EE2 Signals and Linear Systems Pier Luigi Dragotti Electrical & Electronic Engineering Department Imperial College London URL: http://www.commsp.ee.ic.ac.uk/~pld/Teaching/ E-mail: p.dragotti@imperial.ac.uk PLD Autumn 2012 Thursday‚ 27 September 12 Signals and Linear Systems Lecture 1 Aims and Objectives “The concepts of signals and systems arise in a variety of fields and the techniques associated with these notions play a central role in many areas of science and technology
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18 Math 070 Chapter 7 Rational Expressions and Equations (7.1) Sec. 7.1 Simplifying Rational Expressions To reduce an algebraic fraction: factor first‚ then cancel _____________________________. 1. 4w3 28w 2 2. 27 a 3 33 3. y 2 7 y 18 y2 6y 8 19 Math 070 Chapter 7 Rational Expressions and Equations (7.2) Sec. 7.2 Multiplying and Dividing Rational Expressions To multiply algebraic fractions: factor first‚ next cancel __________________________ and then
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Higher Level Mathematics Internal Assessment Type I Shadow Functions Contents Introduction: Functions/Polynomials 3 Part A: Quadratic Polynomials 4 Part B: Cubic Polynomials 12 Introduction: In mathematics‚ function is defined as a relationship‚ or more of a correspondence between the set of input values and the set of output values. Also‚ a rule is involved‚ or as it may be referred to‚ a ‘set of ordered pairs’ that assigns a unique output for each of the input. The
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1.1. Equations and Graphs In each of problems 1 - 4‚ find (a) an ordered pair that is a solution of the equation‚ (b) the intercepts of the graph‚ and (c) determine if the graph has symmetry. 1. 2. 3. 4. 5. Once a car is driven off of the dealership lot‚ it loses a significant amount of its resale value. The graph below shows the depreciated value of a BMW versus that of a Chevy after years. Which of the following statements is the best conclusion about the data? a. You should
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PARTIAL DIFFERENTIAL EQUATIONS I YEAR B.Tech By Mr. Y. Prabhaker Reddy Asst. Professor of Mathematics Guru Nanak Engineering College Ibrahimpatnam‚ Hyderabad. SYLLABUS OF MATHEMATICAL METHODS (as per JNTU Hyderabad) Name of the Unit Unit-I Solution of Linear systems Unit-II Eigen values and Eigen vectors Name of the Topic Matrices and Linear system of equations: Elementary row transformations – Rank – Echelon form‚ Normal form – Solution of Linear Systems – Direct Methods –
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Balancing Equations Balancing equations is a fundamental skill in Chemistry. Solving a system of linear equations is a fundamental skill in Algebra. Remarkably‚ these two field specialties are intrinsically and inherently linked. 2 + O2 ----> H2OA. This is not a difficult task and can easily be accomplished using some basic problem solving skills. In fact‚ what follows is a chemistry text’s explanation of the situation: Taken from: Chemistry Wilberham‚ Staley‚ Simpson‚ Matta Addison Wesley
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=a In an equation‚ absolute values have two possibilities when talking about equations ∣a+b∣ =x = a+b=x = a+b= -x e.g. Solve ∣x-4∣=8 x-4=8 OR x-4= -8 x=12 x=-4 Sub both answer into the equation ∣12-4∣ =8 OR ∣-4-4∣ =8 8=8 8=8 Both solution re true so x=12 or x=-4 Absolute inequalities (method 1) If ∣a+b∣ ≤x∣a+b∣ <x= -x≤a+b ≤x-x<a+b<x e.g. ∣2x-1∣<3 -3<2x-1<3 +1-3<2x<3+1 -2<2x<4
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6 Systems Represented by Differential and Difference Equations Recommended Problems P6.1 Suppose that y 1(t) and y 2(t) both satisfy the homogeneous linear constant-coeffi cient differential equation (LCCDE) dy(t) + ay(t) = 0 dt Show that y 3 (t) = ayi(t) + 3y2 (t)‚ where a and # are any two constants‚ is also a solution to the homogeneous LCCDE. P6.2 In this problem‚ we consider the homogeneous LCCDE d 2yt + 3 dy(t) + 2y(t) = 0 dt 2 dt (P6.2-1) (a) Assume that a solution to
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On Mathieu Equations by Nikola Mišković‚ dipl. ing. Postgraduate course Differential equations and dynamic systems Professor: prof. dr. sc. Vesna Županović The Mathieu Equation An interesting class of linear differential equations is the class with time variant parameters. One of the most common ones‚ due to its simplicity and straightforward analysis is the Mathieu equation. The Mathieu function is useful for treating a variety of interesting problems in applied
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DIFFERENTIAL EQUATIONS: A SIMPLIFIED APPROACH‚ 2nd Edition DIFFERENTIAL EQUATIONS PRIMER By: AUSTRIA‚ Gian Paulo A. ECE / 3‚ Mapúa Institute of Technology NOTE: THIS PRIMER IS SUBJECT TO COPYRIGHT. IT CANNOT BE REPRODUCED WITHOUT PRIOR PERMISSION FROM THE AUTHOR. DEFINITIONS / TERMINOLOGIES A differential equation is an equation which involves derivatives and is mathematical models which can be used to approximate real-world problems. It is a specialized area of differential calculus but it involves
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