Business Calculus: Core Concepts, Structure, and Success Strategies

Calculus for Students in the Social and Biological Sciences

Course Overview

This course introduces fundamental concepts of calculus tailored for students in social, biological, and business sciences. The curriculum emphasizes limits, continuity, derivatives, integrals, and their applications to real-world problems, with a focus on building both conceptual understanding and problem-solving skills.

• Credit: 1.5 units

• Prerequisites: Grade C+ or higher in Math 120 or equivalent

• Course Materials: Online e-Textbook, video lectures, quizzes, and assignments via Brightspace

Learning Objectives

By the end of the term, students should be able to:

• Understand and apply the concepts of limits, continuity, derivatives, and integrals

• Interpret the meaning of an integral in various contexts

• Communicate mathematical arguments and solutions effectively

• Solve problems involving rates of change, optimization, and accumulation

Course Structure

Weekly Topics and Schedule

The course is organized into weekly modules, each focusing on a key calculus concept. Pre-class videos, quizzes, and assignments reinforce learning.

Week	Topic	Important Events
1	Limits	MLM CRT, MLM Assignment 1
2	Continuity, Continuous Functions	Video quiz 2, MLM Assignment 2
3	Average and Instantaneous Rate of Change	Video quiz 3, MLM Assignment 3
4	Graphical Differentiation	Video quiz 4, GWT #1
5	Derivative rules	Video quiz 5, MLM Assignment 4
6	The Chain Rule	Video quiz 6, Midterm #1
7	Derivatives of exponential functions	MLM Assignment 5
8	Derivatives of logarithmic functions	Video quiz 7, MLM Assignment 6
9	Relative and absolute extrema, optimization	Video quiz 8, GWT #2
10	Implicit differentiation, Second Derivative Test	MLM Assignment 7
11	Curve sketching, Extreme Value Theorem, Critical Point Theorem	Video quiz 9, GWT #3
12	Related Rates	MLM Assignment 8
13	Definite and Indefinite Integrals	Video quiz 10, GWT #4
14	Applications of definite integrals	MLM Assignment 9
15	Area under curves, Fundamental Theorem of Calculus	MLM Assignment 10
16	Exam Period	Final Exam (date TBD)

Key Concepts and Definitions

• Limit: The value that a function approaches as the input approaches a certain point. $\lim_{x \to a} f(x)$

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

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

• Chain Rule: Used to differentiate composite functions. $\frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x)$

• Exponential and Logarithmic Functions: Functions involving $e^x$ and $\ln(x)$, with specific differentiation rules.

• Optimization: Finding maximum or minimum values of functions, often using derivatives.

• Definite Integral: Represents the accumulation of quantities, such as area under a curve. $\int_a^b f(x) \, dx$

• Fundamental Theorem of Calculus: Connects differentiation and integration. $\frac{d}{dx} \int_a^x f(t) \, dt = f(x)$

Assessment and Grading

Grades are based on a combination of online quizzes, assignments, gateway tests, midterms, and a final exam. Students must meet minimum performance thresholds in both online and in-person assessments to pass.

Component	Weight
Online Readiness Test	3%
Weekly Assignments	10%
Weekly Quizzes	10%
Gateway Tests (GWT)	16%
Midterms	34%
Final Exam	27%

Success Strategies

• Stay organized: Keep track of deadlines and complete coursework regularly.

• Use available resources: Access video lectures, quizzes, discussion forums, and office hours.

• Practice problem-solving: Work through examples and seek help when needed.

• Communicate: Ask questions and participate in discussions to clarify concepts.

Permitted Tools

• Permitted: In-class use of laptops/tablets for note-taking, Sharp EL-510R calculator for exams, pencils, and paper.

• Not Permitted: Video/audio recording, smart glasses, phones, or unauthorized calculators during exams.

Additional info:

• This syllabus is designed for a calculus course relevant to business, social, and biological sciences, focusing on practical applications and foundational theory.

• Some topics and assessment details have been inferred from the context and standard course structures.