Multivariable calculus Calculus 2B for Business Administration Lecturer: Nguyen Minh Quan‚ PhD Dr. Nguyen Minh Quan (HCMIU-VNU) Chapter 2. Multivariable calculus Summer 2013 1 / 80 Contents 1 Functions of several variables 2 Partial derivatives 3 Maxima and minima. Optimization 4 Constrained Optimization 5 Total differentials and approximations 6 Double integrals Dr. Nguyen Minh Quan (HCMIU-VNU) Chapter 2. Multivariable calculus Summer 2013
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a stochastic process with the following properties: (a.) The number of possible outcomes or states is finite. (b.) The outcome at any stage depends only on the outcome of the previous stage. (c.) The probabilities are constant over time. If x0 is a vector which represents the initial state of a system‚ then
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Chap-04 B.V.Ramana August 30‚ 2006 10:13 Chapter 4 Calculus of Variations function of the independent variable y(x)‚ which is a function. Thus L{y(x)} = Y cn c2 A O c1 X B x2 x1 4.1 INTRODUCTION Calculus of variations deals with certain kinds of “external problems” in which expressions involving integrals are optimized (maximized or minimized). Euler and Lagrange in the 18th century laid the foundations‚ with the classical problems of determining a closed curve in the plane
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Directed Line Segment: VECTORS • A line segment with direction is called a directed line segment. • If ‘A’ and ‘B’ are two distinct points in the space‚ then the ordered pair (A‚ B) is called as a directed line segment and is denoted by """""# . ! • In """""# ‚ ‘A’ is called initial point and ‘B’ is called terminal ! point of """""# . ! • The distance from ‘A’ to ‘B’ is called the length or magnitude of """""# . The length or magnitude of """""# ! ! is denoted by ’"""""# ’. Thus
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Tuple Relational Calculus ( TRC ) Introduction Procedural Query language query specification involves giving a step by step process of obtaining the query result e.g.‚ relational algebra usage calls for detailed knowledge of the operators involved difficult for the use of non-experts Declarative Query language query specification involves giving the logical conditions the results are required to satisfy easy for the use of non-experts Prof P Sreenivasa Kumar‚ Department of CS&E‚ IITM. 1 TRC
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Free Response Questions 1969-2005 Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom 1 AP Calculus Free-Response Questions 1969 AB 1 Consider the following functions defined for all x: f1 ( x) = x f 2 ( x) = x cos x f3 ( x) = 3e2 x f 4 ( x) = x − x Answer the following questions (a‚ b‚ c‚ and d) about each of these functions. Indicate your answer by writing either yes or no in the appropriate space in the given rectangular grid. No justification
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Pure Mathematics – Unit 1 Vectors Find the magnitude and direction of the vectors – 3i + 4j‚ -5i + 12j‚ -10j‚ i – j The vector XY has magnitude 10 units and is inclined at 300 to the x-axis. Express XY as a column vector The vector PQ has magnitude 5 units and is inclined at 1500 to the x-axis. Express PQ as a column vector Find numbers m and n such that m 35 + n 21= 49 If a = 38+ λ and b = λ3 where a and b are parallel‚ find λ. The position vectors of points A and B are 2-1
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Find the x coordinates of all relative extreme points of[pic]. |A)[pic] |B) [pic] |C) [pic] |D) [pic] |E) [pic] | [pic] First find the derivative of the function[pic]‚ f ’(x): |[pic] |= |[pic] |apply power rule
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Addition of Force Vectors Abstract The purpose‚ of this experiment‚ was to prove that there is a relation between the magnitude of the resulting vector‚ and the angle between the vectors that are being added. The test was performed by creating a balance between three weights tied to strings on a pulley that transferred the string on top of a graduated disc‚ which made easy the measurement of the angles between them. After performing the experiment‚ my group concluded that there is a relation
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Integral calculus is the study of mathematical integration dealing with integrals. These integrals‚ also known as area under the curve‚ are used to determine the following: areas‚ volumes‚ and lengths. There are a multitude of areas of real-world mathematics to which integral calculus is used. Integration is most often applied in physics‚ biology‚ and even chemistry. Integration is applied to physics in many situations. One important situation is finding the moment of inertia. The moment of inertia
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