Math 190 - Calculus for Business & Social Sciences

Fall 2005 Course Syllabus

James Jones, Professor of Mathematics
Mathematics & Sciences Division, Richland Community College

Course Meeting Information

Section 01 meets from 3:30 pm to 5:20 pm on Mon and Wed in room S137.

Instructor Information

James Jones, Professor of Mathematics.
Phone: 875-7211, ext 490
Office: C223

Office Hours

These are the times are scheduled for my office hours. If these times are inconvenient for you, you may also catch me before or after class or make an arrangement to meet some other time.


Student Audience

Students in business or social sciences who need a calculus course. Mathematics, engineering, and science majors should probably take one or more semesters of Calculus & Analytic Geometry instead.


Successful completion (C or better grade) in Math 116, College Algebra, or satisfactory score on the Mathematics placement exam.

Course Description

MATH 190 - Calculus for Business & Social Science

Hours: 4 lecture - 0 lab - 4 credit

Math 190 is an introductory calculus course for the non-mathematics major. The course includes sequences, limits, differentiation and integration of polynomials, and exponential and logarithmic functions with applications to business and social science. A graphing calculator is required.

Applicable toward graduation where program structure permits.

Illinois Articulation Initiative (IAI)

The mathematics component of general education focuses on quantitative reasoning to provide a base for developing a quantitatively literate college graduate. Every college graduate should be able to apply simple mathematical methods to the solution of real-world problems. A quantitatively literate college graduate should be able to:

Courses accepted in fulfilling the general education mathematics requirement emphasize the development of the student's capability to do mathematical reasoning and problem solving in settings the college graduate may encounter in the future. General education mathematics courses should not lead simply to an appreciation of the place of mathematics in society, nor should they be merely mechanical or computational in character.

To accomplish this purpose, students should have at least one course at the lower-division level that emphasizes the foundations of quantitative literacy and, preferably, a second course that solidifies and deepens this foundation to enable the student to internalize these habits of thought.

Math 190, Calculus for Business & Social Science, satisfies the Illinois Articulation Initiative Definition of a General Education Mathematics Course. It corresponds to M1 900B, Calculus for Business and Social Sciences.

The IAI course description for M1 900B follows.

M1 900-B: Calculus for Business and Social Sciences (3-5 semester credits)

This course is designed specifically for students in business and the social sciences and does not count toward a major or minor in mathematics. It may be taken before or after a course in finite mathematics. The course emphasizes application of the basic concepts of calculus rather than proofs. Topics include curve sketching and recognition of curves, techniques of differentiation applied to polynomial, rational, exponential, and logarithmic functions, maxima and minima of a function of one or more variables, partial derivatives, LaGrange multipliers, and elementary techniques of integration. Application to the worlds of business and social science should be stressed throughout the course. Prerequisite: College Algebra with a grade of C or better.

For more information on the Illinois Articulation Initiative, visit their website at

General Course Objectives

While learning calculus is certainly one of the goals of this course, it is not the only objective. Upon completion of this course, the student should be able to ...

Specific Course Objectives

In all of the following objectives, the student should be able to think, show, and tell what is happening. Concentration will not be on the memorization of formulas but on the conceptual understanding of the calculus. Technology may be used to obtain the results, but the emphasis is on the fundamentals of calculus, not the technology.

Upon successful completion of this course, the student should be able to ...

In addition to the objectives specific to this course, the student will also be expected to demonstrate mathematical reasoning and ability to solve problems using technology when appropriate.

A detailed topical outline of the content covered in this course is at the end of this syllabus.

Type of Instruction

Discussion, problem solving, activities, individual and group work, student questions, student participation, and lecture. Students are expected to have read the material before class and are strongly encouraged to come to class with a list of questions and to ask these questions.

Method of Evaluation

Could include any of the following: problem solving exams, objective exams, essays, research papers, oral presentations, group projects, individual projects, classroom activities, quizzes, and homework.

Grading Policy

Letter grades will be assigned to final adjusted scores as follows:

Consideration may be given to such qualities as attendance, class participation, attentiveness, attitude in class, and cooperation to produce the maximum learning situation for everyone.

The instructor will give you a grade sheet so that you can record your scores and keep track of your progress in the course. If you are concerned about your grades, see the instructor.

Assignments are due at the beginning of the class period on the date they are due. The instructor may be gracious and allow you to turn them in later that day without counting them late, but do not count on his graciousness. Late assignments lose 20% of their value per class period. The instructor reserves the right to apply this rule to missed exams as well as regular assignments.

Special Projects

Special projects may be included in the course requirements. These will be selected from videotape reviews, research papers, research projects, group projects, and a mathematics notebook.

Written Work

All written work should be in a typed (word processor) format. There should be a cover page with the title of the assignment and the student's name. All work should be double spaced. Papers are to be stapled together in the upper left hand corner. All reference works used, including books, videos, etc., are to be cited using APA (preferred) or MLA notation. All work is to utilize the English language correctly. It is suggested that the Student Learning Center be utilized for assistance in the preparation of written work. If written work is submitted late, the instructor may take appropriate deductions from the grade.

