Riley Business Calculus Syllabus and Course Structure Overview

Course Overview

This syllabus outlines the structure, objectives, and policies for a college-level Business Calculus course. The course covers fundamental topics such as functions, limits, derivatives, and their applications in business and economics.

Course Objectives

• Understand functions, limits, and derivatives with a focus on real-world applications.

• Apply differentiation techniques to solve business-related problems.

Learning Outcomes

• Interpret quantitative information (formulas, graphs, tables, models).

• Formulate and solve quantitative problems using appropriate methods.

• Evaluate logical arguments and present quantitative results effectively.

• Apply derivatives as a tool to analyze change in business and economics.

• Understand and compute insights related to derivatives.

Course Topics and Weekly Schedule

Week	Lecture Topics	Textbook Sections
1	Class Introduction, Functions and Graphing	1.1
2	Linear and Quadratic Functions	1.3
3	Polynomial Functions and Rational Functions	1.4
4	Exponential and Log Functions	1.5, 1.6
5	Review and Exam 1
6	Limits, Continuity	2.1, 2.3
7	Infinite Limits, Rate of Change, Derivative	2.4, 2.6
8	Derivatives and Applications	2.7, 2.8
9	Product/Quotient Rules	3.1
10	The Chain Rule, Review and Exam 2	3.4
11	Summary of Implicit Differentiation, History of Derivatives	3.5, 3.7
12	Derivatives and Graphs	4.1
13	Optimization, Absolute Max and Min	4.2
14	Review for Final Exam

Key Topics Covered

Functions and Graphs

Functions are mathematical relationships that assign each input exactly one output. In business calculus, functions model relationships such as cost, revenue, and profit.

• Linear Functions: $f(x) = mx + b$

• Quadratic Functions: $f(x) = ax^2 + bx + c$

• Exponential Functions: $f(x) = a e^{bx}$

• Logarithmic Functions: $f(x) = a \\ln(x) + b$

Example: A company's revenue as a function of units sold can be modeled by a linear function.

Limits and the Derivative

Limits describe the behavior of functions as inputs approach a certain value. The derivative measures the rate of change of a function, which is essential for analyzing trends in business.

• Limit Definition: $\\lim_{x \\to a} f(x)$

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

Example: The derivative of a cost function gives the marginal cost.

Additional Derivative Topics

Advanced differentiation techniques include the product rule, quotient rule, and chain rule, which allow for the differentiation of more complex functions.

• Product Rule: $\\frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)$

• Quotient Rule: $\\frac{d}{dx}\\left[\\frac{u(x)}{v(x)}\\right] = \\frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2}$

• Chain Rule: $\\frac{d}{dx}f(g(x)) = f'(g(x))g'(x)$

Example: Calculating the derivative of a profit function that depends on another variable.

Graphing and Optimization

Graphing derivatives helps visualize function behavior, while optimization techniques are used to find maximum and minimum values, crucial for business decision-making.

• Critical Points: Where $f'(x) = 0$ or $f'(x)$ is undefined.

• Absolute Max/Min: Highest/lowest values of a function on a given interval.

Example: Maximizing profit by finding the vertex of a quadratic revenue function.

Assessment and Grading

• Exam 1: 20%

• Exam 2: 20%

• MyMathLab Homework: 20%

• MyMathLab Quizzes: 20%

• Final Exam: 20%

Grade	Score Range
A	90-100
B	80-89
C	70-79
D	60-69

Required Materials

• Textbook: Sobecki, Applied Calculus for Business, Economics, Life Sciences, and Social Sciences.

• Calculator: Scientific calculator (TI 30X IIS recommended).

• Online Platform: MyMathLab for homework and quizzes.

Academic Policies

• Follow the GMU Honor Code: No plagiarism, cheating, or unauthorized collaboration.

• Accommodations available for students with learning differences or special needs.

Additional info:

• This syllabus provides a comprehensive overview of the Business Calculus course, including weekly topics, grading, and policies. For detailed content on each chapter, refer to the course textbook and lecture notes.