18.04 | Spring 2018 | Undergraduate

Complex Variables with Applications

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 …
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.
Learning Resource Types
Exams with Solutions
Lecture Notes
Recitation Notes
Problem Sets with Solutions
A color rectangle with grids on the left and color parabolas on the right.
In the figure above, f(z) = maps the first two quadrants to the entire plane. (Image courtesy of Jeremy Orloff.)