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 II

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 Section Content Suggested Problems Section 3.1 growth/decay linear models dP/dt = kP half-life Newton's Law of Cooling/Heating dT/dt = k(T-Tm) ambient temperature Mixtures dx/dt = (input rate of salt) - (output rate of salt) inflow volume equals outflow volume inflow volume does not equal the outflow volume 3, 5, 11, 14-15, 21, 25 Section 4.1 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 4.2 Reduction of Order Standard Form y2 = u(x)y1(x) 2, 6, 9 ,11 Section 4.3 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 4.4 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 4.6 Variation of Parameters Standard Form Construction Fundamental Set of Solutions for Homogeneous Problem Solution for u1' and u2' 1, 2, 6, 8, 11 Section 4.7 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

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