ࡱ> OQNa bjbj D.AbAb..''''''''8'$(<'DV(V(V(V(V(E)E)E)?DADADADADADAD$FLIeD'E)E)E)E)E)eD''V(V(zD...E)'V('V(?D.E)?D..R@)CV(*V~)9B+DD0DWBIg*I<)C)CI'GCE)E).E)E)E)E)E)eDeD],2E)E)E)DE)E)E)E)IE)E)E)E)E)E)E)E)E).B p&: GROSSMONT COLLEGE Official Course Outline MATHEMATICS 285 DIFFERENTIAL EQUATIONS Course Number Course Title Semester Units Semester Hours MATH 285 Differential Equations 3 3 hours lecture: 48-54 hours 96-108 outside-of-class hours 144-162 total hours Course Prerequisites A C grade or higher or Pass in MATH 280 or equivalent. Corequisite None Recommended Preparation None. Catalog Description The course is an introduction to ordinary differential equations including both quantitative and qualitative methods as well as applications from a variety of disciplines. Introduces the theoretical aspects of differential equations and systems of equations, including establishing when solutions exist and various techniques for obtaining solutions (series solutions, Laplace transforms, separation of variables, variation of parameters, etc). Course Objectives The student will: Create and analyze mathematical models using ordinary differential equations. Identify the type of a given differential equation and select and apply the appropriate analytical technique for finding the solution of first order and selected higher order ordinary differential equations. Apply the existence and uniqueness theorems for ordinary differential equations. Find power series solutions to ordinary differential equations. Determine the Laplace Transform and inverse Laplace Transform of functions. Solve Linear Systems of ordinary differential equations. Instructional Facilities a. Standard classroom equipped with: 1) Whiteboards 2) Overhead projector/document camera 3) SmartCart Special Materials Required of Student Graphing calculator. MATHEMATICS 285 DIFFERENTIAL EQUATIONS page 2 Course Content Solutions of ordinary differential equations. First order DE including separable, homogeneous, exact, and linear. Existence and uniqueness of solutions. Applications of first order differential equations such as circuits, mixture problems, population modeling, orthogonal trajectories, and slope fields. Second order and higher order linear differential equations. Fundamental solutions, independence, Wronskian. Nonhomogeneous equations. Applications of higher order differential equations such as the harmonic oscillator and circuits; Variation of parameters. Laplace Transforms. Series Solutions Systems of Ordinary differential equations Method of Instruction The development of problem-solving techniques may be achieved by using a variety of instructional techniques including instructor presented lecture and examples, individual and group work, and daily problem assignments. Methods of Evaluating Student Performance a. Homework and problem sets b. Quizzes a. Exams c. In-class comprehensive final exam Outside Class Assignments a. Homework and problems sets b. Take-home tests Texts Required Text(s): Zill, Dennis G. First Course in Differential Equations. Pacific Grove, CA: Brooks/Cole Publishing Co., 2011, 10th edition. Supplementary texts and workbooks: None. Addendum: Student Learning Outcomes Upon completion of this course, our students will be able to do the following: Categorize differential equations and use appropriate theorems, formulas, and algorithms to solve them. Use the appropriate technology to solve problems requiring differential equations. Formulate, analyze, and differentiate mathematical conceptions requiring differential equations and manipulate them numerically, graphically, and symbolically as well as have the ability to transition between these representations. Communicate the mathematical process and assess the validity of the solution. Date approved by the Governing Board: December 11, 2012   VWdeqr ! 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