Seward County Community College/Area Technical School
Course Syllabus

1. TITLE OF COURSE: MA2304 - Business Calculus
2. COURSE DESCRIPTION: 4 credit hours of lecture per week. An introduction to calculus and the methods of calculus with applications to business, economics, the social and behavioral sciences, life sciences as in ecology, health, and agriculture and other fields. For the non-mathematics majors needing some skills of calculus. For each unit of credit, a minimum of three hours per week with one of the hours for class and two hours for studying/preparation outside of class is expected.
   Pre-requisite: MA1173 - College Algebra or its equivalent.
3. PROGRAM AND DEPARTMENT MISSION STATEMENT: The Mathematics Department at Seward County Community College/ATS will enhance a student's ability to think critically using mathematical principals, ideas, and concepts in order to function in a society with ever-changing technology.
4. TEXTBOOK AND MATERIALS:
   • Larson, Ron. Brief Calculus: An Applied Approach, Houghton Mifflin Company, 8th edition, 2009.
   • Texas Instruments 83, 83 plus, 84, or 84 plus Graphing Calculator.
5. SCCC/ATS OUTCOMES:
   • Outcome #2 - Communicate ideas clearly and proficiently in writing, appropriately adjusting content and arrangement for varying audiences, purposes, and situations.
   • Outcome #4 - Demonstrate mathematical skills using a variety of techniques and technologies.
   • Outcome #5 - Demonstrate the ability to think critically by gathering facts, generating insights, analyzing data, and evaluating information.
   • Outcome #6 - Exhibit skills in information and technological literacy.
   • Outcome #9 - Exhibit workplace skills that include respect for others, teamwork competence, attendance/punctuality, decision making, conflict resolution, truthfulness/honesty, positive attitude, judgment, and responsibility.
6. COURSE OUTCOMES:
   • The students will see calculus as a mathematical tool in the solution of problems relating to professional activities.
   • The student will acquire skills in the techniques of differential and integral calculus.
   • The student will become familiar with various applications of these techniques in undergraduate courses in their major and subsequent careers.
   • Graphs and Functions
     • The student will interpret real-life data that is presented graphically.
     • The student will find the points of intersection of two graphs algebraically and graphically.
     • The student will find the break-even point for a business.
     • The student will use linear equations to solve real-world problems.
     • The student will evaluate functions, find domain and range of functions, and combine functions to form other functions.
     • The student will find compositions of functions and inverses of functions.
     • The student will use functions to model real-world situations.
   • Limits and Continuity
     • The student will determine limits of functions analytically, geometrically, and numerically.
     • The student will determine the continuity of a function.
     • The student will use analytical and graphical models of real-life data to solve real-life problems.
     • The student will use the concepts of limits and continuity to describe mathematical situations.
   • The Derivative, Slope, and Rate of Change
     • The student will interpret the slope of a graph in a real life setting.
     • The student will use the limit definition to find the derivative of a function.
     • The student will determine the slope of a graph and the equation of a tangent line to a graph.
     • The student will find the average and instantaneous rates of change of a quantity in a real-life problem.
     • The student will find the velocity and acceleration of a function.
     • The student will find marginal revenue, marginal cost, and marginal profit and explain what is meant by these terms.
     • The student will explain graphic and analytic interpretations of the derivative of a function and specifically discuss how these concepts can be applied in business and economics.
   • Derivative Rules
     • The student will use basic derivative rules to find the derivative of a function.
     • The student will use the product rule to find the derivative of a function.
     • The student will use the quotient rule to find the derivative of a rational function.
     • The student will use the chain rule to find the derivative of a composite function.
     • The student will find higher-order derivatives.
   • Implicit Differentiation and Related Rates
     • The student will find the derivative of am implicitly defined function.
     • The student will use derivatives to answer questions about real-life situations.
     • The student will solve related-rates problems.
   • Graphing Functions
     • The student will define and explain how to find critical points, intervals where a function is increasing and decreasing, relative extreme, points of inflection, and intervals where a function is concave up and concave down.
     • The student will find items listed in F1.
     • The student will find intervals on which a real-life model is increasing or decreasing, find minimum and maximum values, and interpret the results in context.
     • The student will find the point of diminishing returns of an input-output model.
     • The student will use asymptotes to answer questions about real life.
     • The student will find infinite limits and limits at infinity.
     • Use the fist and second derivative of a function to analyze the graph of a function.
   • Optimization and Differentials
     • The student will solve real-life optimization problems, including business and economics problems.
     • The student will find the price elasticity of demand for a demand function.
     • The student will use differentials to approximate changes in functions.
     • The student will use differentials to approximate changes in real-life models.
     • The student will use differentials to approximate error propagation.
   • Exponential and Logarithmic Functions
     • The student will evaluate limits of exponential and logarithmic functions in real-life situations.
