MAC 2233 Syllabus

Miami Dade College – North Campus Fall 2023

Course Syllabus - Please note that the instructor reserves the right to modify the course syllabus as
he/she deems necessary to address unforeseeable circumstances.

Course Title: Business Calculus

Course Number: MAC 2233
Class Number: 11455
Schedule: Tues & Thurs 6:40 to 9:25 P.M.
Term: 2237_Fall 2023

Catalog Description An introduction to the basic concepts of differential and integral calculus for business
majors. Topics include limits, continuity, differentiation and integration of
polynomial, exponential and logarithmic functions, with applications to business.
Prerequisites MAC 1105 with a grade of “C" or better.
Credit Hours 3 Credits
Instructor’s Name Garfield Jugar
Instructor’s
gjugar@mdc.edu
Email Address
Instructor’s
Zoom Meeting request via email
Office Location
Instructor
After Class or email request to schedule time.
Office Hours
Remote Learning
https://mdc.instructure.com/courses/39180
Course Link
Textbook Title, Calculus for Business, Economics, and the Social and Life Sciences, 11th edition, (Brief
Edition and Author Edition) by Laurence D. Hoffman, Gerald L. Bradley, Sobecki, and Price (McGraw-Hill).
The ISBN number is: 978-007-729-273-7
Class Times Tues & Thurs 6:40 to 9:25 P.M.
Instructional
MDC Live
Method
Class Majority of the communication in the course will be done through email. Student
Communication should attempt to reach me via email and should expect a response within 24 hours.
Policy If no response or emergency, students are allowed to contact me via SMS (305-767-
6600).
 Attendance Policy Students with 3 or more unexcused absences may be withdrawn by the instructor.
Students are still responsible for withdrawing themselves if they want to receive a
“W”.
Grading Policy There are five possible grades in this course: ‘A’, ‘B’, ‘C’, ‘D’ or ‘F’.
• A grade of ‘A’ or ‘B’ or ‘C’ promotes the student to the next course.
• A grade of ‘D’ or ‘F’ means the student must repeat the course.
• A grade of ‘F’ will adversely affect your GPA, so be careful!
Academic Students may be penalized on an assignment grade or receive a “F” in the overall
Dishonesty Policy grade in the course if they cheat. Please refer to the Student Rights and
Responsibilities Handbook for the official Academic Dishonesty Policy.
https://www.mdc.edu/procedures/Chapter4/4035.pdf
ADA In compliance with the Americans with Disabilities Act (ADA), all qualified students
enrolled in this course are entitled to reasonable accommodations. Please notify the
instructor during the first week of class of any accommodation needed for this
course. Also contact the ACCESS Services Department at (305) 237-1272 or visit Room
6112 or their webpage at: http://www.mdc.edu/north/accessservices/
Make-Up Policy There will be no make-up exam allowed. Students are allowed to drop the lowest
exam grade. In you miss any additional exams, you can replace it your final exam
grade. Late submissions are not allowed due to the fast-paced nature of this course.
Students should make every effort to take note of due dates in Canvas and submit
assignments on time.
Course  Computer with audio/video capability and internet access
Requirements  Scientific calculator
Online Assignment See Assignment Schedule
Math Center (Online) https://www.mdc.edu/online/resources/tutoring.aspx
Technical Support For canvas go to: https://design.instructure.com/courses/178
for online platform
Withdrawal Dates See calendar https://www.mdc.edu/academics/calendar/
*Students are expected to initiate the withdrawal process.
Chairperson of the Dr. Irma Cruz-White icruzwhi@mdc.edu 305-237-1144
Dept. Of Math

Course Evaluation/Grading Policy/Grading Scale/Assessment Methodizing

Grade Weights by Category

Category of Assignments Percentage

Homework (Including Reviews) 15%
5 Chapter Discussions 10%
4 Tests (Drop Lowest Exam Grade) 45%
Final Exam 30%
TOTAL: 100%
Grading Scale
Average Score Grade
90% – 100% A
80% – 89% B
70% – 79% C
60% – 69% D
Below 60% F
Course Outline & Assignment Schedule
Calculus for Business, Economics, and the Social and Life Sciences, 11th edition, (Brief Edition) by
Laurence D. Hoffman, Gerald L. Bradley, Sobecki, and Price (McGraw-Hill). The ISBN number is: 978-
007-729-273-7
With access to CONNECT: ISBN: 978-007-792-843-8
Note: This schedule assumes classes will meet 2 times per week, with 165 (2 hrs & 45 minus) - minute
class periods.
Week Date Assignment Book Title and Chapter
Intro to Business Calculus
Sec 1.5 – Limits
Homework 1 & 2.1 Sec 1.6 – One-Sided Limts & Continuity
Week 1 10/24 & 10/26 Discussion – Chapter 1 (Functions, Sec 2.1 – The Derivative
Graphs, and Limits) Sec 2.2 – Techniques of Differentiation
Sec 2.3 – Product & Quotient Rules
(High-Order Derivatives)

