Mathematics & Statistics Texas Tech University Kent Pearce Department of Mathematics and Statistics Texas Tech University Lubbock, Texas 79409-1042 Voice: (806)742-2566 x 226 FAX: (806)742-1112 Email: kent.pearce@ttu.edu

 Math 3354 Differential Equations I Spring 2013 Zill & Cullen Differential Equations with Boundary Value Problems Cole & Brooks

Review Exam III

You may bring a notecard to the exam with review information you have prepared for the exam.

 Section Content Suggested Problems Section 5.1 Linear Dynamical Systems Hooke's Law Newton's Second Law Spring/Mass Equilibrium Position Coordinate System Orientation Free Undamped Motion mx" + kx = 0 x" + ω2x = 0 Alternative Form of Solution Amplitude Phase Angle Free Damped Motion mx" + βx' + kx = 0 x" + 2λx' + ω2x = 0 Overdamped, Critically Damped, Underdamped Driven or Forced Motion mx" + βx' + kx = f(t) x" + 2λx' + ω2x = F(t) Transient vs Steady-State Solutions 3, 6, 9, 10, 21, 22, 26, 29 Section 7.1.1 Definition of Improper Integral Basic Definition of Laplace Transform Transforms of Basic Functions (Theorem 7.1) Exponential Order Theorem 7.1.2 Sufficient Condition for Existence Laplace Transform of Piece-wise Continuous Function 3, 5, 9, 13, 21, 24, 27, 31, Section 7.2 Inverse Transforms Theorem 7.2.1 Partial Fraction Expansions and Linearity Transforms of Derivatives Solving linear initial-value problems Procedure Diagram Solve First Order Linear IVPs Solve Second Order Linear IVPs 3, 4, 8, 15, 17, 20, 23, 26, 27, 32, 34, 36 Section 7.3 Translation on the s-axis First translation/shifting theorem (Theorem 7.3.1) Unit step function Piece-wise Defined Functions Translation on the t-axis Second translation/shifting theorem (Theorem 7.3.2) Alternative Version of Theorem 7.3.2 Solving linear initial-value problems 3, 6, 9, 10, 11, 14, 16, 18, 19, 22, 24, 26, 29, 37, 41, 43, 44, 47, 63, 65, 68 Section 7.4 Derivatives of Transforms (Theorem 7.4.1) Convolution Theorem (Theorem 7.4.2) Transform of a Period Function (Theorem 7.4.3) Solving linear initial-value problems 3, 6, 9, 11, 13, 21, 23, 50, 51 Section 7.5 Unit Impulse Function Dirac Delta Function Solving linear initial-value problems 1, 3, 6, 9

Home | Vita | Pre-Prints | Courses | Pre Lims | Links | Jokes

Comments maybe be mailed to: kent.pearce@ttu.edu