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[Skip to main content](https://www.khanacademy.org/math/differential-equations/laplace-transform#main-content) If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains \*.kastatic.org and \*.kasandbox.org are unblocked. Explore Select a category to view its courses Search Donate [Log in](https://www.khanacademy.org/login?continue=%2Fmath%2Fdifferential-equations%2Flaplace-transform)[Sign up](https://www.khanacademy.org/signup?continue=%2Fmath%2Fdifferential-equations%2Flaplace-transform) [Search for courses, skills, and videos](https://www.khanacademy.org/search) ## Welcome to Khan Academy\! So we can give you the right tools, let us know if you're a... Learner Teacher Parent [Differential equations3 units · 8 skills](https://www.khanacademy.org/math/differential-equations) [Unit 1First order differential equations](https://www.khanacademy.org/math/differential-equations/first-order-differential-equations) [Unit 2Second order linear equations](https://www.khanacademy.org/math/differential-equations/second-order-differential-equations) [Unit 3Laplace transform](https://www.khanacademy.org/math/differential-equations/laplace-transform) 1. [Math](https://www.khanacademy.org/math) 2. [Differential equations](https://www.khanacademy.org/math/differential-equations) # Unit 3: Laplace transform ## About this unit The Laplace transform is a mathematical technique that changes a function of time into a function in the frequency domain. If we transform both sides of a differential equation, the resulting equation is often something we can solve with algebraic methods. ## [Laplace transform](https://www.khanacademy.org/math/differential-equations/laplace-transform/laplace-transform-tutorial/v/laplace-transform-1) ### Learn - [Laplace transform 1 (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/laplace-transform-tutorial/v/laplace-transform-1) - [Laplace transform 2 (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/laplace-transform-tutorial/v/laplace-transform-2) - [L{sin(at)} - transform of sin(at) (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/laplace-transform-tutorial/v/laplace-transform-3-l-sin-at) - [Part 2 of the transform of the sin(at) (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/laplace-transform-tutorial/v/laplace-transform-4) ## [Properties of the Laplace transform](https://www.khanacademy.org/math/differential-equations/laplace-transform/properties-of-laplace-transform/v/laplace-transform-5) ### Learn - [Laplace as linear operator and Laplace of derivatives (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/properties-of-laplace-transform/v/laplace-transform-5) - [Laplace transform of cos t and polynomials (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/properties-of-laplace-transform/v/laplace-transform-6) - ["Shifting" transform by multiplying function by exponential (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/properties-of-laplace-transform/v/more-laplace-transform-tools) - [Laplace transform of t: L{t} (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/properties-of-laplace-transform/v/laplace-transform-of-l-t) - [Laplace transform of t^n: L{t^n} (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/properties-of-laplace-transform/v/laplace-transform-of-t-n-l-t-n) - [Laplace transform of the unit step function (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/properties-of-laplace-transform/v/laplace-transform-of-the-unit-step-function) - [Inverse Laplace examples (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/properties-of-laplace-transform/v/inverse-laplace-examples) - [Dirac delta function (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/properties-of-laplace-transform/v/dirac-delta-function) - [Laplace transform of the dirac delta function (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/properties-of-laplace-transform/v/laplace-transform-of-the-dirac-delta-function) ## [Laplace transform to solve a differential equation](https://www.khanacademy.org/math/differential-equations/laplace-transform/laplace-transform-to-solve-differential-equation/v/laplace-transform-to-solve-an-equation) ### Learn - [Laplace transform to solve an equation (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/laplace-transform-to-solve-differential-equation/v/laplace-transform-to-solve-an-equation) - [Laplace transform solves an equation 2 (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/laplace-transform-to-solve-differential-equation/v/laplace-transform-solves-an-equation-2) - [Using the Laplace transform to solve a nonhomogeneous eq (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/laplace-transform-to-solve-differential-equation/v/using-the-laplace-transform-to-solve-a-nonhomogenous-eq) - [Laplace/step function differential equation (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/laplace-transform-to-solve-differential-equation/v/laplace-step-function-differential-equation) ## [The convolution integral](https://www.khanacademy.org/math/differential-equations/laplace-transform/convolution-integral/v/introduction-to-the-convolution) ### Learn - [Introduction to the convolution (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/convolution-integral/v/introduction-to-the-convolution) - [The convolution and the Laplace transform (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/convolution-integral/v/the-convolution-and-the-laplace-transform) - [Using the convolution theorem to solve an initial value prob (Opens a modal)](https://www.khanacademy.org/math/differential-equations/laplace-transform/convolution-integral/v/using-the-convolution-theorem-to-solve-an-initial-value-prob) Our mission is to provide a free, world-class education to anyone, anywhere. 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If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains \*.kastatic.org and \*.kasandbox.org are unblocked. Select a category to view its courses ## Welcome to Khan Academy\! So we can give you the right tools, let us know if you're a... About this unit The Laplace transform is a mathematical technique that changes a function of time into a function in the frequency domain. If we transform both sides of a differential equation, the resulting equation is often something we can solve with algebraic methods. Learn