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Oscar Nieves
Oscar Nieves

1.1K Followers

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Jul 18

Why even solvable problems are often unsolvable

Solvability is a very interesting concept in mathematics by which one can determine, using sophisticated methods of proof and analysis, whether a certain problem can be solved, be it an equation, system of equations, integral, etc. …

Mathematics

6 min read

Why even solvable problems are often unsolvable
Why even solvable problems are often unsolvable
Mathematics

6 min read


Mar 29

Solving an integral equation with a simple trick

In a paper published in 2011 by Waldemar Klobus (Motion on a vertical loop with friction) an interesting integral equation (more precisely, a Volterra integral equation of the 2nd kind) appears: which describes the motion of an object around a circular loop as shown in Fig.1 below:

Mathematics

4 min read

Solving an integral equation with a simple trick
Solving an integral equation with a simple trick
Mathematics

4 min read


Mar 26

Solving difficult integrals with substitution

Integration by substitution is a very powerful tool for evaluating integrals where the answer may not seem as obvious at first, but under appropriate variable transformations, we can obtain simple and elegant solutions. …

Mathematics

4 min read

Solving difficult integrals with substitution
Solving difficult integrals with substitution
Mathematics

4 min read


Mar 23

Cauchy’s Integral Formula

In my previous article (Contour integrals — a simple introduction) I discussed how to perform integrals of complex-valued functions in the complex plane, along a defined contour C by using techniques from line integrals on the real plane. …

Mathematics

6 min read

Cauchy’s integral formula
Cauchy’s integral formula
Mathematics

6 min read


Mar 23

Contour integrals — a simple introduction

When dealing with functions of complex variables, such as f(z) where z = x + iy, their integration with respect to z must be done in a slightly different way than integrals of real-valued functions. The techniques are usually a bit difficult for university students to pick up, especially because…

Mathematics

4 min read

Contour integrals — a simple introduction
Contour integrals — a simple introduction
Mathematics

4 min read


Feb 19

Numba: Python’s lord and savior

When it comes to high performance computing (HPC), people often think of programming languages like C/C++ or Fortran, especially in the scientific community. Some more adventurous people may even try Julia. However, almost no one ever thinks “let me write a HPC application in Python” unless they really know what…

Python

7 min read

Numba: Python’s lord and savior
Numba: Python’s lord and savior
Python

7 min read


Jan 30

Differentiating inverse functions

Functions such as arcsin(x), arccos(x), arctan(x), etc. are considered to be inverse functions of sin(x), cos(x) and tan(x) respectively. They have their own properties and as such, they have derivatives which are noticeably different from their ordinary counterparts. In my previous article: https://medium.com/@oscarnieves100/implicit-differentiation-in-a-nutshell-46031531f34b I discussed how to use implicit differentiation…

Mathematics

3 min read

Differentiating inverse functions
Differentiating inverse functions
Mathematics

3 min read


Jan 30

Implicit differentiation in a nutshell

What is implicit differentiation? When we are dealing with derivatives of functions in calculus, we often encounter functions such as y = f(x) where some variable y can be explicitly expressed as a function of an independent variable x, so the differentiation process is straight-forward, the derivative of y is…

Mathematics

5 min read

Implicit differentiation in a nutshell
Implicit differentiation in a nutshell
Mathematics

5 min read


Jan 19

Essential math for quantum mechanics

All the things you need to know. Quantum mechanics — and by extension quantum field theory — is a subfield of physics concerned with studying the dynamics of single and many-particle systems at the quantum scale, often designated as “quantum systems” which can encompass fundamental particles (e.g. quarks, leptons, bosons)…

Science

7 min read

Essential math for quantum mechanics
Essential math for quantum mechanics
Science

7 min read


Jan 19

Bivariate nonlinear regression using Python

In my previous article: https://oscarnieves100.medium.com/univariate-nonlinear-regression-in-python-deb91d1085cd, I discussed how to do nonlinear regression in Python for univariate data using the module scipy.optimize and the function curve_fit. Now, I will extend that to bivariate regression using the same technique. Unbeknownst to some people, Python’s curve_fit function can also be used for bivariate…

Data

6 min read

Bivariate nonlinear regression using Python
Bivariate nonlinear regression using Python
Data

6 min read

Oscar Nieves

Oscar Nieves

1.1K Followers

I write stories about applied math, physics and engineering.

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