Differentiation Formulas for Solving Ordinary Differential Equations 1.0 Introduction In mathematics‚ if y is a function of x‚ then an equation that involves x‚ y and one or more derivatives of y with respect to x is called an ordinary differential equation (ODE). The ODEs which do not have additive solutions are non-linear‚ and finding the solutions is much more sophisticated because it is rarely possible to represent them by elementary function in close form. In addition‚ the ODEs is use to solve
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SYSTEM OF LINEAR EQUATIONS IN TWO VARIABLES Solve the following systems: 1. x y 8 x y 2 by graphing by substitution by elimination by Cramer’s rule 2. 2 x 5 y 9 0 x 3y 1 0 by graphing by substitution by elimination by Cramer’s rule 3. 4 x 5 y 7 0 2 x 3 y 11 0 by graphing by substitution by elimination by Cramer’s rule CASE 1: intersecting lines independent & consistent m1m2 CASE 2: parallel lines
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Elements of Information Theory Thomas M. Cover‚ Joy A. Thomas Copyright 1991 John Wiley & Sons‚ Inc. Print ISBN 0-471-06259-6 Online ISBN 0-471-20061-1 Elements of Information Theory Elements of Information Theory Thomas M. Cover‚ Joy A. Thomas Copyright 1991 John Wiley & Sons‚ Inc. Print ISBN 0-471-06259-6 Online ISBN 0-471-20061-1 WILEY SERIES IN TELECOMMUNICATIONS Donald L. Schilling‚ Editor City College of New York Digital Telephony‚ 2nd Edition John Bellamy Elements of
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The Vector equation of a plane To find the vector equation of a plane a point on the plane and two different direction vectors are required. The equation is defined as: where a is the point on the plane and b and c are the vectors. This equation can then be written as: The Cartesian equation of a plane The cartesian equation of the plane is easier to use. The equation is defined as: One of the advantages to writing the equation in cartesian form is that we can easily find the normal
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Instructions: 1. Write your name‚ class and class number in the spaces provided on this cover. 2. This paper consists of THREE sections‚ A(1)‚ A(2) and B. Each section carries 20 marks. 3. Attempt ALL questions in this paper. Write your answers in the spaces provided. Supplementary answer sheets will be supplied on request. Write your name and class number on each sheet. 4. Unless otherwise specified‚ all working must be clearly shown. 5. Unless otherwise specified‚ numerical answers should either be exact
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The goal for this experiment is to determine which out of the four balanced chemical equations best represent the thermal decomposition of sodium bicarbonate. The guiding question will be answered with the outcome of the sodium bicarbonates thermal decomposition and it being plugged in into the four balanced chemical equations. John Dalton atomic theory explains two fundamental laws of chemistry which are the law of conservation of mass and the law of definite proportions. The atomic theory states
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"Financial accounting produces information for external parties such as stockholders‚ suppliers‚ banks‚ and government regulatory agencies" (Horngren‚ Sundem‚ & Stratton‚ 2005‚ p. 5). "Financial accountants prepare financial statements based on general ledgers and participate in important financial decisions involving mergers & acquisitions‚ benefits/ERISA planning and long-term financial projections"(Accounting: Job Options‚ 2000). These reports are used by owners of a business‚ or by people who
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Ridley College Grade 11 Physics Formal Lab Report By David Deng The Electromagnetic Force: An Equation Introduction This lab is to measure the determinant factors of the size of electromagnetic force that affect with electric and magnetic fields. The electromagnetic force is carried by the photon and is responsible for atomic structure‚ chemical reactions‚ the attractive and repulsive forces associated with electrical charge and magnetism‚ and all other electromagnetic phenomena. According
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Colleen Cooper Solving Quadratic Equations MAT 126 Survey of Mathematical Methods Instructor: Kussiy Alyass October 1‚‚ 2012 Solving Quadratic Equations Using correct methods to solve quadratic equations can make math an interesting task. In the paper below I will square the coefficient of the x term‚ yield composite numbers‚ move a constant term and see if prime numbers occur. I will use the text and the correct formulas to create the proper solutions of the two projects that are
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along with more detailed examples and explanations. The personal computer has revolutionized the way we work and play. The kind and amount of data we work with in petrophysics can be easily handled in spread sheet programs that are under the full control of the user. The second section of Archie Unleashed examines several data sets and techniques for handling these data and defines a simple spreadsheet to do the calculations. Section 1. The Archie Equation -water saturation as
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