Calc 2: Integrals & Sums
We'll wrestle with reversing the derivative, then explore the behavior of sums and their connection to functions!
Ratings 3.00 / 5.00
What You Will Learn!
- Exploring the connection between reversing a derivative ("integration") and area under the curve
- Developing problem solving techniques for integration
- Understanding the connection between limits, sequences, and sums of sequences ("series")
- Developing problem solving techniques for determining whether a series converges
- Extending series to include a variable, primarily to enable approximating common functions
Description
A typical calculus 2 course covers two main topics: integrals and sums.
Integrals describe the area under a curve over a specific interval, and are the inverse operation of a derivative. Because it's not tied to a specific approach (unlike derivatives, which are generated by the difference quotient), we'll get to explore the puzzle-like world of integration. You'll learn how to think about questions like:
What is the relationship between areas, antiderivatives, and the values input into these?
What tools do we have based on our known derivatives? What about based on our known derivative rules?
Is the integral a linear operator — meaning sums & constant multiples can be "pulled apart" — like its inverse can?
What can we do with a function once we are able to integrate it?
Sums take a list of terms (a sequence) and add them all up. The most interesting property of a sum is whether or it converges (eventually sums to a specific number) or diverges (doesn't). Then, with some clever calculus, we can use these series to approximate more complex functions that are hard to evaluate otherwise! You'll learn how to think about questions like:
What is convergence, and how do I get a "feel" for whether a series converges or diverges?
How can we use properties or other series to help us identify convergence for series we don't already know?
How can we generate approximations for functions as sums of polynomials?
What ways can we extend these approximations, and how accurate are they?
Can't wait to get started! Calculus 2 is an exciting opportunity to flex your creative muscles in a field that just gets more creative the deeper you dive in. Let's go!
Who Should Attend!
- Lovers and future lovers of math who are ready to learn by exploring concepts
- Calc 2 is a common early college course for technical fields of study, and is a big step toward a more creative understanding of math