Calculus is the study of the infinites and the infinitesimals. Calculus is what allows us to find the rates at which variables change, the areas and volumes of complex shapes, and solve infinite summations. It models the world around us through derivatives and antiderivatives, and is used widely in physics, economics, machine learning, and many other fields - too many to name.
Calculus I
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Limits and Discontinuities
Limits are what make all of Calculus possible. They pop up over and over again throughout future lessons. -
Limit Properties
There are numerous properties for limits that make them useful and easier to calculate. Learn them here. -
Indeterminate Forms
There are seven forms that do not give enough information to solve a limit. These are known as the indeterminate forms and require more work to solve. -
e, the Universal Growth Constant
The most important number in Calculus. -
Derivatives
Derivatives measure the rate of change. They're a powerful concept that is the gateway into Calculus. -
Derivative Rules
Derivatives might be hard at first, but these rules turn calculating them into a step-by-step process. -
Derivatives of Certain Functions
There are a few functions whose derivatives frequently show up and therefore should be known by heart. -
L'Hôpital's Rule
A tool for solving limits in indeterminate forms. -
Implicit Differentiation
Implicit Differentiation is a technique that combines algebra with differentiation, and is particularly useful in finding derivatives of implicit functions. -
Antiderivatives
The inverse of a derivative. -
Antidifferentiation Rules and Methods
Despite antiderivatives being much harder to solve than derivatives, there are still numerous tricks and methods to solve them. -
The Limit Definition of an Integral
An integral is the area underneath a curve - learn how to calculate this using limits. -
Integration
There is a much easier way to calculate the area under a curve that doesn't involve solving limits or summations at all! This is known as solving an integral, and uses antidifferentiation instead.