🗺️ Map of Content - Differential Equations
In order to solve this differential equation you look at it until a solution occurs to you.
Series solutions
Power series solutions
Power Series Solutions I - From polynomials to power series
Power Series Solutions II - First steps with power series
Power Series Solutions III - A more representative example
Power Series Solutions IV - Analytic functions and ordinary points
Frobenius series solutions
Frobenius Series Solutions I - Slightly generalizing power series
Frobenius Series Solutions II - Some illustrative examples
Frobenius Series Solutions III - Frobenius theory
Fourier series solutions
There cannot be a language more universal and more simple, more free from errors and obscurities...more worthy to express the invariable relations of all natural things [than mathematics].
Fourier series solutions I - A problem with power series
Fourier series solutions II - Periodic functions
Fourier series solutions III - Series representations of periodic functions
Fourier series solutions IV - Computing Fourier coefficients
Fourier series solutions V - Computing some Fourier series
Fourier series solutions VI - Inner product spaces
Fourier series solutions VII - Solving differential equations with Fourier series
Transform methods
The Fourier transform
Fourier transform I - Pushing Fourier series to the limit
Fourier transform II - The Fourier transform and inverse transform
Fourier transform III - Properties of the Fourier transform
Fourier transform IV - Derivatives
Fourier transform V - Convolution
Fourier transform VI - Solving differential equations
The Laplace transform
Laplace transform I - Desperate times
Laplace transform II - The inverse Laplace transform
Laplace transform III - The Shifting Theorems
Laplace transform IV - Convolution redux
Laplace transform V - Solving differential equations
Distributions
Coming someday