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Master Syllabus

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Administrative Unit: Computer and Mathematical Sciences Department
Course Prefix and Number: MATH 201
Course Title: Calculus and Analytic Geometry I
Number of:
Credit Hours 5
Lecture Hours 5
Lab Hours 0
Catalog Description:

The first part of the three-part calculus series. Topics include: review of algebra and trigonometry; functions and limits; derivatives and their applications; the integrals and their applicatations.  Prerequisite: Grade of C or higher in MATH 180 or a score of 26 or higher on the math portion of the ACT or 590 or above SAT score or a passing score on the Columbia College math placement exam. G.E.

Prerequisite(s) / Corequisite(s):

Grade of C or higher in MATH 180 or a score of 26 or higher on the math portion of the ACT or 590 or above SAT score or a passing score on the Columbia College math placement exam.

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

A TI-84 calculator is required for this course. This calculator will be allowed on most assessment opportunities in this course.

By Finney, R. & G. Thomas (Addison-Wesley)
By Stewart (Brookes-Cole)
Course Objectives
  • To understand procedural and conceptual aspects of basic calculus ideas such as limit, derivatives and integrals.
  • To use appropriate technology, such as graphing calculators and computers, to deepen mathematical understandings and solve real-word problems.
  • To establish connections between calculus and other disciplines.
    Measurable Learning
  • Identify basic algebraic and trigonometric functions from numerical, graphical, symbolic and analytic perspectives.
  • Apply limit laws to calculate limits of sums, differences, products and quotients of functions.
  • Distinguish between one-sided and two-sided limits and describe their existence from geometric and analytic points of view.
  • Evaluate limits using the precise definition of the limit.
  • Determine if functions are continuous and identify removable, infinite and jump discontinuities.
  • Apply the Intermediate Value Theorem to prove the existence of roots of functions.
  • Explain derivatives as instantaneous rates of change.
  • Differentiate functions explicitly and implicitly and identify cases where functions are not differentiable.
  • Differentiate composite functions using the Chain Rule.
  • Apply differential and integral calculus to solve problems in the natural and social sciences.
  • Compute higher order derivatives and interpret them from a physical point of view.
  • Use linear approximations and differentials to approximate functions and solve applied problems.
  • Apply the Mean Value Theorem to establish basic properties of differentiable functions.
  • Compute limits at infinity and identify horizontal asymptotes.
  • Sketch graphs of functions based on information about their first and second derivatives.
  • Solve optimization problems.
  • Use Newton’s method to solve equations and identify limitations of the method.
  • Find antiderivatives of functions with and without initial conditions.
  • Compute definite integrals as the limit of Riemann sums and approximate integrals using finite Riemann sums.
  • Evaluate definite and indefinite integrals using the Fundamental Theorem of Calculus and the method of substitution.
  • Compute areas and volumes using definite integrals.
    Topical Outline:
  • Review of functions
  • Limits and continuity
  • Derivatives
  • Applications of derivatives (including curve sketching)
  • Integrals
  • Applications of integrals

    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: 30

    Library Resources:

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

    Prepared by: Suzanne Tourville 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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