Course Overview

Introduction to Brief Calculus (MAT 143)

This course provides an intuitive approach to calculus, emphasizing conceptual understanding and applications to business. The curriculum covers differentiation, curve sketching, optimization, integration, and partial derivatives, preparing students for quantitative reasoning and analytical problem-solving.

• Course Credits: 3

• Required Textbook: Calculus and Its Applications (3rd Edition) by Bittinger, Ellenbogen, and Surgent

• Emphasis: Conceptual understanding, applications, and written solutions

Course Student Learning Outcomes

Core Calculus Competencies

• Limits: Explain the concept of a limit and its role in defining the slope of a tangent line and instantaneous rate of change.

• Computation: Compute limits, derivatives, partial derivatives, and integrals using various techniques.

• Applications: Apply properties of derivatives to solve problems involving marginal cost, curve sketching, optimization, and elasticity of demand.

• Definite Integrals: Set up definite integrals to solve business-related problems.

• Mathematical Reasoning: Use correct mathematical notation and logical reasoning to solve multistep problems.

General Education Learning Outcomes

Quantitative, Analytical, and Communication Skills

• Communication: Express oneself effectively in written forms and demonstrate comprehension of information accessed through reading.

• Critical Thinking: Reach sound conclusions based on logical analysis of evidence.

• Quantitative Literacy: Use numbers, symbols, measurements, and relationships of quantities to make decisions and analyze data.

• Graphical, Symbolic, and Numerical Methods: Analyze, organize, and interpret data using various mathematical methods.

Course Content Structure

Chapter Breakdown and Topics

• Chapter 1: Differentiation (Sections 1.1 - 1.8)

• Chapter 2: Exponential and Logarithmic Functions (Sections 2.1 - 2.6)

• Chapter 3: Applications of Differentiation (Sections 3.1 - 3.5, 3.7, 3.8)

• Chapter 4: Integration (Sections 4.1 - 4.5)

• Chapter 6: Functions of Several Variables (Sections 6.1, 6.2)

Assessment and Evaluation

Grading and Exam Structure

• Exams (3): 70% of grade

• Online Homework: 10% of grade

• Final Exam: 20% of grade

• No extra credit

Letter Grade Scale

Key Calculus Topics Covered

Differentiation

Differentiation is the process of finding the derivative of a function, which represents the rate of change or slope at any given point. It is foundational for understanding instantaneous rates and tangent lines.

• Definition: The derivative of a function is defined as

• Applications: Marginal cost, curve sketching, optimization

• Example: If , then

Exponential and Logarithmic Functions

These functions are essential in modeling growth and decay processes, and their derivatives and integrals are widely used in business and economics.

• Exponential Function:

• Logarithmic Function:

• Derivative of Exponential:

• Derivative of Logarithm:

• Application: Compound interest, population growth

Applications of Differentiation

Derivatives are used to solve real-world problems such as optimization (finding maxima and minima), elasticity of demand, and marginal analysis.

• Optimization: Finding the maximum or minimum values of functions

• Elasticity of Demand:

• Marginal Cost: The derivative of the cost function with respect to quantity

Integration

Integration is the reverse process of differentiation and is used to calculate areas under curves, total accumulated quantities, and solve business-related problems.

• Definition: The definite integral of from to is

• Indefinite Integral:

• Application: Total revenue, area under demand curves

• Example:

Functions of Several Variables

Calculus extends to functions involving more than one variable, allowing for partial derivatives and multivariable optimization.

• Partial Derivative: denotes the derivative of with respect to , holding other variables constant

• Application: Business models with multiple factors, such as cost depending on price and quantity

Practice Problems by Section

Recommended Exercises

Practice problems are assigned for each section to reinforce understanding and application of calculus concepts. Students should complete these problems to prepare for exams and quizzes.

