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 2012 Zill & Cullen Advanced Engineering Mathematics Jones & Bartlett

Review Exam I
 Section Content Suggested Problems Section 1.1 definition of a differential equation classification type order linearity notation: Leibnitz vs. Newton definition of a solution of an ODE explicit vs implicit solutions family of solutions one-parameter family of solutions 1-8 Section 1.2 initial-value problem (IVP) first and second order IVP existence and uniqueness Theorem 1.1 2, 4, 7, 11, Section 2.1 direction fields Section 2.2 definition of a separable equation method of solution initial-value problem 5, 5, 7, 8, 10, 12, 18, 24-26 Section 2.3 definition of a linear equation homogeneous standard form of a linear equation linearity property of solutions of the homogeneous equation method of solution find integrating factor exp(int(p(x)dx)) integrate the product of the integrating factor and f(x) formualte the general solution of the linear equation initial-value problem functions defined by integration 3, 5, 7, 10-12, 14, 16, 18, 25, 26, 29 Section 2.4 definition of an exact equation M(x,y)dx + N(x,y)dy = 0 criterion for being exact method of solution initial value problem integrating factors 2-5, 7-9, 11, 14, 16, 19, 21, 23 Section 2.5 homogeneous functions degree homogenous first-order ODE method of solution substitution y = ux substitution x = vy Bernoulli equations method of solution u=y1-n reduction to separable substitution u = Ax + By + C 3-4, 6-7, 10-12, 15-16, 21, 23-24, 27-28 Section 2.6 tangent line approximation slope from the direction field Euler's Method yn+1 = yn + h f(xn,yn) error estimates numerical solvers None Section 2.7 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 2.8 population dynamics logistic equation solution of logistic equation modifications of the logistic equation None

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