Calculus is the mathematics that deals with nonlinear phenomena, which is to say almost everything. It gets its start from the observation that complexity often reveals itself primarily over long time intervals or large distances. On the short term, and for small variable changes, the world is simpler because it is approximately linear. How can you find a good linear approximation? How can you knit together simple local behavior into a more complicated global picture? These two questions are answered by the twin halves of calculus: differentiation and integration (including differential equations). In the 21st century computing is an essential element in all aspects of mathematics.
This course is for students who have had some calculus who want to include some review along with new material. The topics are
- Functions for modeling, including 2 and 3 variable functions
- Differentiation, including partial derivatives
- Approximation and optimization, including the method of Lagrange mulitipliers for constrained optimization
- Integration, including double integration over rectangles
- Differential equations, including the logistic equation
- Introduction to Mathematica for calculus