Weierstrass introduced the idea that there exist functions that are continuous for every value of $x$ but do not possess a derivative at any value of $x$. We now consider the celebrated Weierstrass function, which exhibits this property. In this note, I will demonstrate that such a function exists using Weierstrass’s construction. The Weierstrass Function…
Memory is the human ability to store, retain, and recall information when needed. Instead of getting lost in technical definitions, let’s explore ten practical methods to enhance your memory: 1. Simple Repetition Method This classical method is widely used for memorizing poems or any text by reading it repeatedly. The more you read, the more…
In this list, I have collected all useful and important free online calculus textbooks, mostly in downloadable pdf format. Feel free to download and use these. Elementary Calculus : An approach using infinitesimals by H. J. Keisler https://www.math.wisc.edu/~keisler/keislercalc-12-23-18.pdf Multivariable Calculus by Jim Herod and George Cain http://people.math.gatech.edu/~cain/notes/calculus.html Calculus by Gilbert Strang http://ocw.mit.edu/ans7870/textbooks/Strang/strangtext.htm Calculus Bible by…
Let $ \mathbf{Q}$ be the set of rational numbers. It is well known that $ \mathbf{Q}$ is an ordered field and also the set $ \mathbf{Q}$ is equipped with a relation called “less than” which is an order relation. Between two rational numbers there exists an infinite number of elements of $ \mathbf{Q}$. Thus, the system…
Looking for Free Algebra and Topology PDF E-books? I’ve compiled a comprehensive list of high-quality, free e-books covering Algebra, Topology, and other related mathematics topics. These resources are ideal for both students and teachers seeking valuable content for their studies or teaching. Download these now and enhance your learning experience! Let’s start. Abstract Algebra Online by…
In this article, we will formulate the D’ Alembert’s Ratio Test on convergence of a series. Let’s start. Statement of D’Alembert Ratio Test A series $ \sum {u_n}$ of positive terms is convergent if from and after some fixed term $ \dfrac {u_{n+1}} {u_n} < r < {1} $ , where r is a fixed…
All about the Light Absorption’s theory on the basis of Jablonski diagram. According to the Grotthus – Draper Law of photo-chemical activation: Only that light which is absorbed by a system, can bring a photo-chemical change. However it is not true that all the kind of light(s) that are absorbed could bring a photo-chemical change.…
Problem solving is more than just finding answers. Learning how to solve problems in mathematics is simply to know what to look for. Mathematics problems often require established procedures. To become a problem solver, one must know What, When and How to apply them. To identify procedures, you have to be familiar with the different…
I was reading a book on ancient mathematics problems from Indian mathematicians. Here I wish to share one problem from Bhaskaracharya‘s famous creation Lilavati. Who was Bhaskaracharya? Bhaskara II, who is popularly known as Bhaskaracharya, was an Indian mathematician and astronomer from the 12th century. He’s especially known for the discovery of the fundamentals of…
Henry Poincaré was trying to save the Old classical theory of Physics by Suitable Adjustments & Modifications in it. When the experiments, like Michelson Morley Experiment, in search of the ether drift failed, it began to be increasingly realized that there was no such thing as an absolute or privileged frame of reference and that…
The Collatz Conjecture is one of the Unsolved problems in mathematics, especially in Number Theory. The Collatz Conjecture is also termed as 3n+1 conjecture, Ulam Conjecture, Kakutani’s Problem, Thwaites Conjecture, Hasse’s Algorithm, and Syracuse Problem. Collatz Conjecture Statement If you keep repeating this procedure, you shall reach the number 1 at last. Illustrations » Starting…
Topic: Beta & Gamma functions The Gamma function and Beta functions belong to the category of special transcendental functions and are defined in terms of improper definite integrals. Definitions of Beta and Gamma functions are given below. But before that, let’s quote the statement of Dirichlet’s theorem so that we can work around Liouville’s extension…
