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University of Louisville

Engineering Fundamentals

ENGR 205

Robinson

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 β1 {πΉ π )} for a given πΉ 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¦ = πΆ 2 + πΆ 4 π
π 1 2
2 Find a general solution to the difference equatioπ+2π¦β 4π¦ π+1 + 4π¦ π 2 ,π
π π2
Answer: π¦ π 2 (πΆ + 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,
(β2)( ( ) ( )) β1 β 2β

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