Calc 1: Limits & Derivatives
What you'll 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
Requirements
- Experience with algebra and trigonometry — take a look at our other courses if you need a refresher!
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!
Who this course is for:
- 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
Instructor
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- 3 Students
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Passion, content expertise, and finely-honed pedagogy — all in one place. We make no assumptions, except that you want to truly learn the content! This is where you'll #LearnToLearn. We channel over 15 years of experience into everything we do, and we're positive our course design will take you from where you are to where you want to go. Led by head instructor Grant Elledge, our friendly & patient team is ready to learn & grow with you!