smashmath.github.io Open in urlscan Pro
2606:50c0:8002::153  Public Scan

Form analysis
0 forms found in the DOM

Text Content

Toggle navigation
 * about(current)
 * blog
 * teaching
 * 




SMASHMATH

i am a math phd student and tutor

Taylor Fisher

discord: eigentaylor

e

california CA

exp⁡(x)=∑n=0∞xnn!

math phd student, dork extraordinaire.

i like differential equations and linear algebra.

here are some math posts ive written if you want to look at them i guess

if you want to support me, i have a ko-fi.

--------------------------------------------------------------------------------

personal favorites:

 * Constant Coefficient ODEs Made Simple with Linear Operators
 * Shortcuts for Finding Eigenvalues and Eigenvectors
 * Solving systems of first-order ODEs like a baller
 * The Alpha Method (Generalized Exponential Response Formula)

--------------------------------------------------------------------------------

my research stuff:

things ive discovered independently derived. i think they’re all cool, but only
a few of them are actually useful, in my opinion.

 * Function Interpolation: a method to get a function (which is a linear
   combination of some given set of basis functions) that satisfies certain
   conditions using determinants, given that one exists and is unique. for
   example, a determinant which gives the unique lowest degree polynomial that
   passes through a certain set of points.

 * A formula for some particular solutions to certain ODEs: a determinant
   formula which gives a particular solution to any linear constant-coefficient
   ordinary differential equation which has a forcing function of exponential
   nature (ex. g(t)=tneαtcos⁡(βt)). Uses results from Function Interpolation.

 * Constructing integer systems of differential equations with integer
   solutions: methods to construct nice systems with nice solutions. useful for
   professors/textbook authors to make good lecture examples or exam problems.
   somewhat of a work in progress. i also have a post for second order systems.

 * matrix exponential stuff: i really love matrix exponentials.
   1. Matrix Exponential Formulas for 2x2 Matrices
   2. Matrix Exponentials Using Differential Equations
   3. Exponentials of Symmetric Matrices Using the Spectral Theorem
   4. Matrix Exponential Formulas for 2x2 Matrices Using Laplace Transforms
   5. Another approach to matrix exponential formulas: coming soon…
 * New Ways to Calculate Normalized Solutions to Linear Constant-Coefficient
   Differential Equations: solve just one set of n first-order initial value
   problems to get the n normalized solutions to an n-th order differential
   equation. this should be the fastest way to find them using a computer.
   alternatively, find one normalized solution and get the others recursively.


NEWS

Jun 12, 2022 back with a few new posts Dec 9, 2021 2x2 matrix exponentials post
rewritten Dec 6, 2021 updating posts to the distill theme Dec 6, 2021 i have a
twitter now which i might update maybe Dec 6, 2021 new news now


LATEST POSTS

Jul 27, 2024 Why do we row reduce? What IS a matrix? May 14, 2024 Introduction
to Least Squares Part 2 (Electric Boogaloo) Mar 23, 2024 The Wonderful World of
Projectors

best way to contact me is through discord (eigentaylor). please send a message
when adding.
© Copyright 2024 . Powered by Jekyll with al-folio theme. Hosted by GitHub
Pages. Last updated: October 09, 2024.