Attendance Policy

Regular attendance is essential for satisfactory completion of this course. If you have excessive absences, you cannot develop to your fullest potential in the course. Students who, because of excessive absences, cannot complete the course successfully, will be administratively dropped from the class at midterm. Students whose attendance is occasional or sporadic may be dropped from the class at midterm. If a student stops attending after midterm, it is the student's responsibility to withdraw to avoid an "F". The instructor has the ability, but not responsibility, to drop students who are not regularly attending at any time during the semester. The safest way to make sure you're not dropped for non-attendance is to continue to attend classes.

The student is responsible for all assignments, changes in assignments, or other verbal information given in the class, whether in attendance or not.

If a student must miss class, a call to the instructor (RCC's phone system has an answering system) should be made or an email message sent. When a test is going to be missed, the student should contact the instructor ahead of time if at all possible. Under certain circumstances, arrangements can be made to take the test before the scheduled time. If circumstances arise where arrangements cannot be made ahead of time, the instructor should be notified and a brief explanation of why given by either voice or email. This notification must occur before the next class period begins. At the instructors discretion, the score on the final exam may be substituted for the missed exam.


A TI-82 or TI-83 graphing calculator is recommended for this course. Calculators may be used to do homework. Calculators may be used on exams and/or quizzes in class unless otherwise announced. If you are purchasing a calculator, consider getting the TI-83 instead of the TI-82. The TI-86 calculator is acceptable, but the TI-85 doesn't do tables. The TI-89 or TI Voyage calculators will work, but are overkill for this class.

There are no calculator programs that we will be using during this class, so you do not have to have a TI calculator. However, if you have a different (Casio, Sharp, HP) graphing calculator, you will be on your own as far as figuring out how to use it. Make sure that your calculator can find zeros, maximums, minimums, and intersections for graphs and display a table of values.

Additional Supplies

The student should bring a pencil and calculator to class each day. You may occasionally want a ruler or graph paper. There will be a paper punch and stapler in the classroom.


Practice is necessary for successful understanding of mathematical concepts. In this class, that practice primarily takes the form of homework. There will be assigned homework problems from each of the sections. This homework should be attempted and checked before the next class period.

Homework may be collected for a grade, but even if it is not, the student should work as many problems as necessary to ensure a good understanding of the concepts.


In this course, we will concentrate on understanding the concepts of calculus. There will be instances when we will use the calculator or computer to aid in our understanding or remove some of the tediousness of the calculations (especially in the area of numerical approximations). There may be some projects, homework, or portions of a test that require you to use technology to complete.

Here are some of the technology tools that we will use.

TI-82/TI-83 Graphing Calculator

Besides needing a calculator for arithmetic manipulation, we will also use the graphing and table features of the calculator.

Microsoft Excel

Microsoft Excel is a spreadsheet program that comes with MS Office. MS Office 2003 is loaded in the classroom and is also available on most of the machines in the College, including those in the open computer lab, C239. We will not be using any special features of Excel that depend on a particular version, so Excel 97 or newer should work fine. While we will use Excel in class, the instructions should be generic enough that you can use any other spreadsheet package without too much difficulty.


Derive is an computer algebra system that can perform symbolic manipulation of algebraic expressions and equations. We will use Derive primarily as an aide to checking our calculations or when answers get really nasty. For the most part, you will be expected to perform the algebraic manipulations yourself. Richland has a site license for Derive version 6, but that license does not allow you to take a copy home. If you have money to burn and would like a copy, you can order it from MathWare at


WinPlot is a free graphing software package for Windows written by Rick Parris at Phillips Exeter Academy in NH. The software is useful for creating graphs and it is easy to copy/paste the graphs into other applications. You may download the software by right-clicking your mouse on the word "WinPlot" at the top of the page and choosing save.


DPGraph is a 3D graphing package that will be useful for visualizing the graphs of multi-variable functions. The software is not free, but Richland has a site license that allows students to download and use it without additional charge. You may download it from (be sure to find the entry for Richland Community College)

Additional Help

The student is encouraged to seek additional help when the material is not comprehended. Mathematics is a cumulative subject; therefore, getting behind is a very difficult situation for the student. There are several places where you can seek additional help in your classes.


I try to make myself as available to the students as I can. My office hours are listed at the beginning of this syllabus, but those are just the times I'm scheduled to be in my office. Grab me and ask me questions if you see me in the hallway. Ask questions before or after class. If I'm in my office and it's not my scheduled office hours, go ahead and stop in.

The instructor should be considered the authoritative source for material related to this class. If a tutor or other student says something that disagrees with the instructor, believe the instructor.

Study Groups

Probably the best thing you can do for outside help is to form a study group with other students in your class. Work with those students and hold them accountable. You will understand things much better if you explain it to someone else and study groups will also keep you focused, involved, and current in the course.

Student Learning Center

The Student Learning Center is located in rooms S116, S117, and S118. There is mathematics tutoring available in room S116. The Student Learning Center and the tutoring is a service that Richland Community College offers you free of charge.

