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Midterm

# ENGR 205 Midterm: ENGR 205 Unit 3 Study Guide Premium

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School
University of Louisville
Department
Engineering Fundamentals
Course
ENGR 205
Professor
Robinson
Semester
Summer

Description
ENGR 205 - Fall Unit 3 Study Guide Unit Content: Section Pages Content Supplemental Linear Difference Equations Material 4.6 189-192 The Method of Variation of Parameters 7.2 353-357 The Definition of the Laplace Transform, Linearity, Piecewise Continuity, Exponential Order, Existence, Table of Transforms 7.3 361-365 Translation in "π ", Property of the Laplace Transform, Laplace Transforms of Derivatives 7.4 366-370 Inverse Laplace Transforms (Excluding Partial Fractions) Learning objectives: A1. Find a general solution to a given difference equation whose auxiliary equation yields: (a) real, (b) complex root. If initial conditions are given, find the arbitrary constants. B2. Use the method of variation of parameters to solve a given D.E. B3. Find the Laplace transform of a given π(π‘) using the definition. B4. Find the Laplace transform of a given π(π‘) using tables. B5. Determine whether a given π(π‘) is continuous, piecewise continuous, or neither on a specified interval and sketch its graph. B6. Determine whether or not a given function is of exponential order. B7. Find the Laplace transform of a given D.E. with specified initial conditions. B8. Determine β β1 {πΉ π )} for a given πΉ π  . Unit 3 Homework Problems Homework 3A (5 pts) # Notes/Hint/Answer #1-5 Find a general solution to the given difference equation (and the solution to the initial value problem for #3) 1 Find a general solution to the difference equatioπ+2π¦β 6π¦ π+1 + 8π¦ π 0, Answer: π¦ = πΆ 2 + πΆ 4 π π 1 2 2 Find a general solution to the difference equatioπ+2π¦β 4π¦ π+1 + 4π¦ π 2 ,π π π2 Answer: π¦ π 2 (πΆ + 1 π + 2 8 ) 3 Find a general solution to the difference equation and the solution to the initial value problem: 7 1 2 1 3 π¦π+2 β 2π¦ π+1 + π¦π= π,π¦ =01,π¦ = 1; Answer: π¦ π 1 + π 3 π + 2 6 4 Find a general solution to the difference equatioπ+2π¦β 6π¦ π+1 + 11π¦ π 0, (β2)( ( ) ( )) β1 β 2β
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