Complex Variables with Applications

A color rectangle with grids on the left and color parabolas on the right.

In the figure above, f(z) = z2 maps the first two quadrants to the entire plane. (Image courtesy of Jeremy Orloff.)


MIT Course Number


As Taught In

Spring 2018



Cite This Course

Course Description

Course Features

Course Description

Complex analysis is a basic tool with a great many practical applications to the solution of physical problems. It revolves around complex analytic functions—functions that have a complex derivative. Unlike calculus using real variables, the mere existence of a complex derivative has strong implications for the properties of the function. Applications reviewed in this class include harmonic functions, two dimensional fluid flow, easy methods for computing (seemingly) hard integrals, Laplace transforms, and Fourier transforms with applications to engineering and physics.

Other Versions

Other OCW Versions

OCW has published multiple versions of this subject. Question_OVT logo

Archived versions: Question_avt logo

Related Content

Jeremy Orloff. 18.04 Complex Variables with Applications . Spring 2018. Massachusetts Institute of Technology: MIT OpenCourseWare, License: Creative Commons BY-NC-SA.

For more information about using these materials and the Creative Commons license, see our Terms of Use.