The next step in mathematics, calculus changes everything while relying on all that has been learned before it.
Limits are the backbone of all of calculus. Limits tell us where we are when we can't be somewhere, in a sense, but there is much more to them than that.
Our first application of limits: taking derivatives, will take some conceptual getting-used to. An understanding of derivatives is essential to their definition and use.
What exactly is a derivative? In this series, our understanding of the derivative will be expanted to include a number of functions and formulas.
There are more then one way to take a derivative. The power rule is perhaps the least complicated, yet not least important, method of doing this.
The product rule is another method for taking derivatives, and one that is absolutely necessary to know for any use of calculus.
Perhaps the most important form of taking derivatives, the chain rule is also perhaps the most conceptually challenging that we've covered. After some experience with its use, however, it will serve you loyally in all of your calculus adventures.
A fascinating form of differentiation to say the least, the implicit form of taking derivatives brings differentiation to a whole new level.
Derivatives of important functions used in innumerable situations demonstrated.
An important limits rule that we can apply with our new knowledge of derivative taking.
Why learn calculus and derivatives? While only scratching the surface, in this series we introduce some useful and hopefully compelling applications of the math covered in the previous sections.
A new application of calculus is afoot! However, before we can understand that new idea, we must look back to its roots in algebra and limits.
Recall, then prove the formulas memorized in geometry class using calculus!
Some practice using the various techniques for solving integrals.