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Like its predecessor, this book by the renowned physicist Sir Rudolf Peierls draws from many diverse fields of theoretical physics to present problems in which the answer differs from what our intuition had led us to expect. In some cases an apparently convincing approximation turns out to be misleading; in others a seemingly unmanageable problem turns out to have a simple answer. Peierls's intention, however, is not to treat theoretical physics as an unpredictable game in which such surprises happen at random. Instead he shows how in each case careful thought could have prepared us for the outcome. Peierls has chosen mainly problems from his own experience or that of his collaborators, often showing how classic problems can lend themselves to new insights. His book is aimed at both graduate students and their teachers. Praise for Surprises in Theoretical Physics: "A beautiful piece of stimulating scholarship and a delight to read. Physicists of all kinds will learn a great deal from it."--R. J. Blin-Stoyle, Contemporary Physics

Mathematical physics. --- Physical mathematics --- Physics --- Mathematics --- "quantum mechanics. --- Abraham finding. --- Brillouin Zones. --- Condensed Matter. --- Decaying States. --- Electromigration. --- Euler equation". --- Field Theory. --- Hydrodynamics. --- Ising model. --- Isospin of Nuclei. --- Magnetoresistance. --- Nuclear Physics. --- Peierls Transition. --- Phonon Drag. --- Projection Method. --- Pseudomomentum. --- Rotational States. --- Shock Waves. --- Wave Function. --- microscopic theory. --- relaxation time.

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This book contains a collection of twelve papers that reflect the state of the art of nonlinear differential equations in modern geometrical theory. It comprises miscellaneous topics of the local and nonlocal geometry of differential equations and the applications of the corresponding methods in hydrodynamics, symplectic geometry, optimal investment theory, etc. The contents will be useful for all the readers whose professional interests are related to nonlinear PDEs and differential geometry, both in theoretical and applied aspects.

Research & information: general --- Mathematics & science --- adjoint-symmetry --- one-form --- symmetry --- vector field --- geometrical formulation --- nonlocal conservation laws --- differential coverings --- polynomial and rational invariants --- syzygy --- free resolution --- discretization --- differential invariants --- invariant derivations --- symplectic --- contact spaces --- Euler equations --- shockwaves --- phase transitions --- symmetries --- integrable systems --- Darboux-Bäcklund transformation --- isothermic immersions --- Spin groups --- Clifford algebras --- Euler equation --- quotient equation --- contact symmetry --- optimal investment theory --- linearization --- exact solutions --- Korteweg–de Vries–Burgers equation --- cylindrical and spherical waves --- saw-tooth solutions --- periodic boundary conditions --- head shock wave --- Navier–Stokes equations --- media with inner structures --- plane molecules --- water --- Levi–Civita connections --- Lagrangian curve flows --- KdV type hierarchies --- Darboux transforms --- Sturm–Liouville --- clamped --- hinged boundary condition --- spectral collocation --- Chebfun --- chebop --- eigenpairs --- preconditioning --- drift --- error control --- adjoint-symmetry --- one-form --- symmetry --- vector field --- geometrical formulation --- nonlocal conservation laws --- differential coverings --- polynomial and rational invariants --- syzygy --- free resolution --- discretization --- differential invariants --- invariant derivations --- symplectic --- contact spaces --- Euler equations --- shockwaves --- phase transitions --- symmetries --- integrable systems --- Darboux-Bäcklund transformation --- isothermic immersions --- Spin groups --- Clifford algebras --- Euler equation --- quotient equation --- contact symmetry --- optimal investment theory --- linearization --- exact solutions --- Korteweg–de Vries–Burgers equation --- cylindrical and spherical waves --- saw-tooth solutions --- periodic boundary conditions --- head shock wave --- Navier–Stokes equations --- media with inner structures --- plane molecules --- water --- Levi–Civita connections --- Lagrangian curve flows --- KdV type hierarchies --- Darboux transforms --- Sturm–Liouville --- clamped --- hinged boundary condition --- spectral collocation --- Chebfun --- chebop --- eigenpairs --- preconditioning --- drift --- error control