Franklyandjournal.wordpress.com Website Review

a site concerning various topics in mathematics, physics and chemistry. posts are usually in a casual 'textbook' format. and the subjects pertaining this blog are often at an undergraduate level. therefore, we are not just limited to our ‘standard’ definition of distance to define a metric space. as long as our ‘distance’ function satisfies the above properties, we can conclude our set is a metric space. an easy starting example is in fact our ‘standard’ three listed properties. the absolute value of any value is always greater than or equal to zero so property 1 is met. we can only get a property four is the infamous ‘triangle-inequality’, which can be proved by using the cauchy-schwarz inequality.  let us consider a more unconventional metric space. consider the finite collection of metric spaces: and so the fourth property is satisfied. therefore, this is a metric space. let us try to remove the abstraction and define our distance this is interesting compared to our ‘standard’ euclidean definition of distance, denoted by nevertheless, there may be some informalities and may not follow an obvious order in which information may be presented. i will be completely honest, i have never expected anyone to read these papers let alone anyone relying on them. these little guides primarily serve as notes for me and writing them helps me consolidate the content a bit better. > a brief introductory quantum mechanics guide that begins with the > wave function and finishes with the schrödinger equation. (last > primarily an application and exercise for multivariable calculus > that attempts to derive the four maxwell equations from mostly > introduction to the permutation group and covers composition of > permutations, cycle notation and finishes with dihedral groups. > a derivation of the heat equation from topics covered in > multivariable calculus and the intuition behind it. (last edited