A guide to mathematical methods for physicists : with problems and solutions / Michela Petrini (University Pierre and Marie Curie, France) Alberto Zaffaroni (University of Rome Tor Vergata, Italy), Gianfranco Pradisi (University of Milano-Bicocca, Italy).
Publication Info.
London : World Scientific Publishing Europe Ltd., [2018]
Machine generated contents note: pt. I Complex Analysis -- 1.Holomorphic Functions -- 1.1.Complex Functions -- 1.2.Holomorphic Functions -- 1.3.Singularities of Holomorphic Functions -- 1.4.The Riemann Sphere and the Point at Infinity -- 1.5.Elementary Functions -- 1.6.Exercises -- 2.Integration -- 2.1.Curves in the Complex Plane -- 2.2.Line Integral of a Function Along a Curve -- 2.3.Cauchy's Theorem -- 2.4.Primitive of a Holomorphic Function -- 2.5.Holomorphic Functions, Differential Forms and Vector Fields -- 2.6.Cauchy's Integral Formula -- 2.7.Morera's Theorem for a Simply Connected Domain -- 2.8.Other Properties of Holomorphic Functions -- 2.9.Harmonic Functions -- 2.10.Exercises -- 3.Taylor and Laurent Series -- 3.1.Power Series -- 3.2.Taylor Series -- 3.3.Laurent Series -- 3.4.Analytic Continuation -- 3.5.Exercises -- 4.Residues -- 4.1.Residue of a Function at an Isolated Singularity -- 4.2.Residue Theorem -- 4.3.Evaluation of Integrals by Residue Method
Note continued: 10.Linear Operators in Hilbert Spaces II: The Infinite-Dimensional Case -- 10.1.Operators in Normed Spaces -- 10.2.Operators in Hilbert Spaces -- 10.3.Eigenvalues and Spectral Theory -- 10.4.Exercises -- pt. III Appendices -- Appendix A Complex Numbers, Series and Integrals -- A.1.A Quick Review of Complex Numbers -- A.2.Notions of Topology, Sequences and Series -- A.3.The Lebesgue Integral -- Appendix B Solutions of the Exercises.
