1Introduction

1.1Sigma Notation

We introduce a new notation for arbitrarily many terms being added together in preparation for Riemann Sums later.

1.3Antiderivative Intro

We discuss the antiderivative at a conceptual level before we dive into the mechanics.

1.4Antiderivatives of Core Functions

We develop rules to quickly determine antiderivatives of most of our core functions.

2Riemann Approximations

2.1Area under the Curve

We discuss how to approximate the area under a curve.

2.2Riemann Approximation Types

We discuss the various types of Riemann Approximation Endpoint Methods.

3The Definite Integral!

3.1Perfect Approximations!

We discuss how to approximate the area under a curve.

3.2Condensing the Notation, the Indefinite Integral!

We develop the algebraic techniques to actually compute the perfect approximation of area under the curve.

4The Indefinite Integral!

4.1Indefinite Integral

We introduce the idea of the indefinite integral - all the antiderivatives!

4.2Classes of Functions

“Indefinite Integrals are a class of functions” - What?

5Fundamental Theorem of Calculus

5.1First Theorem

We present the first fundamental theorem of calculus

5.2Second Theorem

We present the second fundamental theorem of calculus

6U-Substitution

6.1U-Substitution

We introduce the method of U-Sub as a way to unravel a chain rule.

6.2How to see a U-Sub

We give some hints and tips on how to see and predict where a U-Sub might help.

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