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Math 344 - Linear Analysis II Notes
Ryan Tully-Doyle
Contents
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Contents
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Front Matter
1
What you should know
Introduction
Calculus
Linear algebra
Differential Equations
2
Series solutions
Power series
Series solutions at ordinary points
Legendre series
Series solutions at regular singularities
More on Frobenius methods (partial)
Bessel equations
Series as vectors (an introduction to
L
2
)
3
All things Fourier
Periodicity
Complex exponentials and trig functions
Sums of sinusoids
Questions of convergence
First applications
Fourier series and linear algebra
The Fourier transform
Convolution
Applications of convolution
4
The Laplace Transform
The Laplace Transform
Periodic functions
The Laplace transform of derivatives
The shifting theorems
Heaviside functions
Impulses - the Dirac delta “function”
Convolution
Authored in PreTeXt
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Section
3.6
Fourier series and linear algebra