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Mathematics

Calculus

Calculus Theorems

Calculus Review of Trigonometric Identities

Calculus Symbols and Notations

Chain Rule Variations

Calculus Basics

Conic Sections and Quadratic Equations

Implicit Differentiation

Hyperbolic Functions

Infinite Series Convergence Tests

Laplace Transforms

Parametric Equations

Partial Derivatives

Polar Coordinates and Graphs

Stokes' Theorem and Surface Integrals

Taylor and Maclaurin Series

Laplace Transforms

Flashcards

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Heaviside step function, $u(t)$

$\frac{1}{s}$

Exponential decay, $e^{-at}$

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

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

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

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.

Unit impulse, $\delta(t)$

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

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

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

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

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

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

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

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

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

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

$s$

$\frac{1}{t}$

$-\ln(s)$

$\sinh(at)$

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

$\cosh(at)$

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

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