MATH 115 - BUSINESS CALCULUS

**Course Description**

A survey of mathematical techniques used in the managerial, social and life
sciences. Topics include systems of linear equations and matrices, linear
programming, differential calculus, and applications of the derivative.
Prerequisite: A grade of “C” or better in MATH-110 or MATH-105, or placement
exam.

**Textbook**

Required Text: Brief Calculus: An Applied Approach, Eighth Edition, by Larson.

You will also need a calculator (scientific or graphing). Bring your textbook,
calculator, pen or pencil, and paper to each class meeting.

**Mission Statement**

Benedictine University is dedicated to the education of undergraduate and
graduate students from diverse ethnic, racial and religious backgrounds. As an
academic community committed to liberal arts and professional education
distinguished and guided by our Roman Catholic tradition and Benedictine
heritage, we prepare our students for a lifetime as active, informed and
responsible citizens and leaders in the world community.

**Goals, Objectives, and Outcomes**

**Goals:** Students will develop an appreciation for the basic concepts of
differential and integral calculus and their applications to other areas,
particularly in business and social science.

**Common Student Learning Objectives:**

Know and apply the central concepts of the subject matter.

Use technology to enhance learning.

Use inquiry and collaboration to solve problems.

**Course-Based Student Learning Objectives:** Upon completion of the course:

1. Students will become familiar with, be able to evaluate, and understand the
significance and applications of mathematical functions, their limits, and their
continuity.

2. Students will learn to evaluate derivatives, and to use them in various
applications,

including those involving rates of change and optimization.

3. Students will be able to evaluate definite and indefinite integrals and to
use them in solving problems.

4. Students will become familiar with exponential and logarithmic
functions—their properties, limits, derivatives, integrals, and uses in modeling
situations in business and social science.

**Teaching Methodology
**

Lecture, discussion, demonstration, individual and group problem solving

**Course Requirements**

**Attendance:**A lot of material will be covered every week, so it is mandatory that you be present for the entirety of every class session. If, due to unavoidable circumstances, you have to miss part or all of a class, it is your responsibility to find out what you missed, learn the material covered, and make me aware of the reasons for your absence. my cell: 217-473-1783. If any class activities are missed due to an unexcused absence, the grade for that activity will be zero.

Due to the accelerated nature of the course, should you experience a medical condition which prevents you from attending any class(es), appropriate medical documentation must e provided immediately so it may be determined what, if any, accommodations are reasonable or possible.

**Homework:**A listing of the homework assigned for each testing unit will be distributed at the beginning of the unit. It will be turned in on the day of the test for that unit. When doing the homework assignments, you are allowed, and even encouraged, to work together, compare answers, or seek outside help, if this helps you in learning the material. You are not allowed, however, to merely copy someone else’s answers. This defeats the purposes of doing the homework: to give you practice and help you learn by doing, and to let me and you both know how well you understand.

In addition to handing in the assigned homework, you are also expected to read
each section of the book as it is covered in class, and do as many additional
exercises, other than those assigned to be turned in, as you need to for extra
practice.

In class, there will be review quizzes, practice exercises, or individual or
group problems.

**Tests:** There will be two unit tests, and a comprehensive final exam which
focuses primarily on Chapters 4 and 5. The testing schedule listed in the course
outline will be followed as closely as possible. Tests must be taken when
scheduled. In case of emergency, other arrangements can be made, but you must
contact me before or very soon after the test—do not wait until the following
week. Otherwise, you get a score of 0 for the missed test.

**Means of Evaluation**

**Homework:** 15%; **Quiz:** 15%; **Tests** (including final exam): 70%

**Grade:** 90-100% = A; 80-89% = B; 70-79% = C; 60-69% = D; under 60% = F

**Course Outline**

The following outline is approximate and subject to alteration.

