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"The book of the universe is written in the language of mathematics." Galileo wrote this four hundred years ago, even before Newton and Leibniz discovered calculus. The statement is as valid today as ever: We use functions in all the sciences, and calculus allows us to analyze the functions and draw scientific conclusions. Calculus III is a third semester calculus course for students who have previously been introduced to the basic ideas of differential and integral calculus. In this course we will take the concepts of single-variable calculus (Calc I and II) and look at their generalizations to functions of two or three variables. Topics include: - Vectors and curves in space
- Functions of several variables, partial derivatives, gradients
- Multiple integrals, different coordinate systems
- Vector calculus, theorems of Stokes and Green
The material we take up in this course has applications in physics, chemistry, biology, environmental science, astronomy, economics, statistics, and just about everything else. We want you to leave the course not only with computational ability, but with the ability to use these notions in their natural scientific contexts, and with an appreciation of their mathematical beauty and power. |