Calculus: Single Variable Part 3 - Integration

Integrating Differential Equations
-Our first look at integrals will be motivated by differential equations. Describing how things evolve over time leads naturally to anti-differentiation, and we'll see a new application for derivatives in the form of stability criteria for equilibrium solutions.

Techniques of Integration
-Since indefinite integrals are really anti-derivatives, it makes sense that the rules for integration are inverses of the rules for differentiation. Using this perspective, we will learn the most basic and important integration techniques.

The Fundamental Theorem of Integral Calculus
-Indefinite integrals are just half the story: the other half concerns definite integrals, thought of as limits of sums. The all-important *FTIC* [Fundamental Theorem of Integral Calculus] provides a bridge between the definite and indefinite worlds, and permits the power of integration techniques to bear on applications of definite integrals.

Dealing with Difficult Integrals
-The simple story we have presented is, well, simple. In the real world, integrals are not always so well-behaved. This last module will survey what things can go wrong and how to overcome these complications. Once again, we find the language of big-O to be an ever-present help in time of need.