Exercises and Problems in Mathematical Methods of Physics

• Κύριος συγγραφέας: Cicogna, Giampaolo (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 1st ed. 2018.
• Σειρά: Undergraduate Lecture Notes in Physics,
• Θέματα: Physics.; Fourier analysis.; Operator theory.; Functions of complex variables.; Integral transforms.; Operational calculus.; Group theory.; Mathematical Methods in Physics.; Fourier Analysis.; Operator Theory.; Functions of a Complex Variable.; Integral Transforms, Operational Calculus.; Group Theory and Generalizations.

This book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based. The exercises and problems are proposed not in a random order...

Πίνακας περιεχομένων:

• 1 Hilbert spaces
• 1.1 Complete sets, Fourier expansions
• 1.1.1 Preliminary notions. Subspaces. Complete sets
• 1.1.2 Fourier expansions
• 1.1.3 Harmonic functions; Dirichlet and Neumann Problems
• 1.2 Linear operators
• 1.2.1 Linear operators defined giving T en = vn, and related Problems
• 1.2.2 Operators of the form T x = v(w;x) and T x = ån vn(wn;x)
• 1.2.3 Operators of the form T f (x) = j(x) f (x)
• 1.2.4 Problems involving differential operators
• 1.2.5 Functionals
• 1.2.6 Time evolution Problems. Heat equation
• 1.2.7 Miscellaneous Problems
• 2 Functions of a complex variable
• 2.1 Basic properties of analytic functions
• 2.2 Evaluation of integrals by complex variable methods
• 2.3 Harmonic functions and conformal mappings
• 3 Fourier and Laplace transforms. Distributions
• 3.1 Fourier transform in L1(R) and L2(R)
• 3.1.1 Basic properties and applications
• 3.1.2 Fourier transform and linear operators in L2(R)
• 3.2 Tempered distributions and Fourier transforms
• 3.2.1 General properties
• 3.2.2 Fourier transform, distributions and linear operators
• 3.2.3 Applications to ODE's and related Green functions
• 3.2.4 Applications to general linear systems and Green functions
• 3.2.5 Applications to PDE's
• 3.3 Laplace transforms
• vvi Contents
• Groups, Lie algebras, symmetries in physics
• 4.1 Basic properties of groups and representations
• 4.2 Lie groups and algebras
• 4.3 The groups SO3; SU2; SU3
• 4.4 Other direct applications of symmetries to physics
• Answers and Solutions. .