Calculus: Understanding the mathematics of continuous change.

Calculus is the mathematical study of things that change: cars accelerating, planets moving around the sun, and economies fluctuating. To study these changing quantities, a new set of tools - calculus - was developed in the 17th century, forever altering the course of math and science.

This course sets you on the path to calculus fluency. The first part provides a firm intuitive understanding of limits, the central idea underlying the entire subject. The second part applies limits to define derivatives, an indispensable tool for measuring change. By the end of the course, you'll have practical calculus experience that any aspiring scientist, engineer, or mathematician needs.

The course will cover the system of real numbers, functions, and their graph, the limit of a function, continuity, the derivative, the geometric interpretation of the derivative, higher-order derivatives, the Mean Value Theorem, L’Hospital’s rule theorem of extreme value, applications of extreme problem, increasing and decreasing functions, concavity, inflection points, sketching the graph of functions, Taylor and Maclaurin series.

After completing this course students are required to have the ability:

CO 1. to understand the fundamental concepts of one variable calculus such as functions, limit, derivative, differential, and geometry interpretation.

CO 2. to solve the standard problems in calculus such as properties on real numbers, functions, limits, and derivatives.

CO 3. to apply the concepts of calculus to solve problems in mathematics and sciences especially related to optimization problems.

CO 4. to use limit and derivative to obtain the information about a function such as increasing or decreasing, concavity, extreme points, and inflection points, including sketching its graph.

CO 5. to determine the Taylor series and Mac-Laurin series of a function.