Welcome to the Spring 2025 Semester!

I am thrilled to welcome you to Calculus 1. Whether you are aspiring to be an engineer, a scientist, or simply looking to expand your mathematical horizons, this course is the foundation for understanding how the world changes and moves. We have an exciting semester ahead of us!

Getting Started: The Essentials

To ensure a smooth start to the semester, please review the following critical information and set up your accounts immediately.

  • Class Syllabus: Please download and read the full syllabus carefully. It contains the grading policy, schedule, and expectations.
    (Note: Please refer to the attached document for the full file).
  • Class Notes: The notes for our first session are available. It is highly recommended that you print these out or load them onto your tablet before class begins to follow along.

Homework Setup: WebAssign

Homework is a vital part of mastering Calculus. We will be using WebAssign for our assignments. You can access the homework platform immediately using the specific course key below:

Course Key: trcc.mohegan 8254 5716

Please log in and register as soon as possible so you do not fall behind on the initial assignments.

The Big Picture: What is Calculus?

Before we dive into the textbook, it is helpful to understand the "Big Picture" of what we are studying. Calculus is fundamentally the study of change. In this course, we will focus on three pillars:

  1. The Limit: This is the tool we use to study the behavior of functions as they get infinitely close to a specific point. It is the foundation of everything else we do. $$ \lim_{x \to a} f(x) = L $$
  2. The Derivative: This measures the instantaneous rate of change. Geometrically, if you have a curve, the derivative tells you the slope of the tangent line at any single point. The definition of the derivative relies on the limit: $$ f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} $$
  3. The Integral: While derivatives deal with rates of change, integrals deal with accumulation, such as finding the area under a curve. $$ \int_{a}^{b} f(x) \, dx $$

By the end of this semester, you will understand the beautiful connection between these concepts known as the Fundamental Theorem of Calculus.

Next Steps

Take a deep breath and get ready to learn. Make sure your WebAssign account is active, review the syllabus, and come to class ready to ask questions. I look forward to exploring these concepts with you!