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Ordinary Differential Equations:Cheat Sheet/Few Useful Definitions
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Wronskian of Two Functions
Definition
The Wronskian of two functions is given by
Useful Facts
If two functions are linearly dependent on an interval, then their Wronskian vanishes on that interval.
Laplace Transforms
Definition
The Laplace transform of at a complex number is
Properties
Linearity:
If then:
for
Laplace Transform of Few Simple Functions
Convolution
Definition
The convolution of and is
Properties
Convolution is:
Associative
Commutative
Distributive over addition
First Order Ordinary Differential Equations Ordinary Differential Equations:Cheat Sheet