- Topics At a Glance
- Indefinite Integrals Introduction
- Integration by Substitution: Indefinite Integrals
- Legrange (Prime) Notation
- Leibniz (Fraction) Notation
- Integration by Substitution: Definite Integrals
- Integration by Parts: Indefinite Integrals
- Some Tricks
- Integration by Parts: Definite Integrals
- Integration by Partial Fractions
- Integrating Definite Integrals
- Choosing an Integration Method
- Integration by Substitution
- Integration by Parts
- Integration by Partial Fractions
- Thinking Backwards
- Improper Integrals
- Badly Behaved Limits
- Badly Behaved Functions
- Badly Behaved Everything
- Comparing Improper Integrals
- The
*p*-Test - Finite and Infinite Areas
- Comparison with Formulas
**In the Real World****I Like Abstract Stuff; Why Should I Care?**- How to Solve a Math Problem

Limits are something the human race (at least, the mathematicians) have created as a result of trying to find a way to think about infinity.

Another way of thinking about infinity involves things called **infinitesimals**. An infinitesimal is a number that's bigger than 0, but smaller than all normal everyday fractions. If ε is an infinitestimal, then

...

...

and yet,

0 < ε.

This website has a great discussion of limits and infinitesimals.