Mathematical Methods of Theoretical Physics

This book contains very explicit proofs and demonstrations through examples for a comprehensive introduction to the mathematical methods of theoretical physics. It also combines and unifies many expositions of this subject, suitable for readers with interest in experimental and applied physics.
Contents: Why Mathematics?Linear Vector Spaces:Finite-Dimensional Vector Spaces and Linear AlgebraMultilinear Algebra and TensorsGroups as PermutationsProjective and Incidence GeometryFunctional Analysis:Brief Review of Complex AnalysisBrief Review of Fourier TransformsDistributions as Generalized FunctionsDifferential Equations:Green's FunctionSturm–Liouville TheorySeparation of VariablesSpecial Functions of Mathematical PhysicsDivergent SeriesBibliographyIndex
Readership: Undergraduate students in Mathematical Physics and Computer Science. Linear Vector Spaces;Hilbert Spaces;Spectral Theorem;Commutativity;Multilinear Algebra;Group Theory;Fourier Analysis;Complex Analysis;Generalized Functions;Distributions;Green's Functions;Ordinary Differential Equations;Fuchsian Differential Equations;Liouville Theory;Special Functions of Mathematical Physics;Frobenius Method;Divergent Series0Key Features:Very detailed explicit proofs and demonstrations by examplesCombines and unifies many expositions of the subjectShould be accessible to a very wide range of students; also ointerested in experimental and applied physics