Oscillatory Solutions to the Airy Differential Equation

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We solve the Airy differential equation using the Fourier transform. We formally solve the equation without appealing to convergence issues, stationary phase or distributional issues (we will address these issues in further videos). By taking the real and imaginary parts of the Fourier solution, we arrive at the classical Airy functions. We then prove that the solutions to the Airy equation have an infinite number of roots if x is negative using the Sturm Separation Theorem (   • The Sturm Separation Theorem for Seco...  ). • #mikethemathematician, #mikedabkowski, #profdabkowski

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