Department Chair

  • John O'Neill
    Associate Dean, School of Business
    Associate Professor of Quantitative Business Analysis
    Associate Professor of Mathematics
    Siena Hall 301B
    (518) 783-2386
    joneill@siena.edu

QBUS 110 Math for Decision Making II Course Guide

Course Description

The primary focus of this course is to have students apply appropriate mathematical models to common business situations, developing their ability to analyze and interpret the results. Students will develop their analytical skills through exposure to modeling as well as classical differential and integral calculus.

A wide variety of problems from business may be solved using nonlinear functions. For example, a business manager uses the exponential and logarithmic functions to study the growth of money or the decay of new sales volume. 

Rate of change is an extremely important concept for business managers. Differential calculus is used to measure a rate of change. It can be used to find the marginal profit, marginal cost, and marginal revenue, given the respective profit, total cost, and total revenue functions. Differentiation can be used to minimize average cost, maximize total revenue, and maximize profit.

Techniques applied in business situations such as supply and demand analysis, inventory cost modeling, optimization of profit, revenue and average cost, theory of diminishing return and marginal analysis will also be covered.

Specific, Assessable Learning Outcomes

The student will be able to: 

  1. Model cost, revenue, demand, and supply functions using exponential and logarithmic functions.
  2. Compute derivatives for polynomial, logarithmic, exponential functions and more complex functions which are combinations thereof.
  3. Use differential calculus to find the marginal profit, marginal cost, and marginal revenue, given the respective profit, total cost, and total revenue functions and then to determine the level of production that maximizes revenue or profit for a product or minimizes the average cost of producing a product.
  4. Utilize first and second derivatives to identify critical points, inflection points and associated graphical behavior for a given function.
  5. Use implicit differentiation to solve business problems involving the rates of change of two or more variables. An example of this type of problem might include elasticity of demand or maximization of tax revenue.
  6. Compute antiderivatives for polynomial, exponential and certain rational functions via fundamental antiderivative rules such as the power rule, exponential rule, logarithmic rule and elementary substitution methods.
  7. Use integration to find total revenue functions from marginal revenue functions, to find total cost functions from marginal cost functions and to optimize profit from information about marginal cost and marginal revenue.
  8. Use definite integrals to find area under a curve. More adept students may use definite integrals to approximate the time/total value of a continuous income stream and/or find Producer’s and Consumer’s Surplus.

Course Outline 

  • The development and use of logarithmic and exponential functions and their use in solving common business problems.
  • The development and use of differential calculus to find the rate of change, marginal profit, marginal cost, and marginal revenue, given the respective profit, total cost, and total revenue functions.
  • The development and use of relative maxima and relative minima for finding maximum and/or minimum values of important business functions such as profit, cost, and revenue.
  • The development and use of implicit differentiation techniques from calculus to solve business problems such as elasticity of demand and maximization of taxation revenue.
  • The development and use of integration techniques from calculus to find total revenue functions from marginal revenue functions, to optimize profit from information about marginal cost and marginal revenue, and to find national consumption functions from information about marginal propensity to consume.
  • The development and use of definite integrals from calculus to find area under a curve. Applications of this technique may also include approximating the time/total value of a continuous income stream or determining a consumer’s and producer’s surplus is also explored.

Recommended Teaching Methodology 

This course will be structured in such a way as to facilitate the use of different methods of instruction. Readings, lectures, multimedia presentations, group discussions, and written assignments will be used throughout the course. Work will be done individually and/or in small groups.

The primary focus of the teaching methodologies used will be to prepare the student to understand and apply mathematical tools and reasoning to business situations. Thus, ample time will be devoted to “hands-on” problem solving. 

The readings will come from the required text as well as additional material to be provided by the instructor. Lectures and group discussions will enable the instructor and students to expand on the material presented in the readings. For all testing situations, a departmentally designed formula sheet will be the only supplemental material accompanying any exam.

Assessment Measures 

The following assessment measures will be used.  

  1. Assessment devices (quizzes, homework, exams, etc.) should be given throughout the semester, building up to a comprehensive final exam. The final exam will be used to assess the specific assessable learning outcomes enumerated above.
  2. Writing and/or oral presentation(s) focusing on major areas of study will be given to students to assess their understanding of mathematics and the ability to communicate quantitative results.

Statement of Expectations 

This course satisfies the quantitative reasoning (CAQ) core requirement for the college and is a pre-business core requirement for the School of Business. As such, any student in the course is required to show a D- level proficiency in the course in order to attain credit for the college core and/or attain credit towards the business major. It is normally taken in the student’s second semester of full-time studies. 

To attain the desired levels of proficiency, it is required that students attend class prepared to participate in interactive learning using tools such as the graphical calculator and textbook. Students should remain actively engaged in the material covered in class. 

Of course this is not all that is needed, as classroom learning success is also influenced by student preparation outside of class. It is therefore imperative that students complete out-of-class assignments and textbook reading in a timely fashion. Students will develop and retain the knowledge and skill set described above by continual practice, thereby slowly building and adding onto their knowledge base. “Cramming” in the days before a test is not an effective way to learn the skills necessary to employ mathematical reasoning in the business environment. 

Lastly, it is expected that if you have questions about any course material you will ask those questions so that they may be answered. There are a variety of sources from which answers will come, including (but by no means limited to) the textbook, the QBA Help Lab, a tutor, classmates, and MOST IMPORTANTLY the professor. You can ask questions of the professor in class or after class during the professor’s office hours. Remember that an unasked question is an answer never given.

Prerequisite Knowledge

The most important prerequisites are an interest in the subject, the willingness to commit the necessary resources in terms of time and intellectual effort, and the willingness to actively participate in the learning process. 

Students should have a fundamental understanding of mathematical reasoning as well as be competent in solving applied algebra problems. Successful completion of Mathematics for Decision Making I (QBUS-100) is required before this course can be taken.

Institutional Mechanism for Providing Feedback for Continuous Quality Improvement

The Quantitative Business Analysis department will annually review assessment results for this course. Specifically, assessment results in each of the five learning outcome areas will be analyzed to determine the level of success in achieving these learning outcomes. Any deficiencies in achieving learning outcomes will be addressed and appropriate changes designed to improve the success in achieving these learned outcomes.