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 3350 Higher Mathematics for Engineers and Scientists Spring 2010 Zill & Cullen Advanced Engineering Mathematics Jones & Bartlett

Review Exam II
 Section Content Suggested Problems Section 3.1 Initial-Value and Boundary Value Problems Existence and Uniqueness of IVP Potential Non-Existence/Non-Uniqueness of BVP Homogeneous Equations Operator Notation Vector Space of Solutions of Homogeneous Equation Linear Independence of Solutions of Homogeneous Equation Theorem 3.3 Wronskian Test for Linear Independence Fundamental Set of Solutions Superpostion Principle - Non-Homongenous Equations Section 3.2 Reduction of Order Standard Form y2 = u(x)y1(x) 2, 6, 9 ,11 Section 3.3 Linear, Constant Coefficient, Homogeneous Auxillary or Characteristic Equation Case I: Distinct Real Roots Case II: Repeated Real Roots Case III: Complex Conjuate Roots Special Cases y" + k2y = 0 y" - k2y = 0 3, 5, 10, 13, 15, 18, 24, 31, 33, 34 Section 3.4 Method of Undetermined Coefficients Particular Solution L(y) = f(x) f(x) = polynomial f(x) = exponential f(x) = cosine or sine Glitch in the Method Initial-Value Problem 4, 8, 12, 16, 19, 23, 28, 31 Section 3.5 Variation of Parameters Standard Form Construction Fundamental Set of Solutions for Homogeneous Problem Solution for u1' and u2' 1, 2, 6, 8, 11 Section 3.6 Cauchy-Euler Equation Auxillary or Characteristic Equation Case I: Distinct Real Roots Case II: Repeated Real Roots Case III: Complex Conjuate Roots Non-Homogeneous Equations 1, 4, 9, 11, 15, 19 Section 3.8 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

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