Calculus I: Course Overview and Study Guide

Course Introduction

Overview of Calculus I

Calculus I is a foundational college mathematics course focusing on the study of limits, continuity, derivatives, and their applications. The course is designed to introduce students to the fundamental concepts and techniques of differential calculus, with an emphasis on problem-solving and mathematical reasoning.

• Key Topics: Limits, continuity, derivatives, applications of derivatives, and introduction to integration.

• Applications: Real-world problems in science, engineering, and economics.

• Prerequisites: Proficiency in algebra and trigonometry.

Course Materials

Required Textbook and Online Resources

The primary textbook for this course is Calculus: Early Transcendentals by James Stewart (8th Edition). Students will also use the online platform MyMathLab for assignments and quizzes.

• Textbook: Stewart, J. Calculus: Early Transcendentals, 8th Edition.

• Online Platform: MyMathLab (access code required).

• Calculator: TI-83+, TI-84+, TI-84, or TI-89 (no calculator use on some exams).

Course Structure and Assessment

Grading Components

Student performance is assessed through a combination of homework, quizzes, chapter exams, and a comprehensive final exam. Participation in all assignments is mandatory for successful completion of the course.

• Homework & Math Basics Review: 5% of final grade. Assigned via MyMathLab, includes multiple attempts.

• Chapter Quizzes: 25% of final grade. Timed quizzes on MyMathLab, best score of two attempts counted.

• Midterm Exam: 20% of final grade. Covers chapters 1-3, timed and proctored.

• Comprehensive Final Exam: 30% of final grade. Covers chapters 1-5, timed and proctored.

• Coursework Expectations: 20% of final grade. Completion of all assigned work is required.

Major Topics in Calculus I

Limits and Continuity

Limits are the foundation of calculus, describing the behavior of functions as inputs approach specific values. Continuity ensures that functions behave predictably without sudden jumps.

• Definition of a Limit: The value that 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's value at that point.

• Formula:

$\lim_{x \to a} f(x) = L$

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

Derivatives and Differentiation

The derivative measures the rate of change of a function. Differentiation is the process of finding the derivative, which is essential for analyzing motion, growth, and optimization problems.

• Definition of Derivative: The instantaneous rate of change of a function at a point.

• Formula:

$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

• Example: If $f(x) = x^2$, then $f'(x) = 2x$.

Applications of Derivatives

Derivatives are used to solve problems involving rates of change, optimization, and motion. Common applications include finding maximum and minimum values and analyzing the behavior of functions.

• Critical Points: Points where $f'(x) = 0$ or $f'(x)$ is undefined.

• Optimization: Using derivatives to find the maximum or minimum values of functions.

• Example: To find the maximum area of a rectangle with a fixed perimeter, set up an equation and use derivatives to solve.

Introduction to Integration

Integration is introduced as the reverse process of differentiation, used to find areas under curves and accumulate quantities.

• Definition of Integral: The area under the curve of a function over an interval.

• Formula:

$\int_a^b f(x) \, dx$

• Example: $\int_0^2 x \, dx = 2$

Course Policies and Student Responsibilities

Attendance and Participation

Active participation in synchronous online sessions and completion of all assignments is required. Students must check their college email regularly for updates and communications.

• Attendance: Required for all live sessions and group work.

• Participation: Includes engagement in discussions, group activities, and timely submission of assignments.

Academic Integrity

Students are expected to adhere to college policies regarding academic honesty. Use of unauthorized resources during exams is strictly prohibited.

• Calculator Policy: Only approved calculators may be used; some exams prohibit calculator use.

• Assignment Submission: All work must be completed individually unless group work is specified.

Important Dates and Deadlines

Event	Date	Description
Withdrawal Deadline	11/12/2025	Last day to withdraw from the course with a "W" grade.
Course Engagement Deadline	9/21/2025	Deadline for students to participate in coursework to retain course enrollment.
Final Exam	12/3/2025 - 12/9/2025	Comprehensive final exam covering all course material.

Resources and Support

Academic Support

Students have access to online resources, tutoring, and office hours for additional help. The Academic Success Center (ASC) provides support for mathematics and other subjects.

• Online Tutoring: Available through the college's learning platform.

• Office Hours: Scheduled weekly for individual assistance.

• Resource Center: Academic Success Center for tutoring and study support.

Summary Table: Assessment Breakdown

Assessment Type	Percentage of Final Grade	Description
Homework & Math Basics Review	5%	Online assignments via MyMathLab
Chapter Quizzes	25%	Timed quizzes on MyMathLab
Midterm Exam	20%	Proctored exam covering chapters 1-3
Final Exam	30%	Comprehensive proctored exam
Coursework Expectations	20%	Completion of all assigned work

Additional info:

• Students are encouraged to practice problems regularly and seek help when needed.

• Consistent engagement and timely completion of assignments are crucial for success in Calculus I.