num_pages: 217
description: The goal of this course is for you to understand and appreciate the beautiful subject of calculus. You will see how calculus plays a fundamental role in all of science and engineering, as well as business and economics. You will learn about the 2 major ideas of calculus—the derivative and the integral. Each has a rich history and many practical applications.Calculus is often described as the mathematics of change. For instance, calculus is the mathematics of velocities, accelerations, tangent lines, slopes, areas, volumes, arc lengths, centroids, curvatures, and a variety of other concepts that have enabled scientists, engineers, and economists to model real-life situations.Although precalculus mathematics (geometry, algebra, and trigonometry) also deals with velocities, accelerations, tangent lines, slopes, and so on, there is a fundamental difference between precalculus mathematics and calculus. Precalculus mathematics is more static, whereas calculus is more dynamic.Our study of calculus will be presented in the same order as a university-level calculus course. The material is based on the 9th edition of the bestselling textbook Calculus by Ron Larson and Bruce H. Edwards (Brooks/Cole, 2010). However, any standard calculus textbooks can be used for reference and support throughout the course.Graphing calculators and computers are playing an increasing role in the mathematics classroom. Without a doubt, graphing technology can enhance the understanding of calculus, so some instances where we use graphing calculators to verify and confirm calculus results have been included.As we will see in this course, most of the applications of calculus can be modeled by the 2 major themes of calculus: the derivative and the integral. The essence of the derivative is the determination of the equation of the tangent line to a curve. On the other hand, the integral is best approached by determining the area bounded by the graph of a function.
language: English
title: Understanding Calculus: Problems, Solutions, and Tips
publisher: The Great Courses