# Master Syllabus

 Administrative Unit: Computer and Mathematical Sciences Department Course Prefix and Number: MATH 381 Course Title: Advanced Calculus II
Number of:
 Credit Hours 3
 Lecture Hours 3
 Lab Hours 0
 Catalog Description: A second course in mathematical analysis on the real line. Topics include: the Riemann Integral, infinite series, and sequences and series of functions. Prerequisite: C or higher in MATH 380. Prerequisite(s) / Corequisite(s): C or higher in MATH 380. Course Rotation for Day Program: Offered even Spring. Text(s): Most current editions of the following:Introduction to Real AnalysisBy Bartle, Robert and Donald Sherbert (Wiley) Recommended Course Learning Outcomes Define the Riemann Integral as a limit of Riemann sums. Prove single variable calculus theorems. Determine the convergence of sequences of real numbers and functions and convergence of series of real numbers. Construct the Taylor series approximation of a function. Major Topics/Skills to be Covered: Define the Riemann Integral as a limit of Riemann sums. Determine if a function is integrable and give examples of functions that are not integrable. Prove the Fundamental Theorem of Calculus. Prove the Change of Variable Theorem. Determine if an infinite series of real numbers converges, converges conditionally, or diverges. Compare pointwise, uniform, and bounded convergence for a sequence of functions. Prove the bounded Convergence Theorem. Determine the radius of convergence for a power series. Construct the Taylor series approximation of a function. Recommended maximum class size for this course: 20 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: Suzanne Tourville Date: April 1, 2015
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 learning outcomes and cover the subjects listed in the Major Topics/Skills to be Covered section. 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.