MATH 209 - Fundamental Mathematics II (Business Calculus) Syllabus and Study Guide

Course Overview

Introduction to MATH 209

MATH 209 is a college-level course designed to introduce students to the fundamental concepts of calculus and its applications in business, economics, and the social sciences. The course covers differential and integral calculus, including limits, derivatives, integration, and their business-specific applications.

• Course Focus: Differential calculus (limits, derivatives, differentiation) and selected topics in integral calculus (antiderivatives, definite integrals, integration by substitution).

• Applications: Business and economics applications are emphasized throughout the course.

Course Structure and Topics

Lesson Breakdown

The course is organized into 13 lessons, each focusing on a key topic in business calculus. Below is a summary of the main topics and their relevance to the Business Calculus curriculum:

• Lesson 1: Getting Started

• Lesson 2: Limits and Continuity

• Lesson 3: Derivatives and Differentiation

• Lesson 4: Marginal Analysis

• Lesson 5: Derivatives of Exponential and Logarithmic Functions

• Lesson 6: Applications of Derivatives

• Lesson 7: Related Rates and Elasticity of Demand

• Lesson 8: Second Derivatives and Graphs

• Lesson 9: Optimization and Graphing

• Lesson 10: Antiderivatives and Indefinite Integrals

• Lesson 11: Definite Integrals

• Lesson 12: Applications of Definite Integrals

• Lesson 13: Limits and Definite Integrals

Key Topics and Subtopics

• Functions and Graphs: Understanding the behavior of functions, graphing techniques, and interpreting graphs in a business context.

• Limits and Continuity: Definition of limits, properties, and the concept of continuity. Formula: $\lim_{x \to a} f(x)$

• Derivatives: Definition, rules of differentiation, and applications to rates of change. Formula: $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

• Marginal Analysis: Application of derivatives to economics, such as marginal cost and marginal revenue.

• Exponential and Logarithmic Functions: Differentiation and integration of exponential and logarithmic functions. Formula: $\frac{d}{dx}e^x = e^x$, $\frac{d}{dx}\ln x = \frac{1}{x}$

• Applications of Derivatives: Optimization, related rates, and elasticity of demand in business scenarios.

• Second Derivatives and Graphing: Concavity, inflection points, and their significance in optimization. Formula: $f''(x)$

• Optimization: Techniques for finding maxima and minima of functions, especially in profit and cost analysis.

• Antiderivatives and Indefinite Integrals: Finding functions given their derivatives. Formula: $\int f(x) dx$

• Definite Integrals: Calculating area under curves and total accumulated quantities. Formula: $\int_a^b f(x) dx$

• Applications of Integrals: Business applications such as consumer and producer surplus, total revenue, and cost functions.

Lesson Table

The following table summarizes the lesson titles and corresponding textbook sections:

Lesson	Title	Textbook Sections
1	Getting Started	N/A
2	Limits and Continuity	1.1, 1.2, 1.3
3	Derivatives and Differentiation	2.1, 2.2, 2.3
4	Marginal Analysis	2.4
5	Derivatives of Exponential and Logarithmic Functions	3.1, 3.2
6	Applications of Derivatives	3.3, 3.4
7	Related Rates and Elasticity of Demand	3.5, 3.6
8	Second Derivatives and Graphs	4.1, 4.2
9	Optimization and Graphing	4.3, 4.4
10	Antiderivatives and Indefinite Integrals	5.1, 5.2
11	Definite Integrals	5.3, 5.4
12	Applications of Definite Integrals	5.5, 5.6
13	Limits and Definite Integrals	6.1, 6.2, 6.3

Assessment and Grading

Evaluation Scheme

• Assignments: 10%

• Midterm Test 1: 10%

• Midterm Test 2: 10%

• Final Exam: 70%

Note: A minimum score of 50% on the final exam is required to pass the course.

Letter Grade Conversion Table

Letter	Score (%)
A+	90-100
A	85-89.99
A-	80-84.99
B+	77-79.99
B	73-76.99
B-	70-72.99
C+	67-69.99
C	63-66.99
C-	60-62.99
D+	57-59.99
D	53-56.99
D-	50-52.99
F	0-49.99

Additional Academic Support

• Teaching Assistants: Available for questions and support via email and discussion board.

• Discussion Board: Platform for posting questions and interacting with peers and instructors.

• Math Help Centre: Provides additional tutoring and support for students.

• Student Success Centre: Offers resources for study habits and academic success.

Study Habits and Success Tips

• Allocate regular study time (at least 4 hours per week).

• Complete all assignments and participate in discussions.

• Review formulas, concepts, and textbook readings before assessments.

• Seek help from TAs, instructors, and support centers as needed.

Important Course Policies

• Academic Integrity: Adherence to university policies is mandatory.

• Calculator Policy: Only approved calculators may be used in exams.

• Third-Party Software: Use of generative AI tools for assignments is prohibited.

Conclusion

This syllabus provides a comprehensive overview of the MATH 209 course, including its structure, topics, assessment methods, and support resources. The course is highly relevant to Business Calculus and prepares students for further study and application in business, economics, and related fields.