This course will introduce you to the theory of functions of complex variables, which is a core area of mathematics. It is a basic tool in many mathematical theories. We will cover complex numbers and ...

“There are five fundamental operations in mathematics,” the German mathematician Martin Eichler supposedly said. “Addition, subtraction, multiplication, division and modular forms.” Part of the joke, ...

Trigonometric identities are powerful tools for simplifying complex equations in math and science. Three core groups—reciprocal, quotient, and Pythagorean—form the foundation. Effective strategies ...

You can probably think of a time when you’ve used math to solve an everyday problem, such as calculating a tip at a restaurant or determining the square footage of a room. But what role does math play ...

Now, on to the subject of complex numbers. We have stayed away from this subject until now simply because we did not want to confuse things. Initially, it is easy to think of signals as “real valued.” ...

Analytic functions, also known as holomorphic functions, form the cornerstone of complex analysis, widely studied for their elegant properties and deep connections in both pure and applied mathematics ...