Module 2 provides a basic introduction to the topology of the complex plane followed by an introduction to sequences, series and power series. Most of this theory lifts from the real case. Module 3 covers the basic theorems of the subject. The concept of a path integral is central. Weierstrass in particular developed the theory of complex functions but use of complex variable technique was widespread among 19th century mathematicians, physicists and engineers-many of this era combined the roles.
Some terminology derives from electricity and magnetism.
Fourier series, for 2 p periodic functions. Odd and even functions. Fourier's Theorem stated. Application of Fourier series to the summation of series. Extension to Fourier series of functions of arbitrary period.