     • The student will find the derivative of exponential and logarithmic functions containing the natural base and other bases.
     • The student will graph logistic growth factors.
     • The student will solve compound interest problems.
   • Exponential Growth and Decay
     • The student will use properties of natural logarithms and exponentials to answer real-life problems.
     • The student will solve the logarithmic and exponential equations.
     • The student will solve exponential growth and decay problems.
   • Antiderivatives
     • The student will explain the relationship between the derivative and the antiderivative of a function.
     • The student will evaluate indefinite integrals.
     • The student will find the particular solutions of indefinite integrals to solve applications.
   • Definite Integrals, Areas and Volume
     • The student will explain how the Fundamental Theorem of Calculus relates differential calculus with integral calculus.
     • The student will evaluate definite integrals using the Fundamental Theorem of Calculus.
     • The student will find the area under and between curves using definite integrals.
     • The student will use definite integrals to solve marginal analysis problems.
     • The student will find and use average values of functions to solve real-life problems.
     • The student will find consumer and producer surpluses.
     • The student will find the volume of a solid of revolution to solve real-life problems.
   • Methods of Integration
     • The student will use substitution to find definite and indefinite integrals.
     • The student will use integration by parts to determine integrals.
     • The student will find the present value of future income.
     • The students will use logistics growth functions to model real-life situations.
     • The student will complete the square to determine indefinite integrals.
     • The student will use partial fractions to find indefinite integrals.
     • The student will use integration tables to find indefinite integrals.
     • The student will use reduction formulas to find indefinite integrals.
   • Numerical Integration and Improper Integrals
     • The student will use various methods to approximate definite integrals.
     • The student will evaluate improper integrals.
   • Functions of Several Variables
     • The student will evaluate functions of several variables.
     • The student will use functions of several variables to solve applications.
     • The student will find partial derivatives of functions.
     • The student will find the extrema of functions of two variables.
     • The student will evaluate double integrals.
   • Linear Algebra
     • The student will solve systems of equations using matrices.
     • The student will perform the matrix operations of addition, subtraction, and multiplication.
     • The student will find the inverses of matrices.
7. COURSE OUTLINE:
   • Graphs and Functions
   • Limits and Continuity
   • The Derivative, Slope, and Rate of Change
   • Derivative Rules
   • Implicit Differentiation and Related Rates
   • The First and Second Derivative
   • Optimization
   • Graphing Functions
   • Differential and Marginal Analysis
   • Exponential and Logarithmic Functions
   • Exponential Growth and Decay
   • Antiderivatives
   • Definite Integrals, Area and Volume
   • Methods of Integration
   • Numerical Integration and Improper Integrals
   • Functions of Several Variables
   • Linear Algebra
8. INSTRUCTIONAL METHODS:
   • Lecture. Material will be presented in class by illustrative examples.
   • Reading the Text. Students will be expected to read the text over topics before covering that material in class.
   • Student Questions. Students will be expected to write questions over each section and email those to the instructor before covering that material in class.
   • Class Discussion. Concepts, problems, and applications will be discussed each class period. Discussions may also be carried out over the World Wide Web.
   • Seat Work. Students will be given problems to do in class with instructor supervision.
   • Group Work. Students will be given opportunities to work in group settings on both new material and projects where concepts are applied.
   • Whiteboard Drill. This is used to reinforce concepts and check on the student's understanding.
   • Assignments. Homework will be assigned for each section covered.
   • Individual Help. The instructor is available during office hours and other free time to assist the student.
   • Examinations. Tests and quizzes are given frequently to inform the instructor and the student of progress toward the specific course competencies.
9. INSTRUCTIONAL AND RESOURCE MATERIALS:
   • Textbook
   • TI 83 Graphing Calculator
   • Supplemental materials prepared by instructor.
   • Supplemental materials available through the bookstore (optional.)
   • Whiteboard
   • Computer and Projector
10. METHODS OF ASSESSMENT:
    • SCCC/ATS Outcome #2 will be assessed using the writing of mathematics on class assignments and topic exams.
    • SCCC/ATS Outcome #4 will be assessed and measured by class participation, quizzes, and tests.
    • SCCC/ATS Outcome #5 will be assessed and measured by assignments, tests, and non-tradition problem solving activities.
    • SCCC/ATS Outcome #6 will be assessed and measured by students utilizing calculators to complete assignments.
    • SCCC/ATS Outcome #9 will be assessed through attendance and participation in group activities that require decision making and responsibility.
11. ADA STATEMENT: If you believe that you are entitled to special accommodations under the Americans with Disabilities Act, please contact the Dean of Student Services at 620-417-1016 or visit the office located in the Hobble Academic Building.
    
    Syllabus Reviewed: March 2014