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Master Syllabus

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Administrative Unit: Computer and Mathematical Sciences Department
Course Prefix and Number: MATH 380
Course Title: Advanced Calculus I
Number of:
Credit Hours 3
Lecture Hours 3
Lab Hours 0
Catalog Description:

Rigorous development of some central ideas in analysis including limits, continuity and differentiability. Prerequisite: Grade of C or higher in MATH 222 or MATH 235 and C or higher in MATH 225.

Prerequisite(s) / Corequisite(s):

Grade of C or higher in MATH 222 or MATH 235 and C or higher in MATH 225.

Course Rotation for Day Program: Offered odd Fall.
Text(s): Most current editions of the following:

Introduction to Real Analysis
By Bartle, Robert and Donald Sherbert (John Wiley and Sons, Inc.)
Course Objectives

  •  To describe and explain the theoretical foundations of one-variable calculus.
  • To recognize valid mathematical arguments.
  • To verify precise mathematical definitions as one step in proving mathematical theorems.
  • To provide examples and counterexamples for mathematical statements.
  • To communicate mathematically, formally and informally, both verbally and in writing.

    Measurable Learning
  • Use the Axiom of Completeness and its consequences as a framework for comparing the real numbers, the rational numbers and the integers.
  • Define a topology on the real line and establish its fundamental properties.
  • Give a rigorous definition of the limit of a sequence and connect limits of sequences to the topology of the real line.
  • Give a rigorous definition of the limit of a function and show that the definition is consistent with the definition of limits of sequences.
  • Using the appropriate definition or theorem, establish the limit of a specific sequence of function.
  • Define continuity of a function and prove the intermediate Value Theorem.
  • Define uniform continuity of a function and compare to the concept of continuity.
  • Using the appropriate definition or theorem, show that a specific function is continuous or uniformly continuous.
  • Define the concept of differentiability for functions and prove the Mean Value Theorem.
  • Using the appropriate definition or theorem, show that a specific function is differentiable and compute its derivative.
  • Apply the ideas of limits, continuity and differentiability to establish the basic results used in differential calculus.
    Topical Outline:
  • Topology of the real numbers
  • Limits of sequences
  • Limits of functions
  • Continuity and the intermediate value theorem
  • Differentiability and the mean value theorem

    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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