Learning Accommodation Services

There are accommodations available for students who need extended time on tests, note takers, readers, adaptive computer equipment, braille, enlarged print, accessible seating, sign language interpreters, books on tape, taped classroom lectures, writers, or tutoring. If you need one of these services, then you should see Learning Accommodation Services in room C136.

If you request an accommodation, you will be required to provide documentation that you need that accommodation.

Some of you will need additional time on tests. There is no need to go to learning accommodation services to request that. If you need additional time, just let me know and in most cases, I'll allow you to continue working past the allotted time. You may need to move to another room as there may be another class coming into your room. If you're unable to finish the test by staying late, it may be possible to start the test earlier to gain additional time. There may be circumstances where extra time is not allowed.

Academic Dishonesty

Each student is expected to be honest in his/her class work or in the submission of information to the College. Richland regards dishonesty in classroom and laboratories, on assignments and examinations, and the submission of false and misleading information to the College as a serious offense.

A student who cheats, plagiarizes, or furnishes false, misleading information to the College is subject to disciplinary action up to and including failure of a class or suspension/expulsion from the College.

Non-Discrimination Policy

Richland Community College policy prohibits discrimination on the basis of race, color, religion, sex, marital or parental status, national origin or ancestry, age, mental or physical disability (except where it is a bonafide occupational qualification), sexual orientation, military status, status as a disabled or Vietnam-era veteran.

Electronic Communication Devices

The Mathematics and Sciences Division prohibits the use of cell phones, pagers, and other non-learning electronic communication equipment within the classroom. All equipment must be turned off to avoid disturbances to the learning environment. If a student uses these devices during an examination, quiz, or any graded activity, the instructor reserves the right to issue no credit for these assignments. The instructor needs to approve any exceptions to this policy.

Topical Outline

Hours Topic


  • Precalculus review including absolute values, exponents, radicals, factoring, quadratic formula, finding roots, and simplifying algebraic expressions
  • Cartesian coordinate system, equations of circles, distance formula
  • Lines, slope, equations of lines

Functions, Limits, and the Derivative

  • Definition of functions, determining domain, graphing a function, piecewise functions, vertical line test
  • Algebra of functions including the sum, difference, product, quotient, and composition of functions
  • Using functions as mathematical models. Polynomial and rational models. Applications include supply and demand functions; revenue, cost, and profit functions
  • Limits - intuitive approach, algebraic approach, graphical approach, numerical approach. Indeterminate forms and limits at infinity.
  • One-sided limits and continuity. Properties of continuous functions including polynomial and rational functions. Intermediate value theorem and existence of roots
  • Derivatives. Average and instantaneous rates of change. Slopes of the secant and tangent lines. Function definition of derivative. Relationship between differentiability and continuity


  • Basic rules of differentiation. The derivative of a constant, the power rule, the derivative of a constant multiple, and the addition rule.
  • The product and quotient rules for derivatives.
  • The chain rule and generalized power rule.
  • Marginal functions in economics. Marginal cost, average cost, marginal revenue, marginal profit, elasticity of demand
  • Higher order derivatives
  • Differentials, local linear approximations

Applications of the Derivative

  • Applications of the first derivative. Intervals where function is increasing or decreasing, relative maxima and minima, critical values
  • Applications of the second derivative. Intervals of concavity, inflection points, second derivative test for relative extrema
  • Curve sketching. Asymptotes, intercepts, critical points, points of inflection, relative extrema, increasing/decreasing, concavity
  • Optimization problems. Absolute extrema, absolute extrema on a closed interval
  • Application problems involving optimization

Exponential and Logarithmic Functions

  • Exponential functions. Graphs and properties. Base e.
  • Logarithmic functions. Converting between exponential and logarithmic form. Properties and graphs of logarithmic functions. Natural logarithms.
  • Compound interest, effective rate, continuous compounding
  • Differentiation of exponential functions
  • Differentiation of logarithmic functions. Logarithmic differentiation.


  • Antiderivatives and rules of integration. Indefinite integrals, power rule, constant multiple, sum, exponential functions (base e), and integrals resulting in the natural logarithm. Differential equations and initial value problems.
  • Integration by substitution
  • Area and the definite integral. Riemann sums, the definite integral and its geometric interpretation
  • The fundamental theorem of calculus
  • Evaluating definite integrals. Area under a curve, average value.
  • Area between two curves
  • Applications of the definite integral to business and economics. Consumer's and producer's surplus, future and present value of an income stream, amount and present value of an annuity, Lorentz curves and income distributions

Additional Topics in Integration

  • Integration by parts
  • Integration using tables of integrals
  • Numerical integration. Trapezoid rule, Simpson's rule.
  • Improper integrals

Calculus of Several Variables

  • Functions of several variables, domain, graphs
  • Partial derivatives - first and second order partials
  • Maxima and minima. Saddle points, critical points
  • Optimization problems using Lagrange multipliers
  • Double integrals