Exercises and problems in mathematical methods of physics. (2018)

• Record Type: Book
• Further Information: Note: Giampaolo Cicogna.
• Authors: Cicogna, Giampaolo, 1942-
• Contents: 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.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource (x, 182 pages), illustrations
• Subjects: 530.15; Physics; Mathematical physics; Mathematical physics; Physics; Mathematical Methods in Physics; Fourier Analysis; Operator Theory; Functions of a Complex Variable; Integral Transforms, Operational Calculus; Group Theory and Generalizations; Mathematics -- Mathematical Analysis; Mathematics -- Functional Analysis; Mathematics -- Algebra -- Abstract; Functional analysis & transforms; Complex analysis, complex variables; Integral calculus & equations; Groups & group theory; Fourier analysis; Operator theory; Functions of complex variables; Integral Transforms; Group theory; Science -- Mathematical Physics; Mathematical physics; Electronic books
• Languages: English
• ISBNs: 9783319761657
• Related ISBNs: 331976165X; 9783319761640; 3319761641
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed March 26, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.