Mathematical Physics with Differential Equations

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Yisong Yang (Professor of Mathematics, Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University)

Mathematical Physics with Differential Equations

Yisong Yang (Professor of Mathematics, Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University)

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English

Oxford University Press
04 May 2023

Differential calculus & equations; Applied mathematics; Mathematical physics

Traditional literature in mathematical physics is clustered around classical mechanics, especially fluids and elasticity. This book reflects the modern development of theoretical physics in the areas of field theories: classical, quantum, and gravitational, in which differential equations play essential roles and offer powerful insight. Yang here presents a broad range of fundamental topics in theoretical and mathematical physics based on the viewpoint of differential equations. The subject areas covered include classical and quantum many-body problems, thermodynamics, electromagnetism, magnetic monopoles, special relativity, gauge field theories, general relativity, superconductivity, vortices and other topological solitons, and canonical quantization of fields, for which knowledge and use of linear and nonlinear differential equations are essential for comprehension. Much emphasis is given to the mathematical and physical content offering an appreciation of the interplay of mathematics and theoretical physics from the viewpoint of differential equations. Advanced methods and techniques of modern nonlinear functional analysis are kept to a minimum and each chapter is supplemented with a collection of exercises of varied depths making it an ideal resource for students and researchers alike.

By: Yisong Yang (Professor of Mathematics Professor of Mathematics Courant Institute of Mathematical Sciences New York University)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 240mm, Width: 160mm, Spine: 32mm
Weight: 1g
ISBN: 9780192872616
ISBN 10: 0192872613
Pages: 496
Publication Date: 04 May 2023
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

Preface Notation and Convention 1: Hamiltonian Systems and Applications 2: Schrödinger Equation and Quantum Mechanics 3: Maxwell Equations, Dirac Monopole, and Gauge Fields 4: Special Relativity 5: Abelian Gauge Field Equations 6: Dirac Equations 7: GinzburgDSLandau Equations for Superconductivity 8: Magnetic Vortices in Abelian Higgs Theory 9: Non-Abelian Gauge Field Equations 10: Einstein Equations and Related Topics 11: Charged Vortices and ChernDSSimons Equations 12: Skyrme Model and Related Topics 13: Strings and Branes 14: BornDSInfeld Theory of Electromagnetism 15: Canonical Quantization of Fields Appendices Bibliography Index

Yisong Yang is a Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University. He received his Ph.D. in Mathematics from the University of Massachusetts at Amherst in 1988.