Portland Community College | Portland, Oregon

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

Upon completion of the course students should be able to:

• 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.

• Recognize calculus concepts that are encountered in business and social sciences and communicate what the underlying mathematics indicate to help another person gain insight into the situation.

• Analyze 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.

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 is the final exam that is worth at least 25% of the overall grade.

2. Proctored exams should be worth at least 60% of the overall course grade.

3. 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.

4. At least two of the following additional measures:

   1. Take-home examinations.

   2. Projects/Writing Assignments. (Group and/or individual)

   3. Quizzes. (Group and/or individual)

   4. Graded homework/worksheets.

   5. In-class activities.

1. 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. 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.

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

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

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

   5. Solve applications of limits and continuity.

2. 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.

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

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

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

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

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

   6. Solve applications of rates of change and the derivative.

   7. Identify the local extrema and the intervals over which a function is increasing, decreasing, or constant.

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

   9. Determine the shape of a function from numerical or graphical information about that function’s first and second derivatives.

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

3. Symbolic Differentiation

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

   1. Utilize the power, sum, difference, product, or quotient rules to differentiate polynomial, rational, exponential, and logarithmic functions.

   2. Utilize the chain rule to differentiate a composite function.

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

   4. Solve applications of derivatives of exponential and logarithmic functions.

   5. Differentiate implicit functions.

   6. Solve applications of extrema including optimization and elasticity.

4. The Integral

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

   1. Use the rules for finding the family of antiderivatives of:

      1. polynomial functions

      2. exponential functions

      3. \(f(x) = 1/x\)

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

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

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

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

   6. Evaluate definite integrals using the Fundamental Theorem of Calculus.

   7. Solve applications of integration.

All work in this course will be evaluated for your ability to meet the following writing objectives as well as for "mathematical content."

1. Every solution must be written in such a way that the question that was asked is clear simply by reading the submitted solution.
2. Any table or graph that appears in the original problem must also appear somewhere in your solution.
3. All graphs that appear in your solution must contain axis names and scales. All graphs must be accompanied by a figure number and caption. When the graph is referenced in your written work, the reference must be by figure number. Additionally, graphs for applied problems must have units on each axis and the explicit meaning of each axis must be self-apparent either by the axis names or by the figure caption.
4. All tables that appear in your solution must have well defined column headings as well as an assigned table number accompanied by a brief caption (description). When the table is referenced in your written work, the reference must be by table number.
5. A brief introduction to the problem is almost always appropriate.
6. In applied problems, all variables and constants must be defined.
7. If you used the graph or table feature of your calculator in the problem solving process, you must include the graph or table in your written solution.
8. If you used some other non-trivial feature of your calculator (e.g. SOLVER), you must state this in your solution.
9. All (relevant) information given in the problem must be stated somewhere in your solution.
10. A sentence that orients the reader to the purpose of the mathematics should usually precede symbol pushing.
11. Your conclusion shall not be encased in a box, but rather stated at the end of your solution in complete sentence form.
12. Line up your equal signs vertically.
13. If work is word-processed all mathematical symbols must be generated with a math equation editor.