Linear-Math-In-Infinite-Dimensions-Exercises-and-Thoughts-main-1.toc

\contentsline {section}{\numberline {1}Infinite Dimensional Vector Spaces}{3}
\contentsline {subsection}{\numberline {1.3}Metric Spaces}{3}
\contentsline {subsection}{\numberline {1.5}Hilber Spaces}{3}
\contentsline {section}{\numberline {2}Chapter 2}{10}
\contentsline {subsection}{\numberline {2.1}Subsection 1}{10}
\contentsline {subsection}{\numberline {2.2}Dirac Delta Distribution}{16}
\contentsline {subsection}{\numberline {2.3}The Fourier Integral}{18}
\contentsline {subsection}{\numberline {2.4}Orthonormal Wave Packet Representation}{29}
\contentsline {subsection}{\numberline {2.5}Orthonormal Wavelet Representation}{32}
\contentsline {subsection}{\numberline {2.6}Multiresolutions Analysis}{32}
\contentsline {section}{\numberline {3}Strum-Liouville Theory}{39}
\contentsline {subsection}{\numberline {3.3}Strum-Liouville Systems}{39}
\contentsline {section}{\numberline {4}Green's Function Theory}{51}
\contentsline {subsection}{\numberline {4.3}Pictorial Definition of a Green's Function}{51}
\contentsline {subsection}{\numberline {4.7}The Totally Inhomogeneous Boundary Value Problem}{56}
\contentsline {subsection}{\numberline {4.9}Boundary Value Problem via Green's function: Integral Equations}{62}
\contentsline {subsection}{\numberline {4.11}Spectral Represensation of the Dirac Delta Function}{64}
\contentsline {section}{\numberline {5}Special Function Theory}{66}
\contentsline {subsection}{\numberline {5.1}The Helmholtz Equation}{66}
\contentsline {subsection}{\numberline {5.2}Properties of Hankel and Bessel Functions}{69}
\contentsline {subsection}{\numberline {5.3}Applications of Hankel and Bessel Functions}{70}
\contentsline {subsection}{\numberline {5.4}More Properties of Hankel and Bessel Functions}{74}
\contentsline {subsection}{\numberline {5.5}The Method of Steepest Descent and Stationary Phase}{74}
\contentsline {section}{\numberline {6}Partial Differential Equations}{74}
\contentsline {subsection}{\numberline {6.2}System of Partial Differntial Equations: How to solve Maxwell's equations using Linear Algebra}{74}