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Master Syllabus

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Administrative Unit: Computer and Mathematical Sciences Department
Course Prefix and Number: MATH 222
Course Title: Calculus and Analytic Geometry II
Number of:
Credit Hours 5
Lecture Hours 5
Lab Hours 0
Catalog Description: The second part of the three-part Calculus series. Transcendental functions, techniques of integration, improper integrals, infinite series and power series, parametrized curves and polar coordinates. Prerequisite: MATH 201 with grade of C or higher.
Prerequisite(s) / Corequisite(s): MATH 201 with grade of C or higher.
Course Rotation for Day Program: Offered Fall and Spring.
Text(s): Most current editions of the following:

By Stewart (Brookes-Cole)
Course Learning Outcomes
  1. Demonstrate understanding of the calculus of logarithmic and exponential functions.
  2. Demonstrate understanding of the calculus of inverse trigonometric functions.
  3. Analyze indeterminate forms and apply L’Hospital’s rule to evaluate limits of such forms.
  4. Apply integration rules including substitution, integration by parts, trigonometric identities, trigonometric substitution and partial fractions to evaluate integrals.
  5. Classify improper integrals and distinguish between convergent and divergent improper integrals.
  6. Apply tests for convergence to determine convergence of infinite series.
  7. Find and use Taylor series to approximate functions.
Major Topics/Skills to be Covered:
  • Identify the natural exponential and logarithmic functions as inverses of each other and find their derivatives and integrals.
  • Solve exponential growth and decay problems arising from biology, physics, chemistry, and other sciences.
  • Compute derivatives and integrals of functions containing inverse trigonometric functions.
  • Analyze various indeterminate forms and apply L’Hospital’s Rule to evaluate limits of such forms.
  • Use the Substitution Rule and the Integration by Parts formula to evaluate indefinite and definite integrals.
  • Describe & explain special methods required to integrate trigonometric and rational functions.
  • Apply numerical methods of integration such as Simpson’s Rule and the Trapezoidal Rule to approximate definite integrals.
  • Classify improper integrals and distinguish between convergent and divergent improper integrals.
  • Explore geometric applications of integration, such as the length, the area of a surface, as well as their applications to physics, engineering, economics, and biology.
  • Apply basic calculus ideas to parametric and polar curves to determine the arc length, surface area of revolution, and other geometric characteristics.
  • Use polar coordinates to plot points and regions in the plane. 
  • Apply various tests for convergence to distinguish between absolutely and conditionally convergent and divergent numeric series.
  • Find the radius and the interval of convergence of power series.
  • Find Taylor and Maclaurin series for certain classes of functions.
  • Explore applications of Taylor series and polynomials to approximate functions and definite integrals, to evaluate limits, and solve initial value problems.

Recommended maximum class size for this course: 30

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.

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