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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Linear ------------------------------------------------- Important EXERCISE 27 SIMPLE LINEAR REGRESSION STATISTICAL TECHNIQUE IN REVIEW Linear regression provides a means to estimate or predict the value of a dependent variable based on the value of one or more independent variables. The regression equation is a mathematical expression of a causal proposition emerging from a theoretical framework. The linkage between the theoretical statement and the equation is made prior to data collection
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Linear Functions There are three different ways to write linear functions. They are slope-intercept‚ point-slope‚ and standard form. There are certain situations where it is better to use one way than another to solve a problem. It is important to understand and comprehend the mechanics of these three forms so that you know what form to use when solving a problem. The first form‚ point-slope‚ is written as y-y1=m(x-x1). M is the slope and x1 and y1 correspond to a point on the line. It’s good to
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