MATH 13 - Survey of Calculus

Transfer Status

CSU/UC

Prerequisite

Intermediate Algebra or equivalent

Unit(s)

4.00

• Lecture: 68.00 Contact hours/136.00 Out of class hours/204.00 Total hours/4.00 Unit(s)
• Total: 68.00 Contact hours/136.00 Out of class hours/204.00 Total hours/4.00 Unit(s)

Course Description: Presents a study of the techniques of calculus with emphasis placed on the application of these concepts to business and management related problems. The applications of derivatives and integrals of functions including polynomials, rational, exponential and logarithmic functions are studied. (C-ID MATH 140).

Upon successful completion of this course, the student should be able to:

1. Find the derivatives of polynomial, rational, exponential, and logarithmic functions.
2. Find the derivatives of functions involving constants, sums, differences, products, quotients, and the chain rule.
3. Sketch the graph of functions using horizontal and vertical asymptotes, intercepts, and first and second derivatives to determine intervals where the function is increasing and decreasing, maximum and minimum values, intervals of concavity and points of inflection.
4. Analyze the marginal cost, profit and revenue when given the appropriate function.
5. Determine maxima and minima in optimization problems using the derivative.
6. Use derivatives to find rates of change and tangent lines.
7. Use calculus to analyze revenue, cost, and profit.
8. Find definite and indefinite integrals by using the general integral formulas, integration by substitution, and other integration techniques.
9. Use integration in business and economics applications.

Topic Titles / Suggested Time Topic

Lecture

1. Collaborative Group Work
2. Discussion
3. Homework: Students are required to complete two hours of outside-of-class homework for each hour of lecture
4. Lecture

1. Exams/Tests
2. Quizzes
3. Mid-term and final examinations
4. Daily Homework Assignments, where the student will demonstrate problem-solving skills, Class Assignments and Class Response

Reading Assignments

1. Read the section in the textbook on limits and be able to find the limit of a function graphically and algebraically by using properties of limits and analytic techniques.
2. Read the section in the textbook on antidifferentiation and be able to find the antiderivative of a function, evaluate indefinite integrals using basic rules of antidifferentiation and use initial conditions to determine an antiderivative.

Writing Assignments

1. Describe in words how to find the limit as x approaches 2 for the function 3x - 4. Assume you are teaching it to someone for the first time and write a detailed explanation.
2. Describe in words the process you would go through to evaluate the indefinite integral of x^6 dx. Assume you are explaining it to someone in the class who is having trouble and write a detailed explanation.

Out-of-Class Assignments

1. Review the section in the textbook on limits and do the problems assigned by the instructor, show each step.
2. Review the section in the textbook on antidifferentiation and do the problems assigned by the instructor, showing each step.

Bittinger, M.L. (2016). Calculus and Its Applications. Pearson, 11th.

Other Learning Materials

Scientific calculator or graphing calculator without symbolic algebra capabilities

Mathematics (Masters Required)