Microsoft Word - MATH 285 OUTLINE for WebCMS.docx
Approved: JUNE 2018Effective: FALL 2018 MATERIAL TO BE COVERED SECTIONS FROM TEXT TIME LINE Introduction to Differential Equations: definition and terminology, initial value problems, differential equations as mathematical models1.1-1.3 2 hoursFirst Order Differential Equations: direction fields, autonomous first order DEs, Separable, linear, exact differential equations solutions by substitutions, a numerical method 2.1-2.612 Hours Modeling With First Order Differential Equations: linear models, nonlinear models3.1 – 3.2 4 Hours Higher Order Differential Equations: linear equations, reduction of order, homogeneous linear equations with constant coefficients, the method of undetermined coefficients: superposition approach, the method of undetermined coefficients with annihilators, variation of parameters, Cauchy-Euler Equations. 4.1-4.7 12 Hours Modeling With Higher Order Differential Equations : spring –mass systems: free undamped motion, driven motion, series circuit analogue 5.14 Hours Series Solutions of Linear Equations : solutions about ordinary points 6.22 HoursThe Laplace Transform: definition, inverse transform, transform of derivatives, translation on the s-Axis, translation on the t-Axis 7.1-7.3 10 Hours Systems of Linear First-Order Differential Equations: linear systems, homogeneous linear systems: distinct real eigenvalues, repeated eigenvalues, complex eigenvalues8.1-8.24 HoursNumerical Solutions of Ordinary Differential Equations: Euler methods and error analysis, Runge-Kutta methods9.1-9.2 2 Hours 4-unit class: hours total 57.5 (15 x 3 hours 50 minutes) – hours for exams + 2.5 hour finalThis outline allows for 4 hours of exams. Submitted by: Beydler, Griffith, Guth, Khoddam, Kojima, Nguyen, Pop, Sholars, Tamayo, Tran Math Department Policy can be found at: ................
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