Hello World Example of Web-Controlled LED

Introduction In this post we will demonstrate a minimal example of interfacing ESP8266 with an... Read more

Getting started with ESP8266 using the Arduino IDE

Introduction In an earlier earlier post we saw how to get started with ESP8266 on a NodeMCU bo... Read more

Getting started with ESP8266 using MicroPython

Introduction [image] Microcontrollers sit between the abstract world of bytes and the real worl... Read more

Approximating the Gaussian with simpler bell curves

Introduction Can a Gaussian function be approximated with a set of simpler functions? This is ... Read more

Solving definite integrals with Plancherel's theorem

The Fourier transform The Fourier transform tells us that any signal can be represented in tim... Read more

Differentiation under the integral sign

Introduction Surely you’re joking, Mr Feynman! brought differentiation under the integral sign... Read more

Proving the special cases of the Central Limit Theorem

Introduction The Central Limit Theorem (CLT) states that the distribution of the average value... Read more

Laplace's method

Laplace’s method is a general technique for approximating functions of the form $g(x) = e^{M f(... Read more

Factorial and Stirling's approximation

Solving problems by generalization Expanding the scope of a problem can sometimes be a crucial... Read more

Introducing constrained optimization through two simple examples

Optimization is all around us. Various physical entities are constantly solving some form of opti... Read more

Introduction to Calculus of Variations

Calculus of variations (COV) sits in the gap between calculus and optimization. In regular calcul... Read more