# Calculus

The word Calculus comes from Latin meaning "small stone",

Because it is like understanding something by looking at small pieces.

**Differential Calculus** cuts something into small pieces to find how it changes.

**Integral Calculus** joins (integrates) the small pieces together to find how much there is.

Read Introduction to Calculus or *"how fast right now?"*

## Limits

Limits are all about approaching. Sometimes you can't work something out directly, but you **can** see what it should be as you get closer and closer!

- Introduction to Limits
- Limits and Infinity
- Evaluating Limits
- Limits (Formal Definition)
- L'Hôpital's Rule

## Derivatives (Differential Calculus)

The Derivative is the "rate of change" or slope of a function.

- Introduction to Derivatives
- Slope of a Function at a Point (Interactive)
- Derivatives as dy/dx
- Derivative Plotter (Interactive)
- Derivative Rules
- Power Rule
- Product Rule
- Second Derivative and Second Derivative Animation
- Partial Derivatives
- Differentiable
- Finding Maxima and Minima using Derivatives
- Concave Upwards and Downwards and Inflection Points
- Implicit Differentiation
- Taylor Series (uses derivatives)
- (Advanced) Proof of the Derivatives of sin, cos and tan

## Integration (Integral Calculus)

Integration can be used to find areas, volumes, central points and many useful things.

- Introduction to Integration
- Graphical Intro to Derivatives and Integrals
- Integration Rules
- Integration by Parts
- Integration by Substitution
- Definite Integrals
- Arc Length
- Integral Approximations
- Integral Approximations Calculator and Graph
- Solids of Revolution by Disks and Washers
- Solids of Revolution by Shells
- Fourier Series and Fourier Series Grapher

## Differential Equations

In our world things change, and **describing how they change** often ends up as a Differential Equation: an equation with a **function** and one or more of its **derivatives**:

- Introduction to Differential Equations
- Differential Equations Solution Guide
- Separation of Variables
- First Order Linear Differential Equations
- Homogeneous Differential Equations (Homogeneous Functions)
- The Bernoulli Differential Equation
- Exact Equations and Integrating Factors

Second Order Differential Equations:

- Second Order Differential Equations
- The Method of Undetermined Coefficients
- The Method of Variation of Parameters

If you want more Calculus topics covered, let me know which ones.

### Bonus Topic