MATH 209: Business Calculus Syllabus and Course Structure

Course Overview

Introduction to Business Calculus

This syllabus outlines the structure, policies, and topics for MATH 209: Business Mathematics II at Concordia University. The course covers foundational and advanced topics in calculus with applications to business and economics.

• Instructor: Andrea Panait

• Office: 1.1.916

• Email: [e-mail]

• Class Time: Thursdays from 4:15pm-5:45pm in 1.8.915

• Textbook: Calculus for Business, Economics, Life Sciences and Social Sciences, 14th Edition, by Barnett, Ziegler, & Byleen (Custom Edition)

Course Topics

Weekly Breakdown and Main Chapters

The course is organized into weekly modules, each covering specific chapters and sections relevant to business calculus. Below is a summary of the main topics and their subtopics:

• Week 1: Introduction to Limits

• Week 2: Continuity

• Week 3: The Derivative

• Week 4: Marginal Analysis in Business and Economics

• Week 5: Derivatives of Exponential and Logarithmic Functions

• Week 6: Derivatives of Products & Quotients; Higher-Order Derivatives

• Week 7: Implicit Differentiation

• Week 8: Related Rates; Optimization

• Week 9: Curve Sketching and Graphs; Business Applications

• Week 10: Antiderivatives and Integration

• Week 11: Additional Integration Topics; Area Between Curves

• Week 12: Review

Key Topics and Academic Context

Limits and Continuity

Limits and continuity are foundational concepts in calculus, essential for understanding how functions behave near specific points and for defining derivatives.

• Limit: The value that a function approaches as the input approaches a certain point.

• Continuity: A function is continuous at a point if the limit exists and equals the function's value at that point.

• Formula Example:

$\lim_{x \to a} f(x) = L$

The Derivative

The derivative measures the rate of change of a function with respect to its variable, and is a central tool in business calculus for analyzing trends and optimizing outcomes.

• Definition: The derivative of a function f at point x is the limit of the average rate of change as the interval approaches zero.

• Formula:

$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

• Application: Marginal cost and marginal revenue in economics are derivatives of cost and revenue functions.

Optimization and Graphing

Optimization involves finding maximum or minimum values of functions, which is crucial for business decisions such as maximizing profit or minimizing cost.

• Critical Points: Points where the derivative is zero or undefined.

• Second Derivative Test: Used to determine concavity and classify extrema.

• Formula Example:

$f''(x) > 0$ (function is concave up; minimum) $f''(x) < 0$ (function is concave down; maximum)

Integration

Integration is the process of finding the accumulated area under a curve, which is used in business calculus to compute total cost, revenue, and other aggregate measures.

• Definite Integral: Represents the area under a curve between two points.

• Formula:

$\int_a^b f(x) \, dx$

• Application: Calculating total profit over a time interval.

Course Policies and Structure

Assignments and Exams

• Assignments: Submitted online via MyLabMath. Late assignments are not accepted.

• Midterm Test: Covers material from the first half of the course.

• Final Exam: Comprehensive, covering all course topics.

• Grading Scheme:

Component	Option A	Option B
Assignments	10%	10%
Midterm Test	30%	0%
Final Exam	60%	90%

Note: The higher of the two grading options will be used. There is no "100% final exam" option.

Academic Integrity and Student Services

• Academic Integrity: Students are expected to adhere to the university's code of conduct.

• Student Services: Math Help Centre, MyLabMath support, and other resources are available.

Summary Table: Weekly Topics and Suggested Exercises

Week	Section	Suggested Exercises
1	Introduction to Limits	p. 10: 11, 15, 21, 25, 41, 43, 45, 47
2	Continuity	p. 18: 11, 15, 21, 25, 41, 43, 45, 47
3	The Derivative	p. 28: 11, 15, 21, 25, 41, 43, 45, 47
4	Marginal Analysis in Business and Economics	p. 38: 11, 15, 21, 25, 41, 43, 45, 47
5	Derivatives of Exponential and Logarithmic Functions	p. 48: 11, 15, 21, 25, 41, 43, 45, 47
6	Derivatives of Products & Quotients; Higher-Order Derivatives	p. 58: 11, 15, 21, 25, 41, 43, 45, 47
7	Implicit Differentiation	p. 68: 11, 15, 21, 25, 41, 43, 45, 47
8	Related Rates; Optimization	p. 78: 11, 15, 21, 25, 41, 43, 45, 47
9	Curve Sketching and Graphs; Business Applications	p. 88: 11, 15, 21, 25, 41, 43, 45, 47
10	Antiderivatives and Integration	p. 98: 11, 15, 21, 25, 41, 43, 45, 47
11	Additional Integration Topics; Area Between Curves	p. 108: 11, 15, 21, 25, 41, 43, 45, 47
12	Review	All previous exercises

Conclusion

This syllabus provides a comprehensive overview of the Business Calculus course, including key topics, policies, and resources. Students are encouraged to use the suggested exercises and seek support as needed to master the material.