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Master Syllabus

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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 Analysis
By Bartle, Robert and Donald Sherbert (Wiley)
Course Objectives
  • To understand the theoretical foundations of one-variable calculus.
  • To recognize valid mathematical arguments.
  • To verify precise mathematical definitions as one step in providing mathematical theorems.
  • To provide examples and counterexamples for mathematical statements.
  • To communicate mathematically, formally and informally, both verbally and in writing.
    Measurable Learning
  • 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.
    Topical Outline:
  • Riemann Integral
  • Infinite series
  • Sequences and series of functions
    Culminating Experience Statement:

    Material from this course may be tested on the Major Field Test (MFT) administered during the Culminating Experience course for the degree. 
    During this course the ETS Proficiency Profile may be administered.  This 40-minute standardized test measures learning in general education courses.  The results of the tests are used by faculty to improve the general education curriculum at the College.


    Recommended maximum class size for this course: 20

    Library Resources:

    Online databases are available at You may access them from off-campus using your CougarTrack login and password when prompted.

    Prepared by: Kenneth Felts Date: November 6, 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.

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