Portland Community College | Portland, Oregon

This course is designed for non-mathematics majors in business, life or social science.

Upon successful completionsstudents should be able to:

• Analyze real world business and social science scenarios to recognize when calculus can be applied, formulate problems about the scenarios, creatively model these scenarios (using technology, if appropriate) in order to solve the problems using multiple approaches, judge if the results are
reasonable, and then interpret and clearly communicate the results.
• Appreciate calculus concepts that are encountered in business and social sciences, understand and be able to communicate the underlying mathematics involved to help another person gain insight into the situation.
• Work with calculus concepts in various situations and use correct mathematical terminology, notation, and symbolic processes in order to be prepared for future coursework in business and social sciences that requires the use of and an understanding of the concepts of calculus.

All activities will follow the premise that formal definitions and procedures evolve from the investigation of practical problems. Concepts will be introduced using lecture, group activities, calculator programs, and explorations. Students will communicate their results orally and in writing.

Assessment must include:

1.   At least two proctored, closed book examinations, one of which may be the final exam.

2.   Various opportunities to express – and be graded on – mathematical concepts in writing.  Assessment should be made on the basis of using correct mathematical syntax, appropriate use of the English language, and explanation of the mathematical concept.

3.   At least two of the following additional measures:

a)   Take-home examinations. (Group and/or individual)

b)   Projects. (Group and/or individual)

c)   Quizzes. (Group and/or individual)

d)   Graded homework/worksheets.

e)   In-class activities.

f)    Attendance.

g)   Portfolios.

h)   Individual student conference.

COURSE CONTENT (Themes, Concepts, Issues, and Skills):

THEMES, CONCEPTS, ISSUES:

·        Polynomial, rational, exponential, and logarithmic functions

·        Graphing and interpreting graphs of functions

·        Algebraic manipulation of functions

·        Appropriate use of technology

·        Problem solving and critical thinking

·        Communication and interpretation of results in individual or group settings

SKILLS:

1.0    LIMITS AND CONTINUITY:

The instructional goal is to explore the limit at a point, infinite limits, limits at infinity, continuity at a point and continuity over an interval.

            1.1    Determine or estimate the limit at a point (from the left, from the right, and two-sided) for functions presented in graphical, tabular, or symbolic form.

            1.2    Determine or estimate the limits at infinity for functions presented in graphical, tabular, or symbolic form.

            1.3    Identify points of discontinuity for functions presented in graphical or symbolic form.

            1.4    Identify intervals of continuity for functions presented in graphical form.

            1.5    Solve applications of limits and continuity.

2.0    THE DERIVATIVE:

The instructional goal is to explore the definition of the derivative, the meaning of instantaneous rate of change, and the practical meaning of the derivative as rate of change.

            2.1    Find average rates of change for functions presented in graphical, tabular, or symbolic form.

            2.2    Estimate instantaneous rates of change for functions presented in graphical, tabular, or symbolic form.

            2.3    Estimate derivative values for functions presented in graphical, tabular, or symbolic form.

            2.4    Sketch the graph of the derivative for functions presented in graphical form.

            2.5    Use the formal definition of the derivative to find derivative values and functions.

            2.6    Solve applications of rates of change and the derivative.

            2.7    Identify the local extrema and the intervals over which a function is increasing,     

                     decreasing, or constant.

            2.8    Identify the concavity and points of inflection for a function.

                                 2.9    Determine the shape of a function from numerical or graphical information about that

                                          function’s first and second derivatives.

            2.10  Solve applications of extrema, concavity, and curve sketching.

3.0    SYMBOLIC DIFFERENTIATION:

The instructional goal is to find derivative formulas for functions presented in symbolic form and to interpret the formulas in applied contexts.

         3.1    Utilize the power, sum, difference, product, or quotient rules to differentiate polynomial,

                  rational, exponential, and logarithmic functions.

         3.2    Utilize the chain rule to differentiate a composite function.

         3.3    Solve applications of derivatives of powers, products, quotients, and compositions.

         3.4    Solve applications of derivatives of exponential and logarithmic functions.

         3.5    Differentiate implicit functions.

         3.6    Solve applications of extrema including optimization and elasticity.

4.0    THE INTEGRAL:

The instructional goal is to explore indefinite and definite integrals and to make connections between the derivative and the definite integral.

4.1    Use the rules for finding the family of antiderivatives of:

                     4.1.1   polynomial functions

                     4.1.2   exponential functions

                     4.1.3   f(x) = 1/x

4.2    Use substitution to find the family of antiderivatives of a composite function. 

4.3    Find left-hand and right-hand Riemann sums for functions presented in graphical, tabular, or symbolic form.

4.4    Interpret the practical meaning of the integral in appropriate applications.

4.5    Determine or estimate the total change in a function when the derivative of the function is presented in graphical, tabular, or symbolic form.

4.6    Evaluate definite integrals using the Fundamental Theorem of Calculus.

4.7    Solve applications of integration.