Catalog Description
- Transfer Status
- CSU/UC
- Prerequisite
- Intermediate Algebra or equivalent
- Unit(s)
- 4.00
- Lecture: 34.00 Contact hours/68.00 Out of class hours/102.00 Total hours/2.00 Unit(s)
- Activity: 68.00 Contact hours/34.00 Out of class hours/102.00 Total hours/2.00 Unit(s)
- Total: 102.00 Contact hours/102.00 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. This course will contain the same curriculum as MATH 13 but will also have embedded support to review key intermediate algebra concepts. This course emphasizes in-class activities and applications.
Objectives
Upon successful completion of this course, the student should be able to:
- Find the derivatives of polynomial, rational, exponential, and logarithmic functions.
- Find the derivatives of functions involving constants, sums, differences, products, quotients, and the chain rule.
- 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.
- Analyze the marginal cost, profit and revenue when given the appropriate function.
- Determine maxima and minima in optimization problems using the derivative.
- Use derivatives to find rates of change and tangent lines.
- Use calculus to analyze revenue, cost, and profit.
- Find definite and indefinite integrals by using the general integral formulas, integration by substitution, and other integration techniques.
- Use integration in business and economics applications.
- Graph, determine the domain and range and evaluate of a variety of functions.
- Factor polynomials
- Solve linear, quadratic, rational, and radical equations, and linear inequalities.
- Perform addition, subtraction, multiplication, and division on polynomials, rational expressions, and radical expressions.
- Graph linear, quadratic, and exponential equations in two variables.
- Simplify expressions involving integer and rational exponents using properties of exponents.
Course Content
Topic Titles / Suggested Time Topic
Lecture/Activity
| Topics | Lec Hrs | Act Hrs |
|---|---|---|
Functions and their graphs, including exponential and logarithmic functions | 5.00 | 14.00 |
Limits and intuitive limit definition of derivative | 3.00 | 5.00 |
Increments, tangent lines, and rate of change | 2.00 | 4.00 |
Rules of differentiation including sum, product, quotient, and the chain rule | 6.00 | 12.00 |
Implicit differentiation | 1.00 | 2.00 |
Applications of differentiation such as marginal analysis, optimization, and curve sketching | 6.00 | 12.00 |
Antiderivatives, indefinite and definite integrals | 3.00 | 5.00 |
Multiple techniques of integration including substitution | 3.00 | 5.00 |
Area between curves | 2.00 | 3.00 |
Approximating definite integral as a sum | 1.00 | 2.00 |
Applications of integration in business and economics | 2.00 | 4.00 |
| Total Hours: | 34.00 | 68.00 |
Methods of Instruction
- Collaborative Group Work
- Discussion
- Homework: Students are required to complete one hour of outside-of-class homework for every two hours of activity
- Homework: Students are required to complete two hours of outside-of-class homework for each hour of lecture
- Lecture
Methods of Evaluation
- Exams/Tests
- Quizzes
- Mid-term and final examinations
- Daily Homework Assignments, where the student will demonstrate problem-solving skills, Class Assignments and Class Response
Examples of Assignments
Reading Assignments
- 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.
- 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
- 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.
- 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
- Review the section in the textbook on limits and do the problems assigned by the instructor, show each step.
- Review the section in the textbook on antidifferentiation and do the problems assigned by the instructor, showing each step.
Recommended Materials of Instruction
Bittinger, M.L. (2020). Calculus and Its Applications. Pearson, 12th. 9780135164884.
Minimum Qualifications
Mathematics (Masters Required)