
Description
This course is a continuation of the ideas in 21115 Differential Calculus
and 21116 Integral Calculus. These courses introduce the ideas of
differentiation and integration, respectively.
The first half of the course extends the range of functions for which we can
compute integrals. We introduce three new techniques for use in different
situations.
When combined with the Method of Substitution and Integration by Parts, these
techniques allow us to integrate a wide variety of functions.
The second half of the course will be an introduction to differential
equations, i.e. equations that involve the derivative of a function.
Determining the original function generally involves computing an integral.
Differential equations are ubiquitous in the natural sciences and social
sciences, because they are useful in modeling the behavior of systems
over time. We will discuss how to write a mathematical model for a physical
system, and also how to compute solutions for two fundamental types of
equations.