Sec 2.4 – The Chain Rule

Homework – 2.2 & Test 1 Review Sec 2.5 – Marginal Analysis &
Discussion – Chapter 2 Approx. Using Increments
Week 2 10/31 & 11/02
(Differentiation: Basic Concepts) Sec 2.6 – Implicit
Test 1 – 11/05 (Honorlock) – (1.5 – 2.4) Differentiation & Related
Rates

Sec 3.1 – Increasing & Decreasing

Functions (Relative Exteme)
Sec 3.2 – Concavity & Point of Inflection
Homework – 3
Sec 3.3 – Curve Sketching
Week 3 11/07 & 11/09 Discussion – Chapter 3 (Additional
Sec 3.4 – Optimization: Elasticity of
Applications of the Derivative)
Demand)
Sec 3.5 – Additional Applied
Optimization (Optional)

Sec 4.1 – Exponential Functions:

Continuous Compounding
Homework – 4.1 & Test 2 Review
Sec 4.2 – Logarithmic Functions
Discussion – Chapter 4 (Exponential &
Week 4 11/14 & 11/16 Sec 4.3 – Differentiation of Log and Exp.
Logarithmic Functions)
Functions
Test 2 – 11/19 (Honorlock) – (2.5 – 3.5)
Sec 4.4 – Additional Applications:
Exponential Models
Week 5 11/21 Homework – 5.1 Sec 5.1 – Indefinite Integration and
 Differential Equations
Sec 5.2 – Integration by
Substitution

Sec 5.3 – The Definite Integral &

the Fundamental Theorem of
Homework – 5.2 & Test 3 Review Calculus.
Week 6 11/28 & 11/30
Test 3 – 11/29 (Honorlock) – (4.1 – 5.2) Sec 5.4 – Applying Definite
Integration: Distribution of Wealth
and Average Value

Sec 5.5 – Additional Applications of

Integration to Business and
Homework – 5.3 & Test 4 Review Econmics
Week 7 12/05 & 12/07 Discussion – Chapter 5 (Integration)
Sec 7.5 – Constrained
Test 4 – 12/10 (Honorlock) – (5.3 – 7.5)
Optimization: The Method of
Lagrange Multipliers

Final Exam Review

Week 8 12/12 & 12/14 Final Exam (Honorlock) –
Comprehensive (1.5 – 7.5)
*dates may be modified based on learner needs and as deemed necessary by instructor.

Learning Outcomes
lim f ( x )=L
1. Understand intuitively what x →a means, and evaluate certain limits by using limit properties.
2. Understand and be able to work with one-sided limits.
3. Know the definition of continuity and be able to apply it to certain problems dealing with continuity.
4. Use properties of continuous functions and theorems regarding continuity to test a function for continuity at
a point or on an interval.
f ( x +h )−f (x )
' ' lim
5. Find f ( x ) for certain functions using the definition f ( x )= h→0 h
6. Know the definition of differentiability of a function f at a given number a and know that a differentiable
function is also continuous.
dy
7. Understand, for a function y = f(x), that dx is the slope of the tangent to the graph of y = f(x) at x.
dy Δy dy
= lim =mxm−1
8. Understand that dx Δx →0 Δx , and know how this definition is used to find dx for the
m
function, y=x
9. Apply derivatives to problems involving position, velocity and acceleration of
a moving object.
10. Use formulas to find marginal rates of change in applicable business problems.
11. Find derivatives which require the use of the power rule, the product rule, the quotient rule and the chain
rule.
12. Find higher order derivatives for certain functions.
13. Use the first and the second derivatives to solve problems involving the motion of objects moving in a
straight line.
'
14. Know how to find y by implicit differentiation and know how to use implicit differentiation to solve
problems involving related rates.
15. Understand and apply differentials to approximate the error in a calculated value.
16. Determine for certain functions whether they are increasing or decreasing.
17. Determine for certain functions whether they are concave up or concave down.
18. Use the first derivative test for local extrema.
19. Use the second derivative test for local extrema.
20. Determine where inflection points exist for certain functions
21. Evaluate certain limits of the form:

lim f ( x )=L , lim f ( x )=L, and lim f ( x )=±∞

22. x → ∞ x →−∞ x→ a

23. Understand how limits are used to define horizontal and vertical asymptotes.
24. Graph certain polynomial, radical and rational functions.
25. Solve certain word problems of a geometric nature which requires us to find where a function achieves a
maximum or a minimum (optimization problems).
26. Solve certain word problems related to business which requires us to find where a function achieves a
maximum or a minimum (optimization problems).
27. Differentiate exponential and logarithmic functions.
28. Solve compound interest problems, exponential growth and decay problems and simple bounded growth
problems.
29. Calculate the effective rate of interest on an investment.
30. Define an antiderivative of f(x).
31. Solve problems which require the formulas
n+1
x
∫ x n dx= n+1
+C , if n≠−1 ; ∫ x−1 dx= ln|x|+C and ∫ e x dx=e x +C
32. Evaluating indefinite integrals using u-substitution.
b

∫ f ( x)dx
33. Understand how the definite integral a relates to the area under the graph of y = f(x) from x = a
to x = b.
34. Evaluate definite integrals using the Fundamental Theorem of Calculus.
35. Apply definite integral in certain problems of business and economics.

