21-117: Integration and Differential Equations

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Instructor and TA's

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This course is a continuation of the ideas in 21-115 Differential Calculus and 21-116 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.