**Week 1 – January 8**

A quick review of some preliminary topics from Chapter 0

1.1 The Cartesian Plane and the Distance Formula

1.2 Graphs of Equations

1.3 Lines in the Plane and Slope

1.4 Functions

**Week 2 – January 15**

1.5 Limits

1.6 Continuity

2.1 The Derivative and the Slope of a Graph

2.2 Some Rules for Differentiation

**Week 3 – January 22**

TEST over Chapter 1

2.3 Rates of Change: Velocity and Marginals

2.4 The Product and Quotient Rules

2.5 The Chain Rule

**Week 4 – January 29**

2.6 Higher Order Derivatives

2.7 Implicit Differentiation

2.8 Related Rates

3.1 Increasing and Decreasing Functions

**Week 5 – February 5**

3.2 Extrema and the First-Derivative Test

3.3 Concavity and the Second Derivative Test

3.4 Optimization Problems

**Week 6 – February 12**

3.5 Business and Economics Applications

3.6 Asymptotes

3.7 Curve Sketching: A Summary

3.8 Differentials and Marginal Analysis

**Week 7 – February 19**

TEST over Chapter 2, 3

4.1 Exponential Functions

4.2 Natural Exponential Functions

4.3 Derivatives of Exponential Functions

**Week 8 – February 26**

4.4 Logarithmic Functions

4.5 Derivatives of Logarithmic Functions

4.6 Exponential Growth and Decay

5.1 Antiderivatives and Indefinite Integrals

**Week 9 – March 5**

5.2 The General Power Rule

5.3 Exponential and Logarithmic Integrals

5.4 Area and the Fundamental Theorem of Calculus

5.5 The Area of a Region Bounded by Two Graphs

**Week 10 – March 12**

Final review

FINAL EXAM

**First Class Session:
Students should prepare for the first class session by looking over Chapter 0 in
the textbook, paying particular attention to pages 0-2, 0-3, 0-13, 0-14, 0-15,
0-19, and 0-21. Also, since we will be covering the first three or four sections
of Chapter 1 in the first class session, students may find it helpful to read
over these sections before class begins.
**

**Academic Integrity Statement**

Academic and professional environments require honesty and integrity, and these qualities are expected of every student at Springfield College-Benedictine University. In accordance with such expectations, academic integrity requires that you credit others for their ideas. Plagiarism, whether intentional or not, is a grievous offense. Any time you use words or ideas that are not your own, you must give credit to the author, whether or not you are quoting directly from that author. Failure to do so constitutes plagiarism.

Any incident of plagiarism and/or academic dishonesty may result in serious consequences. Penalties for academic dishonesty vary depending on the severity or extent of the problem but are always serious.

The following are consequences you may face for academic dishonesty:

• a failing grade or “zero” for the assignment;

• dismissal from and a failing grade for the course; or

• dismissal from the Institution.

Please refer to the Springfield College Benedictine University Catalog or the Student Handbook for a complete discussion of the Academic Integrity policy.

**Grade Appeal Process**

According to the Springfield College Catalog, grade appeals must be initiated 90 days prior to the end of one semester after the course in question has been completed. The process for appealing a grade is outlined below.

First, contact the Instructor.

1. A student must appeal to his/her instructor in writing (e-mail is acceptable) and provide specific reasons why his/her grade should be changed.

2. The instructor must respond to the student in writing (e-mail is acceptable) and provide a copy to the division chair.

Second, contact the Division Chair.

3. If the student wishes, he/she may then appeal to the division chair in writing (e-mail is acceptable) and provide specific reasons why his/her grade should be changed without the instructor’s permission. The student should understand that overwhelming evidence must be presented to the division chair to prove that the current grade is incorrect.

4. The division chair must respond to the student in writing (e-mail is acceptable) and provide a copy to the academic dean.

Lastly, contact the Academic Dean.

5. If the student wishes, he/she may appeal to the academic dean in writing (e-mail is acceptable) and provide specific reasons why his/her grade should be changed without the instructor’s or the division chair’s permission. The student should understand that overwhelming evidence must be presented to the academic dean to prove the grade is incorrect.

6. The academic dean must respond to the student in writing (e-mail is acceptable). The

Academic dean’s decision is final.

**Add/Drop Dates**

Last day to drop with 100% refund = 1 week from beginning of class

Last day to withdraw with 25% refund = 2 weeks from beginning of class

Last day to withdraw from class = Beginning of the 8th week of class

**Incomplete Request**

To qualify for an “I” grade, a minimum of 75% of the course work must be completed with a passing grade, and a student must submit a completed Request for an Incomplete form to the Registrar’s Office. The form must be completed by both student and instructor, but it is the student’s responsibility (not the instructor’s) to initiate this process and obtain the necessary signatures.

**Student Withdrawal Procedure**

It is the student’s responsibility to officially withdraw from a course by completing the appropriate form, with appropriate signatures, and returning the completed form to the Advising Office. Please refer to the Student Handbook for important financial information related to withdrawals.

**Americans with Disabilities Act (ADA)**

Springfield College-Benedictine University provides individuals with disabilities reasonable accommodations to participate in educational programs, activities, and services. Students with disabilities requiring accommodations to participate in campus-sponsored programs, activities, and services, or to meet course requirements, should contact the Director of the Resource Center as early in the semester as possible.

If documentation of the disability (either learning or physical) is not already on file, it may be requested. Once on file, an individual student’s disability documentation is shared only at that individual’s request and solely with the parties whom the student wishes it shared. Requests are kept confidential and may be made by emailing or calling (217) 525-1420, extension 291.

**Assessment**

Goals, objectives, and learning outcomes that will be assessed in the class are stated in this syllabus. Instructor will use background knowledge probes, one-minute papers, reflective essays and/or other Classroom Assessment Techniques as deemed necessary in order to provide continuous improvement of instruction.