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Introductory Ideas

If you can, start your study of Calculus with this Chapter: we immediately begin using introductory ideas in Calculus so you can get a sense for what Calculus is about before you dive more deeply into developing the key tools. On the very first screen you’ll be doing Calculus calculations, based on the reasoning-skills you already have. From there we’ll develop one of the most important uses of Calculus, linear approximations, and introduce “differentials.”

We’ll also focus on “average rate of change,” as applied to various scenarios and over different intervals. We’ll then extend to develop first estimates of the instantaneous rate at which a function changes at a given input value, which will lead to the fundamental challenge Calculus is designed to address.

Let’s get started!