# Study Notes

Study Notes on Math, Physics and Chemistry, and other related sciences for students in colleges and those seeking admission in graduate courses.

## Memory Methods

Memory, in human reference, is the ability to store retain and recall information when needed. Without hammering the mind in the definitions, let we look into the ten methods of boosting our memory:  1. Simple Repetition Method The classical method, very popular as in committing poems to memory by reading them over and over. 2. Full Concentration Method Concentrate on the topic content while learning. Do

## Free Online Calculus Text Books

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 Neveln http://www.cs.widener.edu/~neveln/Calcbible.pdf Lecture Notes for Applied Calculus by Karl Heinz Dovermann

## Dedekind’s Theory of Real Numbers

Intro 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 of rational numbers seems to be dense and so apparently

## Free PDF Algebra and Topology Books for Graduates

Looking for free PDF algebra and topology books online? I have gathered a list of free e-books on Algebra, Topology, and Related Mathematics. I hope it will be very helpful to all students and teachers searching for high-quality content. If any link is broken, please email me at gaurav@gauravtiwari.org. Let’s start. Abstract Algebra Online by Prof. Beachy This site contains many of the definitions and theorems from the area

## Jablonski Diagram – Consequences of Light Absorption

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. The absorption of light may result in a number of other phenomena as

## Essential Steps of Problem Solving in Mathematical Sciences

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 problem situations. You must also be good at gathering information, extracting

## Dirichlet’s Theorem and Liouville’s Extension of Dirichlet’s Theorem

Topic Beta & Gamma functions Statement of Dirichlet’s Theorem $\int \int \int_{V} x^{l-1} y^{m-1} z^{n-1} dx dy ,dz = \frac { \Gamma {(l)} \Gamma {(m)} \Gamma {(n)} }{ \Gamma{(l+m+n+1)} }$ , where V is the region given by $x \ge 0 y \ge 0 z \ge 0 x+y+z \le 1$ . Brief Theory on Gamma and Beta Functions Gamma Function If we

## The Lindemann Theory of Unimolecular Reactions

In this article we will learn about the Lindemann Theory of Unimolecular Reactions which is also known as Lindemann-Hinshelwood mechanism. It is easy to understand a bimolecular reaction on the basis of collision theory. When two molecules A and B collide, their relative kinetic energy exceeds the threshold energy with the result that the collision results in the breaking of comes and the formation of new

## Wein’s Formula & Wein’s Laws

Various workers tried to explain the problem of energy distribution in black body radiation and finally the problem was successfully solved by German Physicist Max Planck. Before him, German Physicist Wilhelm Wein and British Physicist Lord Rayleigh & James Jean have tackled this problem and have given important laws. In fact, the work of their scientists paved the way for Planck to give his famous theory

## Albert Einstein and His introduction to the Concept of Relativity

Albert Einstein This name need not be explained. Albert Einstein is considered to be one of the best physicists in the human history. The twentieth century has undoubtedly been the most significant for the advance of science, in general, and Physics, in particular. And Einstein is the most illuminated star of the 20th century. He literally created an upheaval in quick succession, in the year 1905,

## Solving Ramanujan’s Puzzling Problem

Consider a sequence of functions as follows:- $f_1 (x) = \sqrt {1+\sqrt {x} }$ $f_2 (x) = \sqrt{1+ \sqrt {1+2 \sqrt {x} } }$ $f_3 (x) = \sqrt {1+ \sqrt {1+2 \sqrt {1+3 \sqrt {x} } } }$ ……and so on to \$ f_n (x) = \sqrt {1+\sqrt{1+2 \sqrt {1+3 \sqrt {\ldots \sqrt {1+n \sqrt {x} } } } }