Linearization is a way to approximate a non-linear function around a point. In the blog post, I’ll show an implementation of best linearization of an equation around a point using Newton-raphson method. Before proceeding further, please note the following.
Newton raphson is better suited for monotonic functions or in the regions where monotonic behaviour is seen.
This post is meant as an introduction into a simple graphical optimization problem using Python. Consider a simply supported (Euler) beam of uniform rectangular cross section. The objective is to minimize the weight of the beam. Breadth (b) and depth (d) are variable.
My primary use case of ffmpeg had been to reduce the size of the downloaded online lectures. The output format did not actually matter for those videos as it seemed that the humongous file size of Powerpoint screen recording seems to be due to absence of proper encoding (not sure though).
Seaborn is a high level visualisation tool built on top of matplotlib which enables us to work with dataframes easily. We will try to make use of this Automobile dataset and try to gain some information with the help of seaborn plots. This post will be an exploratory one.
The Finite Element Method (FEM) is a mathematical tool using for solving differential equations. It has been popularly used (also, initially developed) for solving elastostatics problems which is to find the displacement $u$ such that, $$ \sigma_{ij,j} + f_i = 0 \text{ in the domain }\Omega $$ To solve this, the domain $\Omega$ is split into finite sub domains $\Omega_e$ in which the solution $u$ is (usually) approximated by a polynomial of certain order which is governed by the regularity requirements of the weak form of above PDE.