Calculus in 3D Geometry‚ Vectors‚ and Multivariate Calculus Zbigniew H. Nitecki Tufts University August 19‚ 2012 ii This work is subject to copyright. It may be copied for non-commercial purposes. Preface The present volume is a sequel to my earlier book‚ Calculus Deconstructed: A Second Course in First-Year Calculus‚ published by the Mathematical Association in 2009. I have used versions of this pair of books for severel years in the Honors Calculus course at Tufts‚ a two-semester
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Resolution of vector Introduction: The main objective of this lab is to add and resolve vectors using three distinct methods. 1) Graphical: When two forces act upon an object‚ their combined effect can be determined by adding the vectors‚ which represent forces. One method of performing this addition is known as graphical method of vector addition. In this method‚ arrows are drawn in the direction of forces. The lengths of arrows are proportional to the magnitude of vectors. The resultant
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"The Force Table" is a simple tool for demonstrating Newton’s First Law and the vector nature of forces. This tool is based on the principle of “equilibrium”. An object is said to be in equilibrium when there is no net force acting on it. An object with no net force acting on it has no acceleration. By using simple weights‚ pulleys and strings placed around a circular table‚ several forces can be applied to an object located in the center of the table in such a way that the forces exactly cancel
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12e 2 Force Vectors Part 2 Copyright © 2010 Pearson Education South Asia Pte Ltd Chapter Objectives • Cartesian vector form • Dot product and angle between 2 vectors Copyright © 2010 Pearson Education South Asia Pte Ltd Chapter Outline 1. 2. 3. 4. 5. Cartesian Vectors Addition and Subtraction of Cartesian Vectors Position Vectors Force Vector Directed along a Line Dot Product Copyright © 2010 Pearson Education South Asia Pte Ltd 2.5 Cartesian Vectors • Right-Handed
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Air Pollution -occurs when gases‚ dust particles‚ fumes (or smoke) are introduced into the atmosphere in a way that makes it harmful to humans‚ animals and plant. This is because the air becomes dirty or contaminated. -the introduction into the atmosphere of chemicals‚ particulates‚ biological materials that cause discomfort‚ disease‚ or death to humans‚ damage other living organisms Air Pollutants -Things that pollute the air -A substance in the air that can be adverse to humans and the environment
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HL Vectors Notes 1. Vector or Scalar Many physical quantities such as area‚ length‚ mass and temperature are completely described once the magnitude of the quantity is given. Such quantities are called “scalars.” Other quantities possess the properties of magnitude and direction. A quantity of this kind is called a “vector” quantity. Winds are usually described by giving their speed and direction; say 20 km/h north east. The wind speed and wind direction together form a vector quantity
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CHAPTER 6 FOREST TYPE CLASSIFICATION USING SUPPORT VECTOR MACHINE CHAPTER 6 Forest Type Classification using Support Vector Machine In this chapter‚ an attempt has been made to classify the forest type using support vector machines (SVMs). SVM is regarded as a powerful technique in order to deal with the classification problems. In this work‚ we have explored different parameters of SVM in order to find the best possible recognition accuracy. The LibSVM tool has been used for the experimentation
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Vector Analysis Definition A vector in n dimension is any set of n-components that transforms in the same manner as a displacement when you change coordinates Displacement is the model for the behavior of all vectors Roughly speaking: A vector is a quantity with both direction as well as magnitude. On the contrary‚ a scalar has no direction and remains unchanged when one changes the coordinates. Notation: Bold face A‚ in handwriting A . The magnitude of the vector is denoted by A A
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Acceleration Velocity Displacement Distance Time Definition 1. Acceleration is the rate of change of velocity with time. Velocity is a vector physical quantity; both magnitude and direction are required to define it. the length of an imaginary straight path‚ typically distinct from the path actually travelled by P. Distance is a numerical description of how far apart objects are. In physics or everyday usage‚ distance may refer to a physical length‚ or an estimation Time in physics is
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each of the following vectors in terms of and (a) (b) (c) (Total 4 marks) 2. The vectors ‚ are unit vectors along the x-axis and y-axis respectively. The vectors = – + and = 3 + 5 are given. (a) Find + 2 in terms of and . A vector has the same direction as + 2 ‚ and has a magnitude of 26. (b) Find in terms of and . (Total 4 marks) 3. The circle shown has centre O and radius 6. is the vector ‚ is the vector and is the vector . (a) Verify
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