Business Calculus: Course Syllabus and Weekly Study Guide

Course Overview

Introduction to Business Calculus

This course provides an introduction to the calculus of one variable, focusing on applications relevant to business and economics. It covers fundamental concepts such as functions, limits, derivatives, and integrals, with an emphasis on real-world problem-solving and marginal analysis.

• Target Audience: Business and economics students (non-computer science majors).

• Textbook: Calculus for Business, Economics, Life Science and Social Sciences by Barnett, Ziegler, and Byleen (14th edition).

• Prerequisites: MATH 111 or MATH 113.

Course Learning Outcomes

• Limits: Find limits of functions, analyze behavior at infinity, and understand continuity/discontinuity.

• Differentiation: Differentiate basic functions and apply results to business and economics problems.

• Optimization: Analyze functions to find maximum and minimum values and interpret their significance.

• Integration: Integrate basic functions and apply results, including marginal analysis in business contexts.

Weekly Lesson Plan and Topics

The following is a structured outline of the main topics and subtopics covered each week, along with relevant textbook sections and suggested practice problems.

Week 1: Functions and Elementary Functions

• Functions: Definition, domain, range, and types of functions.

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

• Review: College Algebra concepts as foundation.

• Practice Problems: 15, 27, 29, 31, 51, 61, 83 (from textbook).

Week 2: Limits and Continuity

• Introduction to Limits: Understanding the concept of a limit.

• Infinite Limits and Limits at Infinity: Analyzing function behavior as input grows large or approaches a point.

• Continuity: Definition and identification of continuous and discontinuous functions.

• The Derivative: Introduction to the derivative as a rate of change.

• Basic Differentiation Properties: Rules for differentiating standard functions.

• Differentials: Linear approximation and differentials.

• Marginal Analysis: Application of derivatives to business and economics (e.g., marginal cost, marginal revenue).

• Practice Problems: 9, 11, 13, 15, 17, 19, 21, 45(c), 47(c), 51, 56, 19, 21, 27, 32, 34, 35, 53, 69, 73, 25, 29, 33, 35, 41, 79, 9, 13, 17, 21, 25, 29, 37, 53, 59, 89, 15, 23, 11, 13, 17, 21, 23, 25, 27, 33, 45.

Week 3: Derivative Techniques and Applications

• Exponential and Logarithmic Functions: Differentiation and applications.

• Product and Quotient Rules: Differentiating products and quotients of functions.

• Chain Rule: Differentiating composite functions.

• Implicit Differentiation: Differentiating equations not solved for y.

• Related Rates: Solving problems involving rates of change in related variables.

• Elasticity of Demand: Application of derivatives in economics to measure responsiveness.

• Practice Problems: 13, 25, 27, 33, 11, 15, 21, 34, 41, 43, 46, 53, 15, 21, 25, 33, 39, 41, 47, 55, 2, 6, 11, 17, 21, 37, 43, 53, 63, 11, 15, 21, 25, 27, 29, 37, 43, 9, 11, 33, 35, 47, 51.

Week 4: Graphing and Optimization

• First and Second Derivatives: Using derivatives to analyze and graph functions.

• L’Hôpital’s Rule: Evaluating indeterminate forms.

• Curve Sketching: Techniques for graphing functions using calculus.

• Absolute Maxima and Minima: Finding and interpreting extreme values.

• Optimization: Solving real-world problems involving maximization or minimization.

• Practice Problems: 27, 33, 35, 40, 55, 17, 23, 25, 31, 33, 35, 9, 21, 25, 27, 29, 33, 35, 41, 49, 59, 67, 3, 5, 21, 31, 45, 75, 77, 9, 17, 25, 29, 33, 37, 45, 49, 67, 71, 17, 19, 21, 25, 27.

Week 5-6: Integration

• Antiderivatives and Indefinite Integrals: Finding functions whose derivative is a given function.

• Integration by Substitution: Technique for integrating composite functions.

• Definite Integrals: Calculating the area under a curve between two points.

• Fundamental Theorem of Calculus: Connecting differentiation and integration.

• Applications: Business and economics applications, including marginal analysis.

• Practice Problems: 9, 19, 43, 45, 49, 51, 55, 59, 69, 9, 13, 17, 21, 25, 33, 43, 79, 80, 31, 33, 41, 45, 49, 25, 27, 31, 33, 39, 41, 57, 59.

Assessment and Grading

Assessment	Learning Outcomes	Grade (%)
Homework (MyLab)	LO 1 to 6	10%
Attendance/Participation/Discussion	LO 1 to 6	5%
Quizzes	LO 1 to 6	10%
2 Tests	LO 1 to 6	25%
Project(s) and Presentation(s)	LO 1 to 6	20%
Final Exam	LO 1 to 6	30%
Total		100%

Grading Scale

Score (%)	Letter Grade
95-100	A
90-94	A-
87-89	B+
84-86	B
80-83	B-
77-79	C+
73-76	C
70-73	C-
65-69	D+
60-64	D
Below 60	F

Academic Policies and Resources

• Attendance: Mandatory for all lectures and assessments.

• Homework: Completed and submitted via Pearson’s MyLab Math.

• Exams: Comprehensive final exam is required to pass the course. No advanced scientific calculators allowed.

• Academic Honesty: All submitted work must be original. Plagiarism or use of unauthorized assistance is strictly prohibited.

• Resources: Course materials, review sheets, and sample exams are available on the university e-learning portal.

Summary Table: Weekly Topics and Textbook Sections

Week	Chapters/Sections	Main Topics
1	1.1–1.6, 2.1	Functions, Elementary Functions, Limits
2	2.2–2.7	Limits, Continuity, Derivatives, Marginal Analysis
3	3.1–3.7	Exponential/Logarithmic Functions, Product/Quotient/Chain Rule, Implicit Differentiation, Related Rates, Elasticity
4	4.1–4.6	Graphing, L’Hôpital’s Rule, Curve Sketching, Optimization
5–6	5.1–5.5	Integration, Substitution, Definite Integrals, Fundamental Theorem

Additional Info

• Students are encouraged to use the e-learning portal for supplementary materials and to check for announcements regularly.

• Suggested practice problems are provided for each topic to reinforce understanding and prepare for assessments.

• Marginal analysis and optimization are emphasized for their importance in business and economics applications.