Implementations of the following numerical integration techniques are given below: Left-hand Riemann sum, Right-hand Riemann sum, Midpoint Rule, Trapezoid Rule, and Simpson's Rule. Modify and evaluate ...

One of the most significant of these questions is the Riemann hypothesis. At its core, the Riemann hypothesis seeks to find and study the pattern and distribution of prime numbers as they get larger ...

A first course in theory of analytic functions of one complex variable: complex differentiability and the Cauchy-Riemann equations, Cauchy Integral Theorem and Cauchy Integral Formula, Taylor and ...

It explores how integrals may be calculated or transformed by a variety of manipulations, and how they may be applied to the solution of differential equations. This aim is achieved by studying the ...

Complex number, Argand plane, derivatives of complex numbers, limits and continuity, derivative and Cauchy Riemann conditions, analytic functions, integration in the complex plane, Cauchy's integral ...

Eur. Math. Soc. (JEMS) 19 (2017), no. 3, 659--723. A Riemann singularity theorem for integral curves, with Jesse Kass, Amer. J. Math. 134 (2012), no. 5, 1143--1165. The moduli space of cubic ...