differential equations The Alpha Method (Generalized Exponential Response Formula) Easy particular solutions to nonhomoegenous constant coefficient linear differential equations with simple exponential/trigonometric forcing functions. Series Solutions Done Quick the fast way to do series solutions. no reindexing required. Tricks for Remembering Laplace Transforms for students and people who forgot Easily Solving Autonomous IVPs Off the Origin Easily solving linear homogeneous constant coefficient initial problems when the initial point is not t=0 Solving Multiple Initial Value Problems with Normalized Solutions Solve one, solve them all. Exact Equations Done Quick speedrun WR New Ways to Calculate Normalized Solutions to Linear Constant-Coefficient Differential Equations The fastest way for a computer, and a fast way by hand. Integrating Factors Explained the most common way to solve first order linear ODE's Linear Differential Equation Interpolation Linear Differential Equations with desired solutions using determinants. Variation of Parameters Using Linear Algebra linear is best frend :) A Formula for Some Particular Solutions Yet another obnoxious formula for solutions to constant coefficient nonhomogeneous ODE's with common forcing functions. systems of differential equations Solving systems of first-order ODEs like a baller some ballin' tips and tricks Matrix Exponential Formulas for 2x2 Matrices Who needs eigenvectors? Implicit Solutions to 2x2 Systems of First-Order Homogeneous Linear Differential Equations Implicit and explicit solutions for all cases. Constructing Systems of Nonlinear First-Order Differential Equations to Model Population Dynamics Build a system with desired behavior. Matrix Exponentials Using Differential Equations ok Solving Second Order Systems of Differential Equations ye Intro To Solving Systems of First Order Differential Equations An attempt at an intuitive derivation linear algebra Shortcuts for Finding Eigenvalues and Eigenvectors Bodacious Column and Row Perspective How to simplify matrix multiplication with the best perspectives (and also find certain inverse matrices fast!) Skew-Symmetric Matrices Are Cool top 10 things YOU didn't know about real skew-symmetric matrices!!! (GONE WRONG) (COPS CALLED) Constructing 2x2 Markov Matrices Build a Markov Chain with desired behavior. Polynomial Interpolation Making your own custom polynomial. Function Interpolation Find a function that matches your requirements Bases for the fundamental spaces of a matrix a lot of students struggle with this so here. row space, column space, null space, and left null space. Bases for the fundamental spaces of a matrix a lot of students struggle with this so here. row space, column space, null space, and left null space. Change of Basis the most confusing thing in linear algebra (don't @ me) Introduction to Least Squares How to find the best solution for an inconsistent system A Different Perspective of Diagonalization An (atttempt at an) intuitive approach to similar matrix decomposition. Exponentials of Symmetric Matrices Using the Spectral Theorem yeah Eigendecomposition of Real Matrices with Complex Eigenvalues An attempt at an intuitive derivation. calculus Introduction to Euler's Formula the best formula Skipping Integration by Parts Using Euler's Formula skip or simplify integrals involving trig functions multiplied by exponentials Finding Taylor Series of Polynomials Using Synthetic Division Wait you can do that? YUP works in progress Constructing Integer 2x2 First Order Systems of Differential Equations with Integer Solutions Nice solutions? Nice. Constructing Integer 2x2 Second Order Systems of Differential Equations with Integer Solutions It's a lot messier. Systems of Linear Difference Equations Like systems of ODEs, but discrete 👀 archive Matrix Exponential Formulas for 2x2 Matrices Using Laplace Transforms this has been rewritten 2x2 Matrix Exponential Formulas with Differential Equations