Power series are infinite series of the form Σaₙxⁿ (where n is a positive integer). Even though this family of series has a surprisingly simple behavior, it can be used to approximate very elaborate functions.
Sequences are like chains of ordered terms. Series are sums of terms in sequences. These simple innovations uncover a world of fascinating functions and behavior.
Make your first steps in evaluating definite integrals, armed with the Fundamental theorem of calculus.
Integrals can be used to find 2D measures (area) and 1D measures (lengths). But it can also be used to find 3D measures (volume)! Learn all about it here.
Riemann sums is the name of a family of methods we can use to approximate the area under a curve. Through Riemann sums we come up with a formal definition for the definite integral.
As with derivatives, solve some real world problems and mathematical problems using the power of integral calculus.
Some functions don't make it easy to find their integrals, but we are not ones to give up so fast! Learn some advanced tools for integrating the more troublesome functions.
If f is the derivative of F, then F is an antiderivative of f. We also call F the "indefinite integral" of f. In other words, indefinite integrals and antiderivatives are, essentially, reverse derivatives. Why differentiate in reverse? Good question! Keep going and you'll find out!
How can we tell whether a series converges or diverges? How can we find the value a series converges to? There is an impressive repository of tools that can help us with these questions. Learn all about it here.
Definite_integrals_introduction
Definite integrals are a way to describe the area under a curve. Make introduction with this intriguing concept, along with its elaborate notation and various properties.
Area_arc_length_using_calculus
Become a professional area-under-curve finder! You will also learn here how integrals can be used to find lengths of curves. The tools of calculus are so versatile!
Fundamental_theorem_of_calculus
So you've learned about indefinite integrals and you've learned about definite integrals. Have you wondered what's the connection between these two concepts? You will get all the answers right here. Beware, this is pretty mind-blowing.
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