Calc 1: Limits & Derivatives
We'll create whole new ways of interacting with functions, then use them to launch into a whole new realm of math!
Description
A typical calculus 1 course covers two main topics: limits and derivatives.
Limits describe what happens to a function near a specific point (but not necessarily at that point). The intimately-related topic of continuity is perhaps the most important underpinning of theorems about functions. You'll learn how to think about questions like:
What does it mean to be "close" to a point?
What can we learn about a function on an interval given that the curve is connected? Smooth?
How do we know what happens in the neighborhood of dividing by zero?
How can we combine limits and the algebra equation for slope to think about the slope of a curve?
Derivatives are functions which describe the slope of a corresponding function. Once we can think about the behavior of the derivative, a whole range of applications present themselves! You'll learn how to think about questions like:
How do we evaluate the slope of a line that isn't straight?
What simplifications can we use in evaluating derivatives based on the different types of basic operations?
What does it mean for the slope to be zero?
How do derivatives of multiple related functions interrelate?
What happens if you take the derivative of the derivative?
Can't wait to get started! Calculus 1 is a gateway into a whole new realm of math and way of thinking. Let's go!
What You Will Learn!
- Understanding what happens as a function approaches a point
- Extending the idea of "slope" from straight lines to all curves
- Applying these slopes to explore the behavior of graphs
- Using these tools in real-world applications
Who Should Attend!
- Lovers and future lovers of math who are ready to learn by exploring concepts
- Calc 1 serves as a gateway to lots of technical fields, and is a common early college course for these kinds of majors