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# Foundations of Calculus

(University of Michigan at Ann Arbor)

### - Overview

In some sense, the prerequisite for Calculus is to have an overall comfort with algebra, geometry, and trigonometry. After all, each new topic in math builds on previous topics, which is why mastery at each stage is so important. There are some preliminaries you need to know to start learning calculus. The emphasis is on functions and graphs, the main building blocks of calculus.

Calculus is the study of how things change. It consists of two branches namely differential calculus and integral calculus. Differential calculus explains the rate of change, the slope of a curve, while integral calculus discusses the continuous summation of parts, the area under the curve. Just as summation describes the addition of discrete parts, integration explains the continuous summation of data.

Please refer to the following for more details.

### - Preliminary Concepts

Here are the most important preliminary concepts in calculus (though not exhaustive):

• Equation of functions
• Special functions
• functions and Graphs
• Derivatives and Integrals
• Minima and Maxima
• Concave or convex functions in a defined interval (saddle points)

[More to come ...]