 25 f (x) = x 3 ! 25xf (x) = polynomial, f (a) = 0 ! f (x) = (x - a)g(x)1 2-3 Polynomials and Rational FunctionsStudents will learn about: Polynomial functionsBeha
CSU Northridge - KFS - 4816
WARM UP EXERCSERoots, zeros, and x-intercepts.f (x) = x 2 ! 25 f (x) = x 2 + 25 f (x) = x 3 ! 25xf (x) = polynomial, f (a) = 0 ! f (x) = (x - a)g(x)1 2-3 Polynomials and Rational FunctionsStudents will learn about: Polynomial functionsBeha
CSU Northridge - KFS - 103
Warm upDescribe in words and shade on the number lines the solutions to: x <3 x!2 <3 x+2 <3 5x < 15!5x < 151Definition of limit of sequence of numberse = 2.7182818284590452353602874713526624977572470936999595Roughly speaking the limit means
CSU Northridge - KFS - 4816
Warm upDescribe in words and shade on the number lines the solutions to: x <3 x!2 <3 x+2 <3 5x < 15!5x < 151Definition of limit of sequence of numberse = 2.7182818284590452353602874713526624977572470936999595Roughly speaking the limit means
CSU Northridge - KFS - 103
Math 103 Section 2.3: Quadratic Functions and Parabolas Parabolas Quadratic equations and functions Graphs of quadratic functions ApplicationsQuadratic Functions and ExpressionsA quadratic function has two forms: f (x) = ax2 + bx + c (standa
CSU Northridge - KFS - 4816
Math 103 Section 2.3: Quadratic Functions and Parabolas Parabolas Quadratic equations and functions Graphs of quadratic functions ApplicationsQuadratic Functions and ExpressionsA quadratic function has two forms: f (x) = ax2 + bx + c (standa
CSU Northridge - KFS - 103
Math 103 Section 1.2: Linear Equations and Graphing Linear Equations in two variables Graphing Ax + By = C Slope of a line Special Forms of a linear equation More applicationsThe Price-demand equation again: d = 1720 .50p. We can represent ma
CSU Northridge - KFS - 4816
Math 103 Section 1.2: Linear Equations and Graphing Linear Equations in two variables Graphing Ax + By = C Slope of a line Special Forms of a linear equation More applicationsThe Price-demand equation again: d = 1720 .50p. We can represent ma
CSU Northridge - KFS - 103
WARM UP EXERCISEPlease take derivatives of the following: y = 3x 4 x + 4 x 1 + x 2/3 x 5 + x7/5110.7 Marginal Analysis in Business and EconomicsThe student will learn about: Marginal cost, revenue, and profit Applications21Marginal Cos
CSU Northridge - KFS - 4816
WARM UP EXERCISEPlease take derivatives of the following: y = 3x 4 x + 4 x 1 + x 2/3 x 5 + x7/5110.7 Marginal Analysis in Business and EconomicsThe student will learn about: Marginal cost, revenue, and profit Applications21Marginal Cos
CSU Northridge - KFS - 103
4.3 Gauss Jordan Elimination! !Any linear system must have exactly one solution, no solution, or an infinite number of solutions. Just as in the 2X2 case: the term consistent and independent is used to describe a system with a unique solution,
CSU Northridge - KFS - 4816
4.3 Gauss Jordan Elimination! !Any linear system must have exactly one solution, no solution, or an infinite number of solutions. Just as in the 2X2 case: the term consistent and independent is used to describe a system with a unique solution,
CSU Northridge - KFS - 103
10.4 The DerivativeThe student will learn about: Rate of change Slope of the tangent line The derivative Existence/Nonexistence of the derivative1Difference Quotient: SlopeThe difference quotient that follows gives the average rate of change of
CSU Northridge - KFS - 4816
10.4 The DerivativeThe student will learn about: Rate of change Slope of the tangent line The derivative Existence/Nonexistence of the derivative1Difference Quotient: SlopeThe difference quotient that follows gives the average rate of change of
CSU Northridge - KFS - 103
Review for Final ReviewTopics 1. Functions and equations and graphing: linear, absolute value, quadratic, polynomials, rational (first 1/3 of semester) 2. Simple Interest, compounded interest, and continuously compounded interest 3. Limits & Continu
CSU Northridge - KFS - 4816
Review for Final ReviewTopics 1. Functions and equations and graphing: linear, absolute value, quadratic, polynomials, rational (first 1/3 of semester) 2. Simple Interest, compounded interest, and continuously compounded interest 3. Limits & Continu
CSU Northridge - KFS - 103
Warm-upA restaurant serves two types of fish dinnerssmall for $5.99 each and a large order for $8.99. One day, there were 134 total orders of fish and the total receipts for these 134 orders was $1024.66. How many small orders and how many large fis