Integral Transforms

PDEs · Axiom Academy

Transform functions into new spaces where problems become easier to solve. Adjust the slider to see how a simple function can be transformed into a completely different representation. Every integral transform follows a similar pattern. Click the formula to reveal its components. Click on each kernel to see how it behaves. Each one has special properties that make it useful for different problems. Converts between time/space and frequency domains. Perfect for analyzing waves and periodic behavior. Converts differential equations into algebraic equations. Ideal for solving initial value problems. Adjust the coefficients to see how integral transforms respect linear combinations. Every integral transform follows this pattern, where K(x,k) is the kernel. Different kernels create different transforms: Fourier: e^(-ikx) for frequency analysis Laplace: e^(-st) for differential equations

This is the written version of the interactive lesson above. See the full PDEs course.