MAC 2233 - Applied Calculus I

Mathematics Department

Credit(s): 3
Contact Hours: 47
Effective Term Fall 2022 (610)

Requisites

Prerequisite MAC 1105 with a minimum grade of C or
Prerequisite MAC 1106 with a minimum grade of C or
Appropriate score on the SPC mathematics placement test or program director approval

Course Description

This course is a geometric and heuristic approach to calculus: differentiation and integration of algebraic, exponential and logarithmic functions, applications to graphing, marginal analysis, optimization and areas. This course cannot be used to satisfy requirements of students majoring in mathematics or engineering. (Note: Credit is only given for MAC 2233 or MAC 2311 or MAC 2311H.)

Learning Outcomes and Objectives

  1. The student will apply relations and functions to calculus concepts by:
    1. identifying algebraic relations and functions in various forms.
    2. interpreting and sketching basic algebraic forms.
    3. classifying graphs of functions with respect to increasing/decreasing, concave up/down, maximum/minimum points, points of inflection, vertical/horizontal asymptotes, and holes.
    4. examining and integrating the graph of a function as an aid in solving applied problems.
  2. The student will determine limits and continuity of a function by:
    1. describing the limit of a function graphically and numerically and algebraically.
    2. interpreting the values for which a function is or is not continuous.
    3. implementing the limit of the difference quotient to find the derivative of a function.
    4. classifying limits to describe asymptotic behavior.
  3. The student will calculate and interpret the derivative of polynomial, rational, radical, exponential and logarithmic functions by:
    1. integrating appropriate derivative concepts to applications in economics, ecology, physical science, social science and biological science problems; including marginal analysis and optimization.
    2. summarizing the derivative using differentiation rules including the sum, product, quotient, power, and chain rules.
    3. implementing the derivative by implicit differentiation.
    4. carrying out higher order derivatives.
    5. examining 1st and 2nd derivatives to identify major characteristics of graphs; including slope of the tangent to a curve, intervals and values for which a function is increasing/decreasing and concave up/down, extrema, and points of inflection.
    6. applying techniques for derivatives such as differentials.
  4. The student will evaluate and interpret the integral of polynomial, rational, radical, exponential and logarithmic functions by:
    1. implementing appropriate integration concepts to applications in economics, ecology, physical science, social science, and biological science problems (such as total cost/revenue/profit, average value, consumption, production rate growth and decay)
    2. calculating the indefinite integral of a function using the antiderivative rules.
    3. determining the antiderivative of a function by using the basic antiderivative theorems.
    4. retrieving the definite integral by using the Fundamental Theorem of Calculus.
    5. summarizing the definite integral to area under the graph of a function.
    6. describing a definite integral by numerical integration.

Criteria Performance Standard

In order to earn a grade of C or better, the student will achieve at the 70% level or higher on classroom measures. Upon successful completion of the course, the student will, with a minimum of 70% accuracy, demonstrate mastery of each of the above stated objectives through classroom measures developed by individual course instructors.

History of Changes

C & I 9/19/85 3 Year Review 2007, DBT 10/17/85 eff20071(0385). Effective Session 19852 Exclusion amended SCN change 1/17/86 effective 20091(0414). Effective Session 19871 DBT 12/15/92 Effective Session 19922 3 YR C&I Review 1992-93 C&I 3/17/98; DBT 4/20/98 Effective Session 19981 Online 2001 C&I 11/13/01, BT 12/18/01 Effective 20021. C&I Approval: 04/13/2004, BOT Approval: 05/21/2004, Effective Term: Fall 2009 (415). C&I Approval: 11/20/2015, BOT Approval: 03/15/2016, Effective Term: Fall 2016 (520).
C&I Approval: , BOT Approval: , Effective Term: Fall 2022 (610)

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