MATH 115-01/02, Applied Calculus, Spring 2012

Abstract

This is a one-semester introduction to di erentiation and integration from the perspective of applied mathematics, as well as the many applications of these ideas in the physical, life, and social sciences. While most of this course is de- voted to calculus of functions of a single independent variable, some attention is paid to functions of several variables. The goals of this class do include learning the mechanics and formalism of di erential and integral calculus; however, our primary goal is that you to learn how to apply the mathematics of calculus to model physical phenomena and solve related problems. The eld of Applied Mathematics is very di erent than the mathematics you may have studied in other courses. Though there may be some overlap, this course will have little in common with a high school calculus class. By its very nature, Applied Mathematics cannot be learned by doing drill exercises from a textbook, or by using pencil and paper to solve problems; applied mathematicians are interested in being able to understand and perform direct computations that arise in applications, not canned problems used to illustrate ideas. For this reason, this course will involve using the software package Mathematica. Learning to use such a software package is a major part of learning Applied Mathematics. Mathematica is not to be considered a tool to learn the book material; rather, it is a way of doing mathematics. The primary objective of this course is that you learn this way of doing mathematics. For this reason, you are strongly encouraged to seriously approach learning Mathematica as a major goal for this course.