What This Document Is
These are lecture notes from a Calculus I (MTH 151) course at Miami University, focusing on the foundational concept of derivatives. The notes explore the idea of a derivative as a rate of change and introduce methods for finding the equation of a tangent line to a curve. It lays the groundwork for understanding how derivatives are calculated and interpreted.
Why This Document Matters
This document is essential for students enrolled in a first-semester calculus course. It serves as a direct companion to lectures, providing a written record of key concepts and examples discussed in class. Understanding derivatives is crucial for success in calculus and forms the basis for many applications in physics, engineering, economics, and other fields. These notes are most valuable when used *during* or immediately *after* a lecture to reinforce learning.
Common Limitations or Challenges
These notes represent a starting point for understanding derivatives. They do not provide extensive practice problems or detailed solutions. Students will still need to work through textbook exercises, complete assignments, and seek clarification during office hours to fully master the material. The notes also assume a basic understanding of functions and limits.
What This Document Provides
This document includes:
* An introduction to the concept of a derivative as the slope of a tangent line.
* Methods for finding the equation of a tangent line to a curve at a given point.
* Examples demonstrating the calculation of derivatives using the limit definition.
* Discussion of differentiability and its relation to the domain of a function.
* Initial exploration of the derivative as a function itself.
This preview *does not* include: comprehensive practice problems, detailed explanations of derivative rules (power rule, product rule, etc.), applications of derivatives (optimization, related rates), or a complete treatment of differentiability.