Business Calculus Syllabus and Course Overview

Course Overview

This syllabus outlines the structure, objectives, and policies for a college-level Business Calculus course. The course focuses on understanding functions, limits, derivatives, and their applications in real-world business contexts. The schedule, grading, and learning outcomes are detailed to guide students through the semester.

Course Objectives

• Interpret quantitative information from formulas, graphs, tables, models, and data.

• Apply quantitative reasoning to formulate and solve problems using appropriate arithmetic, algebraic, and statistical methods.

• Evaluate logical arguments using quantitative reasoning.

• Communicate and present quantitative results effectively.

Learning Outcomes

Upon successful completion of this course, students will be able to:

• Analyze and apply algebraic skills.

• Use derivatives as a tool to analyze change in quantitative models.

• Interpret results in business and IT applications.

• Understand and compute insights related to derivatives.

Course Topics and Schedule

Week	Lecture Topics
1	Course Introduction, How to use MyMathLab
2	Functions and Graphing (1.1), Linear and Quadratic Functions (1.2)
3	Polynomial Functions and Rational Functions (1.4)
4	Exponential Functions (1.5), Log Functions (1.6)
5	Review and Exam 1
6	Limits (2.1), Continuity (2.3)
7	Infinite Limits and Limits at Infinity (2.4), Rate of Change and the Derivative (2.6)
8	Rate of Change and the Derivative (2.6)
9	Derivatives and Applications (2.7, 2.8)
10	Product/Quotient Rules (3.1), The Chain Rule (3.4)
11	Summary of Implicit Differentiation (3.5), Elasticity of Demand (3.7)
12	Derivatives and Graphs (4.1)
13	Second Derivative and Graphing (4.2), Optimization and Absolute Max and Min (4.3)
14	Review for Final Exam

Key Topics and Concepts

Functions and Graphs

• Function: A relation that assigns exactly one output for each input.

• Graphing: Visual representation of functions to analyze behavior and trends.

• Linear and Quadratic Functions: Functions of the form $f(x) = mx + b$ and $f(x) = ax^2 + bx + c$.

• Polynomial and Rational Functions: Polynomial functions involve terms with non-negative integer exponents; rational functions are ratios of polynomials.

• Exponential and Logarithmic Functions: Exponential: $f(x) = a^x$; Logarithmic: $f(x) = \log_a x$.

Limits and Continuity

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

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

• Infinite Limits and Limits at Infinity: Describes behavior as $x$ approaches infinity or as the function grows without bound.

• Notation: $\lim_{x \to a} f(x) = L$

Derivatives and Applications

• Derivative: Measures the rate at which a function changes. Defined as $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

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

• Implicit Differentiation: Used when functions are not solved for $y$ explicitly.

• Elasticity of Demand: $E(p) = \left| \frac{p}{q} \cdot \frac{dq}{dp} \right|$

Graphing and Optimization

• First Derivative Test: Determines where a function is increasing or decreasing.

• Second Derivative Test: Determines concavity and points of inflection.

• Optimization: Finding maximum or minimum values of functions, often in business applications such as profit or cost.

Grading Policy

• Exam 1: 20%

• Exam 2: 20%

• MyMathLab Homework: 20%

• MyMathLab Quizzes: 20%

• Final Exam: 20%

Grade Breakdown:

Grade	Score Range
A	90-100
B	80-89
C	70-79
D	60-69
F	0-59

Required Materials

• Textbook: Barnett, Ziegler, Byleen, Sobecki, Applied Calculus for Business, Economics, Life Sciences, and Social Sciences, 14th edition.

• Calculator: Simple scientific calculator (no graphing or symbolic calculators allowed).

• MyMathLab: Online homework and quiz platform required for the course.

Academic Policies

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

• Accommodations available for students with documented disabilities.

• Support services available for counseling and psychological needs.

Additional info: This syllabus provides a comprehensive overview of the Business Calculus course, including all major topics relevant to the curriculum as outlined in the provided chapter titles.