Business Calculus Syllabus and Course Structure Overview

Course Overview

This syllabus outlines the structure, objectives, and assessment methods for a college-level Business Calculus course. The course focuses on understanding functions, limits, derivatives, and their applications in real-world business contexts.

Course Objectives

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

• Apply quantitative reasoning to solve business-related problems using algebraic, geometric, and statistical methods.

• Evaluate logical arguments using quantitative reasoning.

• Communicate and present quantitative results effectively.

Learning Outcomes

• Analyze and apply algebraic skills.

• Use derivatives to analyze change in quantitative models.

• Interpret results in business and IT contexts.

• Understand and compute derivatives, including their applications.

Course Topics and Weekly Structure

The course is organized into weekly modules, each covering key topics in Business Calculus. Below is a summary of the main topics and their sequence:

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

Key Topics and Concepts

Functions and Graphs

• Definition: A function is a relation that assigns exactly one output for each input.

• Types: Linear, quadratic, polynomial, rational, exponential, and logarithmic functions.

• Graphing: Understanding the shape and behavior of different function types is essential for modeling business scenarios.

• Example: The profit function $P(x) = -2x^2 + 40x - 100$ models profit based on units sold.

Limits and Continuity

• Limit: The value 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 value at that point.

• Infinite Limits: Describes behavior as the function grows without bound near a point.

• Example: $\lim_{x \to 2} (3x + 1) = 7$

Derivatives and Applications

• Derivative: Measures the rate of change of a function with respect to its variable.

• Notation: $f'(x)$ or $\frac{dy}{dx}$

• Rules: Product, quotient, and chain rules for differentiating complex functions.

• Applications: Marginal cost, marginal revenue, and optimization in business contexts.

• Example: If $C(x)$ is the cost function, then $C'(x)$ is the marginal cost.

Graphing and Optimization

• Critical Points: Where the derivative is zero or undefined; used to find maxima and minima.

• Second Derivative: Used to determine concavity and points of inflection.

• Optimization: Finding input values that maximize or minimize a function, such as profit or cost.

• Example: To maximize profit $P(x)$, solve $P'(x) = 0$ and check the second derivative.

Integration (Not detailed in schedule but typically included in Business Calculus)

• Definition: The process of finding the area under a curve, representing accumulation.

• Notation: $\int f(x) dx$

• Applications: Total cost, total revenue, consumer and producer surplus.

Additional info: Integration is a standard topic in Business Calculus, though not explicitly listed in the provided schedule.

Assessment and Grading

• 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	Below 60

Course Policies and Resources

• Use of scientific calculators is allowed; graphing calculators are not permitted.

• Academic honesty is strictly enforced.

• Accommodations are available for students with documented disabilities.

• Support services are available for counseling and psychological needs.

Additional info: For full details on university policies, refer to the official university guidelines and honor code.