LEADER 05612nam 22007695 450 001 9910300546903321 005 20200702033530.0 010 $a3-319-76165-X 024 7 $a10.1007/978-3-319-76165-7 035 $a(CKB)4100000002892447 035 $a(DE-He213)978-3-319-76165-7 035 $a(MiAaPQ)EBC6311804 035 $a(MiAaPQ)EBC5588858 035 $a(Au-PeEL)EBL5588858 035 $a(OCoLC)1029555111 035 $a(PPN)22554749X 035 $a(EXLCZ)994100000002892447 100 $a20180321d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aExercises and Problems in Mathematical Methods of Physics /$fby Giampaolo Cicogna 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (X, 182 p. 8 illus.) 225 1 $aUndergraduate Lecture Notes in Physics,$x2192-4791 311 $a3-319-76164-1 327 $a1 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. . 330 $aThis book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based. The exercises and problems are proposed not in a random order but rather in a sequence that maximizes their educational value. Each section and subsection starts with exercises based on first definitions, followed by groups of problems devoted to intermediate and, subsequently, more elaborate situations. Some of the problems are unavoidably "routine", but others bring to the forenontrivial properties that are often omitted or barely mentioned in textbooks. There are also problems where the reader is guided to obtain important results that are usually stated in textbooks without complete proofs. In all, some 350 solved problems covering all mathematical notions useful to physics are included. While the book is intended primarily for undergraduate students of physics, students of mathematics, chemistry, and engineering, as well as their teachers, will also find it of value. . 410 0$aUndergraduate Lecture Notes in Physics,$x2192-4791 606 $aPhysics 606 $aFourier analysis 606 $aOperator theory 606 $aFunctions of complex variables 606 $aIntegral transforms 606 $aCalculus, Operational 606 $aGroup theory 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 606 $aIntegral Transforms, Operational Calculus$3https://scigraph.springernature.com/ontologies/product-market-codes/M12112 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 615 0$aPhysics. 615 0$aFourier analysis. 615 0$aOperator theory. 615 0$aFunctions of complex variables. 615 0$aIntegral transforms. 615 0$aCalculus, Operational. 615 0$aGroup theory. 615 14$aMathematical Methods in Physics. 615 24$aFourier Analysis. 615 24$aOperator Theory. 615 24$aFunctions of a Complex Variable. 615 24$aIntegral Transforms, Operational Calculus. 615 24$aGroup Theory and Generalizations. 676 $a530.15 700 $aCicogna$b Giampaolo$4aut$4http://id.loc.gov/vocabulary/relators/aut$062317 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300546903321 996 $aExercises and Problems in Mathematical Methods of Physics$91866557 997 $aUNINA