Calculus is a discipline in mathematics that includes the study of limits, derivatives, integrals and infinite series. Calculus 1 involves two major branches, Differential Calculus and Integral Calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of equations.

Calculus 1 videos include the following topics:

1. Test Yourself

   This subject begins with a refresher topic that can be used to diagnose any weak areas used in Caluclus. This topic includes sections about basic mathematics; real numbers; the cartesian plane; and about lines.

2. Functions and Limits

   The first area to explore is that involving various functions and the limits of functions. We start by exploring various functions and their graphs. Afterward, we refresh our knowledge of trigonometric functions and of setting up functions. We then investigate the notion of a limit of a function at a point; theorems on limits; limits that involve infinitity; and continuity.

3. The Derivative

   In this section, we completely explore the concept of the derivative of a function. We start with the geometric interpretation of the derivative such as the rate of change of a function, tangent to a graph, and instanteous velocity. We explore how to find derivatives using the basic definition and then improving finding derivatives using the power and sum, product, quotient, chain, and extended power rules. We explore finding derivatives of trigonometric functions and higher order derivatives. We continue our investigation using implicit differentiation, finding differentials and linear approximation and using Newton's Method for finding derivatives numerically.

4. Applications of the Derivative

   We next focus our attention on applications of the derivative. We invistigate the idea of rectilinear motion and the derivative; related rates; extrema of functions; using Rolles Theorem and the Mean Value Thorem; Graphing using the first derivative and the second derivative and further applications of extrema including applications of the derivative in economics.

5. The Integral

   With a firm foundation of the derivative, we next explore the idea of the antiderivatives which leads to integration. In this topic, we explore finding antiderivatives, evaluating indefinate integrals and using u-substitutions; exploring sigma notation; finding areas under graphs; exploring the Fundamental Theorem of Calculus by exploring definate integrals and the definition of a definite integral. Further, we explore properties of the definite integrals and explore approximate integration using the midpoint, trapezoidal and Simpson's rules.

6. Applications of the Integral

   Similar to applications of the derivative, we explore how integrals can be used. Sections in this topic include finding area and areas bounded by two graphs; volumes by slicing and by revolution; arc length; surfaces of reolution; average value of a function and the Mean Value Theorem for Integrals; rectilinear motion and the integral; work; liquid pressure and force; centers of mass; and the applications to Biology and Business.