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Mathematics

Calculus

Calculus Basics

Calculus Theorems

Calculus Review of Trigonometric Identities

Calculus Symbols and Notations

Chain Rule Variations

Conic Sections and Quadratic Equations

Implicit Differentiation

Hyperbolic Functions

Infinite Series Convergence Tests

Laplace Transforms

Partial Derivatives

Parametric Equations

Polar Coordinates and Graphs

Taylor and Maclaurin Series

Stokes' Theorem and Surface Integrals

Laplace Transforms

Flashcards

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Ramp Function, $t \cdot u(t)$

$\frac{1}{s^2}$

Sine function, $\sin(\omega t)$

$\frac{\omega}{s^2 + \omega^2}$

Unit impulse, $\delta(t)$

$\cosh(at)$

$\frac{s}{s^2 - a^2}$

$\sinh(at)$

$\frac{a}{s^2 - a^2}$

Heaviside step function, $u(t)$

$\frac{1}{s}$

Exponential decay, $e^{-at}$

$\frac{1}{s+a}$

$e^{at} \sin(\omega t)$

$\frac{\omega}{(s-a)^2 + \omega^2}$

Cosine function, $\cos(\omega t)$

$\frac{s}{s^2 + \omega^2}$

Natural logarithm, $\ln(t)$

$-\frac{\ln(s) + \gamma}{s}$ where $\gamma$ is the Euler-Mascheroni constant.

$\frac{1}{s^2}$

$\delta'(t)$ , the derivative of the unit impulse

$s$

$\frac{1}{t}$

$-\ln(s)$

$t^n$ where $n$ is a positive integer

$\frac{n!}{s^{n+1}}$

$e^{at} \cos(\omega t)$

$\frac{s-a}{(s-a)^2 + \omega^2}$

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