• Section 1.1: #21, 22, 23, 24, 25-66, 79, 81, 83

• Section 1.2: #1-59 odd, 83

• Section 1.3: #1-7 odd, 11-15 odd, 21, 25, 29, 45, 49, 51, 53

• Section 1.4: #1, 3, 11, 13 (c & d only), 17, 21, 25, 27, 29, 31, 35, 43

• Section 1.5: #7-55 odd, 59a, 61a, 63, 65, 73, 79, 83, 87

• Section 1.6: #21, 23, 25, 27, 33, 37, 39, 45, 53, 55, 57, 59, 63

• Section 1.7: #3, 5, 9, 11, 13, 17, 19, 23, 25, 29, 41, 49, 53, 57

• Section 1.8: #3, 5, 15, 19, 23, 27, 35, 39, 47

• Section 2.1: #9, 39, 47, 63, 65, 71, 73, 75

• Section 2.2: #3, 5, 7, 9, 11, 15, 31, 33, 47, 49, 51, 53

• Section 2.3: #1-15 odd, 25, 27, 31 a & b

• Section 2.4: #1-11 odd, 13, 15

• Section 2.5: #37, 39-45 odd

• Section 2.6: #1, 3, 7, 13, 15, 19, 21, 25, 27, 29, 31, 33, 35, 37, 39, 47, 55, 57

• Section 3.1: #1, 3, 19, 21, 29, 35, 37, 39, 81, 83

• Section 3.2: #1, 6, 7, 13, 17, 21, 25, 41 (no graphing), 43a

• Section 3.3: #3, 5, 7, 17, 19, 21, 23, 49 a & b, 51 a-c

• Section 3.4: #5, 9, 11, 19, 49, 51, 53

• Section 3.5: #15, 19, 25, 27, 31, 33, 35, 46

• Section 3.6: #25, 27, 29, 31

• Section 3.7: #1, 3, 7, 9, 13-17 odd

• Section 3.8: #37-39

• Section 4.1: #1-29 odd, 37, 39, 57, 59, 61, 63

• Section 4.2: #1-13 odd, 27, 29, 31, 35, 39, 41

• Section 4.3: #9, 11, 15, 19, 21, 43, 45, 49, 63, 65, 67

• Section 4.4: #11, 13, 35, 37, 38, 45, 47, 49

• Section 4.5: #1, 5, 9, 11, 15, 27, 45, 47, 57, 59, 75

• Section 6.1: #1, 3, 5, 7, 13-17

• Section 6.2: #7, 13, 17, 23, 49, 50

Course Schedule and Exam Dates

Weekly Section Coverage

• Weeks 1-3: Differentiation (Sections 1.1 - 1.8)

• Weeks 4-6: Exponential and Logarithmic Functions (Sections 2.1 - 2.6)

• Weeks 7-10: Applications of Differentiation (Sections 3.1 - 3.8)

• Weeks 11-13: Integration (Sections 4.1 - 4.5)

• Week 14: Functions of Several Variables (Sections 6.1, 6.2)

Exam Dates

• Exam 1: Thursday, September 17, 2026 (Chapter 1)

• Exam 2: Tuesday, October 20, 2026 (Sections 2.1-2.6, 3.1-3.3)

• Exam 3: Thursday, November 19, 2026 (Sections 3.1-3.5, 3.7, 3.8, 4.1-4.5)

• Final Exam: Tuesday, December 8, 2026, 6:00-8:00 pm

Additional Academic Policies

• Attendance: Mandatory; participation is expected.

• Make-up Exams: Only for certifiable emergencies.

• Academic Integrity: Adherence to university standards is required.

• Disability Accommodations: Contact Office of Educational Accessibility for support.

• Inclusive Environment: Diversity, equity, and anti-racist policies are central to course culture.

Summary Table: Course Content and Assessment

Additional info: The syllabus includes university policies, accessibility, and anti-racist statements, which are important for the learning environment but not directly related to calculus content. The practice problems and chapter structure align closely with standard calculus topics, including differentiation, integration, and applications.