  
Description  
 A study of the techniques of differential and integral calculus, with an emphasis on the application of these techniques to problems in business and economics.


Course Objectives  
 The student will be able to:
 demonstrate an understanding of elementary functions including finding the derivatives of polynomial, rational, exponential, logarithmic functions, functions involving constants, sums, differences, products, quotients, and the chain rule
 demonstrate understanding of elementary ideas of limits, rates of change, and the derivative.
 apply techniques of differentiation, graphically, numerically and symbolically including sketching graphs of functions using horizontal/vertical asymptotes, intercepts, and the first and second derivatives to determine intervals where the function is increasing/decreasing, is concave up/down, and has local extrema and points of inflection
 use the derivative to solve application problems, including cost/marginal cost, profit/marginal profit, revenue/marginal revenue, optimization problems (max/min), rates of change and tangent lines
 demonstrate understanding of integration, including definite and indefinite integrals by using general integral formulas, integration by substitution and other integration techniques.
 Solve applications problems using definite integrals, including problems drawn from business and economics
 Demonstrate an understanding of antidifferentiation techniques and be able to analyze antiderivatives graphically and numerically.
 Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (G) above
 discuss mathematical problems and write solutions in accurate mathematical language and notation.
 interpret mathematical solutions.

Special Facilities and/or Equipment  
  Graphing Calculator
 When taught hybrid: Four lecture hours per week in facetoface contact and one hour per week using CCC Confer. Students need internet access.

Course Content (Body of knowledge)  
  Demonstrate an understanding of elementary functions
 Linear functions
 Average rate of change
 Exponential functions
 Logarithmic functions
 Exponential growth and decay
 Proportionality and power functions
 Demonstrate understanding of elementary ideas of limits, rates of change, and the derivative.
 Limits
 Approximation of limits numerically and visually from graphs of functions
 Limits and continuity
 Computation of limits algebraically
 Limit definition of the derivative
 Instantaneous rate of change and tangent lines
 The derivative function
 Interpretations of the derivative
 The second derivative
 Marginal cost, profit, and revenue
 Apply techniques of differentiation, graphically numerically and symbolically
 Derivative formulas for powers and polynomials.
 Exponential and logarithmic functions
 The chain rule
 The sum, product, and quotient rules
 Implicit differentiation
 Sketching graphs of functions using horizontal/vertical asymptotes, intercepts, and the first and second derivatives to determine intervals where the function is increasing/decreasing, is concave up/down, and has local extrema and points of inflection
 Use the derivative to solve problems in optimization, with particular emphasis on problems from business and economics.
 Local maxima and minima
 Inflection points
 Global maxima and minima
 Profit cost and revenue
 Average cost
 Elasticity of demand
 Logistic growth
 Demonstrate understanding of elementary ideas of accumulated change and the definite integral.
 The definite integral
 The definite integral as area
 Interpretations of the definite integral
 The fundamental theorem of calculus
 Approximate definite integrals using Riemann sums
 Solve applications problems using definite integrals
 Average value
 Consumer and producer surplus
 Present and future value
 Areas between curves: computation of with definite integrals and in applications (e.g., total profit)
 Demonstrate an understanding of antidifferentiation techniques and be able to analyze antiderivatives graphically and numerically.
 Constructing antiderivatives analytically
 Integration by substitution
 Using the fundamental theorem to find definite integrals
 Integration by parts
 Analyze antiderivatives graphically and numerically
 Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (G) above.
 Calculator/computer utilities for approximating graphs of derivative functions.
 Calculator/computer utilities for evaluating definite integrals
 Calculator/computer utilities for approximating graphs of antiderivative functions
 Discuss mathematical problems and write solutions in accurate mathematical language and notation.
 Use of proper notation
 Interpret mathematical solutions.
 Explain significance of solutions to application problems.

Methods of Evaluation  
  Homework
 Quizzes
 Exams
 Proctored comprehensive final examination

Representative Text(s)  
 Stefan Waner & Steven Costenoble. Applied Calculus. 6th ed. Boston:Brooks/Cole, 2014.

Disciplines  
 Mathematics


Method of Instruction  
  Lecture
 Discussion
 Cooperative learning exercises


Lab Content  
 Not applicable.


Types and/or Examples of Required Reading, Writing and Outside of Class Assignments  
  Homework Problems: Homework problems covering subject matter from text and related material ranging from 30  60 problems per week. Students will need to employ critical thinking in order to complete assignments.
 Reading and study of the textbook, related materials and notes.
 Projects: Student projects covering subject matter from textbook and related materials. Projects will require students to discuss mathematical problems,write solutions in accurate mathematical language and notation and interpret mathematical solutions. Projects may require the use of a computer algebra system such as Mathematica or MATLAB.
 Worksheets: Problems and activities covering the subject matter.
Such problems and activities will require students to think critically. Such worksheets may be completed both inside and/or outside of class.
