Why even solvable problems are often unsolvableSolvability is a very interesting concept in mathematics by which one can determine, using sophisticated methods of proof and analysis…Jul 18, 20233Jul 18, 20233
Solving an integral equation with a simple trickIn a paper published in 2011 by Waldemar Klobus (Motion on a vertical loop with friction) an interesting integral equation (more precisely…Mar 29, 2023Mar 29, 2023
Solving difficult integrals with substitutionIntegration by substitution is a very powerful tool for evaluating integrals where the answer may not seem as obvious at first, but under…Mar 26, 20231Mar 26, 20231
Published inCantor’s ParadiseCauchy’s integral formulaIn my previous article (Contour integrals — a simple introduction) I discussed how to perform integrals of complex-valued functions in the…Mar 23, 2023Mar 23, 2023
Contour integrals — a simple introductionWhen 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…Mar 23, 20233Mar 23, 20233
Numba: Python’s lord and saviorWhen it comes to high performance computing (HPC), people often think of programming languages like C/C++ or Fortran, especially in the…Feb 19, 20233Feb 19, 20233
Differentiating inverse functionsFunctions such as arcsin(x), arccos(x), arctan(x), etc. are considered to be inverse functions of sin(x), cos(x) and tan(x) respectively…Jan 30, 2023Jan 30, 2023
Implicit differentiation in a nutshellWhat is implicit differentiation? When we are dealing with derivatives of functions in calculus, we often encounter functions such as y =…Jan 30, 20231Jan 30, 20231
Bivariate nonlinear regression using PythonIn my previous article: https://oscarnieves100.medium.com/univariate-nonlinear-regression-in-python-deb91d1085cd, I discussed how to do…Jan 19, 2023Jan 19, 2023
Univariate nonlinear regression in PythonRegression analysis is an area of statistics and data science which is used extensively for finding relationships between independent and…Jan 19, 2023Jan 19, 2023
Functional equations: what are they?Most people have heard of algebraic equations, such asJan 10, 2023Jan 10, 2023
Why is physics so difficult to learn?This is a question that a lot of people ask, and I think we can all relate to it. Even as a theoretical physicist, I find myself puzzled…Jan 10, 2023Jan 10, 2023
Combinatorics: the bare minimumCombinatorics is the field of mathematics that deals with counting things, and has a wide range of applications in areas such as…Jan 10, 20231Jan 10, 20231
A seemingly hard, yet simple integralWhen it comes to strange-looking integrals, one must always ask the question: “is it really as strange as it appears to be?”, and then…Jan 6, 20231Jan 6, 20231
What are superconductors and how do they work?A superconductor is a material that can conduct electricity with zero resistance. This may sound strange if you have any basic…Jan 4, 2023Jan 4, 2023
Can the equation sin(x) = 2 be solved?When it comes to solving trigonometric equations, we need to always remember that functions like sin(x) or cos(x) are periodic and as such…Jan 4, 20233Jan 4, 20233
What is the value of i^i?A seemingly difficult number to evaluate, turns out to be quite simple. Recall from Euler’s formula that:Jan 2, 2023Jan 2, 2023
Published inCantor’s ParadiseRotating stuff using imaginary numbersComplex numbers are used frequently in math, science and engineering to model systems that are in a way associated with rotations or…Jan 2, 20231Jan 2, 20231
Why is the variance equal to E[X²] — E²[X] ?In statistics and probability theory, we use the variance of a random variable X, denoted as Var(X), to quantify how large the deviations…Dec 29, 20221Dec 29, 20221
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