Goals and Assignments for the Sixth WeekSixth week goalsReading for September 28, 2004Reading for September 30, 2004Homework due October 5, 2004Reminder: Midterm exam, October 7, 2004, will cover material up to and including September 23 lecture (homework due September 28).College of Engineering and Computer ScienceMechanical Engineering DepartmentMechanical Engineering 501ASeminar in Engineering AnalysisFall 2004 Number: 17472 Instructor: Larry CarettoGoals and Assignments for the Sixth WeekSixth week goalsThis week we will continue our in-depth review of ordinary differential equations. We will examine the solutions to nonhomogenous second order equations and we will discuss solutions to homogenous and nonhomogenous differential equation with orders greater than two. The main engineering application of higher-order equations is in analysis of structures where the deflection of a structural member under load is governed by a fourth-order differential equation.After completing the reading and assignments for this week you should be able to obtain the general and particular solutions to second and higher order, nonhomogenous differential equations with constant coefficients.We will also consider existence and uniqueness theorems for higher-order differential equations.Reading for September 28, 2004Pages 101–108 cover nonhomogenous second-order ordinary differential equations, the general solution as a sum of homogenous solutions and a particular solution, using the method of undetermined coefficients.Pages 111–116 extends previous homogenous examples of mechanical vibrations to systems with forced oscillations.Reading for September 30, 2004Pages 97–100 discuss existence and uniqueness of second order differential equations.Pages 108–111 discuss the method of undetermined coefficients for finding particular solutions.Pages 124–140 consider the solution of ordinary differential equations with orders greater than two.Homework due October 5, 2004Page 103, problem 9. This problem introduces the concept of a particular solution and a general solution by giving you the particular solution and asking you to verify it.Page 108, problem 17. This takes the next step; here you have to find the particular solution yourself.Page 117, problem 13. This problem shows the application of second order equations to oscillations in mechanical systems.Page 141, problem 9. Here you have to apply what you have learned previously to a higher orderequation.Engineering Building Room 1333 Mail Code Phone: 818.677.6448Email: [email protected] 8348 Fax: 818.677.7062Reminder: Midterm exam, October 7, 2004, will cover material up to and including September 23 lecture (homework due September 28).Engineering Building Room 1333 Mail Code Phone: 818.677.6448Email: [email protected] 8348 Fax:
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