# Master Syllabus

 Administrative Unit: Computer and Mathematical Sciences Department Course Prefix and Number: MATH 370 Course Title: Differential Equations
Number of:
 Credit Hours 3
 Lecture Hours 3
 Lab Hours 0
 Catalog Description: Ordinary differential equations and systems with application to the sciences and engineering. Prerequisite: Grade of C or higher in MATH 222 or MATH 235. Prerequisite(s) / Corequisite(s): Grade of C or higher in MATH 222 or MATH 235. Course Rotation for Day Program: Offered odd Spring. Text(s): Most current editions of the following:Elementary Differential EquationsBy Boyce & DiPrima (Wiley) RecommendedElementary Differential Equations with Boundary Value ProblemsBy Edwards & Penney (Prentice Hall) Recommended Course Objectives To master the standard elementary techniques for solving differential equations. To gain an appreciation for the key role that differential equations play in modeling natural phenomena. To use differential equations to formulate and solve real world problems. Measurable Learning Outcomes: Use basic mathematical models to draw direction fields of some first order differential equations. Identify and solve separable, linear and exact differential equations. Solve homogeneous second order linear equations with constant coefficients when the roots of the characteristic equation are real and distinct, repeated and complex. Analyze the relationship between linearly independent functions, fundamental solutions of differential equations and the Wronskian determinant. Solve non-homogeneous second order linear equations with constant coefficients when the roots of the characteristic equation are real and distinct, repeated and complex. Analyze the relationship between linearly independent functions, fundamental solutions of differential equations and Wronskian determinant. Solve non-homogeneous second order linear equations using the method of undetermined coefficients and variation of parameters. Find series solutions of second order linear equations. Analyze series solutions near ordinary and regular singular points. Compute the Laplace transform and the inverse Laplace transform of a function. Solve initial value problems using the Laplace transform method. Determine whether vectors are linearly independent or linearly dependent. Compute eigenvalues and eigenvectors of a matrix. Find the general solution of homogenous linear systems with constant coefficients. Topical Outline: First order differential equations Second order linear equations Series solutions of second order linear equations The Laplace transform Systems of first order linear equations Recommended maximum class size for this course: 30 Library Resources: Online databases are available at http://www.ccis.edu/offices/library/index.asp. You may access them using your CougarTrack login and password when prompted.
Prepared by: Nataliya Latushkina Date: November 7, 2013
NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this course for Columbia College are expected to facilitate learning pursuant to the course objectives and cover the subjects listed in the topical outline. However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.