MATH& 148 Business Calculus (5 credits)
Distribution Area Fulfilled Natural Sciences; Quantitative and Symbolic Reasoning; General Transfer Elective
Formerly MATH 157 - CCN
Prerequisite MATH 147 (preferred) or MATH& 141 with a grade of at least 2.0 or instructor permission.
Course Description
A concise course in calculus covering differential and integral calculus of non-trigonometric functions with an emphasis on business and economics applications.
Course Content
Limits & Continuity
Numerical, graphical, and algebraic methods for limits
Definition of continuity
Determining continuity with graphical and computational methods
Rates of Change and Differentiation
Average rate of change
Definition of the derivative
Estimating instantaneous rates of change with limits
Differentiability
Equation of the tangent line
Differentiation techniques for polynomial, rational, exponential and logarithmic functions
Higher-order derivatives
Applications of Differentiation
Critical points, inflection point, intervals of increase/decrease, concavity, and relative extrema
Graph sketching using first and second derivatives
Applications of the instantaneous rate of change (marginal profit, marginal revenue, and marginal cost)
Applications of optimization (maximizing profit, minimizing cost, minimizing inventory costs, or maximizing yield)
Elasticity of demand
Fundamental Theorem of Calculus
Integration and Applications
Indefinite and definite integrals for xn, ex, ln(x) and linear combinations of these functions
Methods of integration including substitution and a table of integrals
Riemann sums
Area between curves
Area between curves in applications (e.g. interpret the integral of marginal cost as a change in total cost)
Applications of definite integrals (consumers’ surplus, producers’ surplus, and average value of a function on an interval)
Functions of Several Variables
Functions of several variables
Partial derivatives, including first partials, second partials, and mixed partials
Student Outcomes
At the end of the course, students will be able to:
- Evaluate and apply concepts of limits, continuity, and differentiability numerically, graphically and algebraically.
- Calculate the average and instantaneous rates of change of functions and interpret their meaning in business and economics applications.
- Calculate derivatives of polynomial, rational, exponential, and logarithmic functions using techniques including taking the limit of the difference quotient and applying rules of differentiation.
- Apply derivatives to determine the behavior of functions such as intervals of increase and decrease and local and global extrema, and use this information to solve applied optimization problems in business and economics.
- Calculate indefinite and definite integrals, and use them to find the area between curves and to solve applied problems.
- Evaluate functions of several variables and calculate and evaluate partial derivatives.
- Choose, use, and move between appropriate representations (numerical, graphical, and symbolic) to model and solve problems, interpret results, and effectively communicate mathematical processes and solutions in context and to an intended audience.
Degree Outcomes
Quantitative & Symbolic Reasoning: Graduates utilize mathematical, symbolic, logical, graphical, geometric, or statistical analysis for the interpretation and solution of problems in the natural world and human society.
Critical, Creative and Reflective Thinking: Graduates will evaluate, analyze, synthesize, and generate ideas; construct informed, meaningful, and justifiable conclusions; and process feelings, beliefs, biases, strengths, and weaknesses as they relate to their thinking, decisions, and creations.
Effective Communication: Graduates will be able to craft and exchange ideas and information in a variety of situations, in response to audience, context, purpose, and motivation.
Lecture Contact Hours 50
Lab Contact Hours 0
Clinical Contact Hours 0
Total Contact Hours 50
Potential Methods
Discussions
Written Assignments
Projects
Homework
Quizzes
Objective Tests
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