Collegewide Student Learning Outcomes

Purpose: Through the academic disciplines and co-curricular activities, General Education provides multiple,
varied, and intentional learning experiences to facilitate the acquisition of fundamental knowledge and skills and
the development of attitudes that foster effective citizenship and life-long learning.
As graduates of Miami Dade College, students will be able to:
1. Communicate effectively using listening, speaking, reading, and writing skills. Professor will address this
outcome trough all assessments described in the syllabus.
2. Use quantitative analytical skills to evaluate and process numerical data. In this course students will need
to read and identify data from graphs and charts. Students will also learn to develop quantitative skills to
interpret data from graphs. Also, students will solve algebraic equations and inequalities and manipulate
data through unit analysis.
3. Solve problems using critical and creative thinking and scientific reasoning. In the process of solving
mathematical problems, students will need to use critical thinking skills to interpret solutions. Creativity in
solving problems is constantly encouraged in this course and viewed as an important skill in mathematics.
Critical skills are heavily emphasized in this course.
4. Formulate strategies to locate, evaluate, and apply information.
In this course students will often need to solve real-life word problems which apply the mathematical
concepts presented. Students will work to solve these problems and identify relevant information in the
problems in order to be able to solve them.
5. Demonstrate knowledge of diverse cultures, including global and historical perspectives.
In this course, whenever possible, students will be introduced to the use of mathematics through diverse
cultures as well as historical notes on the mathematical concepts you learn.
6. Create strategies that can be used to fulfill personal, civic, and social responsibilities. This outcome is not
reinforced in this course.
7. Demonstrate knowledge of ethical thinking and its application to issues in society. This outcome is not
reinforced in this course.
8. Use computer and emerging technologies effectively. In this course students will be frequently informed
about their progress in the course via email.
9. Demonstrate an appreciation for aesthetics and creative activities.
This outcome is not reinforced in this course.
10. Describe how natural systems function and recognize the impact of humans on the environment. This
outcome is not reinforced in this course.
https://www.mdc.edu/learningoutcomes/

Academic Resources
Ask a Librarian
Need more research help? The Florida Electronic Library connects you to librarians across the State of Florida.
Chat | Email | Text

Library Catalog Search

http://www.mdc.edu/learning-resources/
Online Library Guides (LibGuides by Subject)
http://libraryguides.mdc.edu/

Research Tools and Services

http://www.mdc.edu/learning-resources/research-tools-services/

Students are invited to visit the professor during office/advisement hours. Additional support is available in the
Math Resource Center
Mathematics Resource Center
The Mathematics Resource Center is made available online to provide MDC mathematics students free
tutoring assistance.
To access our virtual space, please visit us at:
https://us.bbcollab.com/collab/ui/session/guest/73dcd2cc5ffb45c5a2d77760f6dd70db
Phone: 305-237-1457 | 305-237-1421 | Contact Person: Carl Louis

Math Center Online Hours of Operation

Monday – Thursday: 8:00 AM – 9:00 PM
Friday: 8:00 AM – 5:00 PM
Saturday: 8:00 AM – 1:00 PM

Remote Learning Resources:

1. Student Support for Remote Learning: https://libraryguides.mdc.edu/remotestudents
Student and Campus Resources

 Student Portal: https://my.mdc.edu/

 Admissions and Registration: https://www.mdc.edu/about/contact/admissions.aspx
 Academic and Career Advisement: https://www.mdc.edu/north/advisement/
 ACCESS Disability Services: https://www.mdc.edu/access/
 Student Life: https://www.mdc.edu/north/student-life.aspx
 TRIO Student Support Services: https://www.mdc.edu/north/trio/
 Singlestop- One Stop Source for Students: https://www.mdc.edu/main/singlestop/
 Learning resources: https://www.mdc.edu/learning-resources/
 The Writing Center: https://www.mdc.edu/north/english/english_support_center.asp

Other

 Statement about your teaching/learning philosophy

 Supplementary material to help students succeed (tutorials, web resources)
 Provide space for 2 - 3 class members" names, telephone, email to contact if they miss class
 Contract & signature
 Your suggestions for success
 What you expect of students and what they can expect from you