{"title":"Jeffrey Rauch","description":null,"products":[{"product_id":"partial-differential-equations-book-jeffrey-rauch-9780387974729","title":"Partial Differential Equations","description":"This book is based on a course I have given five times at the University of Michigan, beginning in 1973. The aim is to present an introduction to a sampling of ideas, phenomena, and methods from the subject of partial differential equations that can be presented in one semester and requires no previous knowledge of differential equations. The problems, with hints and discussion, form an important and integral part of the course. In our department, students with a variety of specialties-notably differen- tial geometry, numerical analysis, mathematical physics, complex analysis, physics, and partial differential equations-have a need for such a course. The goal of a one-term course forces the omission of many topics. Everyone, including me, can find fault with the selections that I have made. One of the things that makes partial differential equations difficult to learn is that it uses a wide variety of tools. In a short course, there is no time for the leisurely development of background material. Consequently, I suppose that the reader is trained in advanced calculus, real analysis, the rudiments of complex analysis, and the language offunctional analysis. Such a background is not unusual for the students mentioned above. Students missing one of the essentials can usually catch up simultaneously. A more difficult problem is what to do about the Theory of Distributions.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51002020462865,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51002023379217,"sku":"NIN9780387974729","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52125829103889,"sku":"NLS9780387974729","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":52716393890065,"sku":"CIN0387974725VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0387974725.jpg?v=1750975315"},{"product_id":"quasiclassical-methods-book-jeffrey-rauch-9780387983103","title":"Quasiclassical Methods","description":"This IMA Volume in Mathematics and its Applications QUASICLASICAL METHODS is based on the proceedings of a very successful one-week workshop with the same title, which was an integral part of the 1994-1995 IMA program on Waves and Scattering. We would like to thank Jeffrey Rauch and Barry Simon for their excellent work as organizers of the meeting. We also take this opportunity to thank the National Science Foun- dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE There are a large number of problems where qualitative features of a partial differential equation in an appropriate regime are determined by the behavior of an associated ordinary differential equation. The example which gives the area its name is the limit of quantum mechanical Hamil- tonians (Schrodinger operators) as Planck's constant h goes to zero, which is determined by the corresponding classical mechanical system. A sec- ond example is linear wave equations with highly oscillatory initial data. The solutions are described by geometric optics whose centerpiece are rays which are solutions of ordinary differential equations analogous to the clas- sical mechanics equations in the example above. Much recent work has concerned with understanding terms beyond the leading term determined by the quasi classical limit. Two examples of this involve Weyl asymptotics and the large-Z limit of atomic Hamiltonians, both areas of current research.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52142557102353,"sku":"NLS9780387983103","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780387983103.jpg?v=1786277323"},{"product_id":"singularities-and-oscillations-book-jeffrey-rauch-9780387982007","title":"Singularities and Oscillations","description":"This IMA Volume in Mathematics and its Applications SINGULARITIES AND OSCILATIONS is based on the proceedings of a very successful one-week workshop with the same title, which was an integral part of the 1994-1995 IMA program on Waves and Scattering.  We would like to thank Joseph Keller, Jeffrey Rauch, and Michael Taylor for their excellent work as organizers of the meeting. We would like to express our further gratitude to Rauch and Taylor, who served as editors of the proceedings. We also take this opportunity to thank the National Science Foun- dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. Avner Friedman Robert Gulliver v PREFACE Thestudyofsingularitiesand oscillationsofwaves has progressed along several fronts. A key common feature is the presence of a small scale in the solutions. Recent emphasis has been on nonlinear waves. Nonlinear problems are generally less amenable than linear problems to broad unified approaches. As a result there is a justifiable tendency to concentrate on problems of particular geometric or physical interest. This volume con- tains a multiplicity of approaches brought to bear on problems varying from the formation ofcaustics and the propagation ofwaves at a boundary to the examination ofviscous boundary layers. There is an examination of the foundations of the theory of high-frequency electromagnetic waves in a dielectric or semiconducting medium. Unifying themes are not entirely absent from nonlinear analysis.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52234137338129,"sku":"NLS9780387982007","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53516481069329,"sku":"NIN9780387982007","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780387982007.jpg?v=1786613858"},{"product_id":"partial-differential-equations-book-jeffrey-rauch-9781461269595","title":"Partial Differential Equations","description":"This book is based on a course I have given five times at the University of Michigan, beginning in 1973. 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Consequently, I suppose that the reader is trained in advanced calculus, real analysis, the rudiments of complex analysis, and the language offunctional analysis. Such a background is not unusual for the students mentioned above. Students missing one of the essentials can usually catch up simultaneously. A more difficult problem is what to do about the Theory of Distributions.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52338907316497,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52338910855441,"sku":"NLS9781461269595","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461269595.jpg?v=1758169207"},{"product_id":"quasiclassical-methods-book-jeffrey-rauch-9781461273493","title":"Quasiclassical Methods","description":"This IMA Volume in Mathematics and its Applications QUASICLASICAL METHODS is based on the proceedings of a very successful one-week workshop with the same title, which was an integral part of the 1994-1995 IMA program on Waves and Scattering. We would like to thank Jeffrey Rauch and Barry Simon for their excellent work as organizers of the meeting. We also take this opportunity to thank the National Science Foun- dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE There are a large number of problems where qualitative features of a partial differential equation in an appropriate regime are determined by the behavior of an associated ordinary differential equation. The example which gives the area its name is the limit of quantum mechanical Hamil- tonians (Schrodinger operators) as Planck's constant h goes to zero, which is determined by the corresponding classical mechanical system. A sec- ond example is linear wave equations with highly oscillatory initial data. The solutions are described by geometric optics whose centerpiece are rays which are solutions of ordinary differential equations analogous to the clas- sical mechanics equations in the example above. Much recent work has concerned with understanding terms beyond the leading term determined by the quasi classical limit. 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