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Master Syllabus

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Administrative Unit: Computer and Mathematical Sciences Department
Course Prefix and Number: MATH 215
Course Title: Differential Calculus
Number of:
Credit Hours 3
Lecture Hours 3
Lab Hours 0
Catalog Description:

The first course in a three part Calculus sequence. The course includes a brief review of algebra and trigonometry, limits, derivatives and their applications. Prerequisite: MATH 180 with a grade of C or higher or a score of 26 or higher on the math portion of the ACT or 590 or above SAT score or passing score on the Columbia College math placement exam. G.E.

Prerequisite(s) / Corequisite(s):

MATH 180 with a grade of C or higher or a score of 26 or higher on the math portion of the ACT or 590 or above SAT score or passing score on the Math Placement exam.

Course Rotation for Day Program:

Not offered in the day program.

Text(s): Most current editions of the following:

By Stewart (Brookes-Cole)
Course Learning Outcomes
  1. Compute limits, analytically or from a graph, or determine that a limit does not exist.
  2. Determine if functions are continuous, analytically or from a graph, and identify different types of discontinuities. 
  3. Compute derivatives of functions or determine that a derivative does not exist. 
  4. Relate the graph of a function to properties of its derivative.
  5. Solve applied problems using calculus.
Major Topics/Skills to be Covered:
  • 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.

Recommended maximum class size for this course: 30

Library Resources:

Online databases are available at the Columbia College Stafford Library.  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.

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