Calculus is the study of change and motion, in the same way that geometry is the study of shape and algebra is the study of rules of operations and relations. It is the culmination of algebra, geometry, and trigonometry, which makes it the next step in a logical progression of mathematics.
Calculus defines and deals with limits, derivatives, and integrals of functions. The key ingredient in calculus is the notion of infinity. The essential link to completing calculus and satisfying concerns about infinite behavior is the concept of the limit, which lays the foundation for both derivatives and integrals.
Calculus is often divided into two sections: Differential Calculus (dealing with derivatives, e.g. rates of change and tangents), and Integral Calculus (dealing with integrals, e.g. areas and volumes). Differential Calculus and Integral Calculus are closely related as we will see in subsequent pages. It is important to have a conceptual idea of what calculus is and why it is important in order to understand how calculus works.
Main Lesson: Brief History of Calculus
A brief history of the invention of calculus and its development.
Main Lesson: Difference Between Calculus and Other Mathematics
A comparison of calculus against other mathematical disciplines.
Main Lesson: Calculus Applications in Algebra and Geometry
Read about how calculus advances algebra and geometry.
Main Lesson: Real Life Applications of Calculus
Some examples of real life applications using calculus.