大葉大學圖書館 |

Heat kernel method and its applications[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515.353
書名/作者:	Heat kernel method and its applications/ by Ivan G. Avramidi.
作者:	Avramidi, Ivan G.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	xix, 390 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Differential equations, Partial.
標題:	Differential equations, Parabolic.
標題:	Heat equation.
標題:	Mathematics.
標題:	Partial Differential Equations.
ISBN:	9783319262666
ISBN:	9783319262659
內容註:	Part I Analysis -- 1 Background in Analysis -- 2 Introduction to Partial Differential Equations -- Part II Geometry -- 3 Introduction to Differential Geometry -- Part III Perturbations -- 4 Singular Perturbations -- 5 Heat Kernel Asymptotics -- 6 Advanced Topics -- Part IV Applications -- 7 Stochastic Processes -- 8 Applications in Mathematical Finance -- Summary -- References -- Index.
摘要、提要註:	The heart of the book is the development of a short-time asymptotic expansion for the heat kernel. This is explained in detail and explicit examples of some advanced calculations are given. In addition some advanced methods and extensions, including path integrals, jump diffusion and others are presented. The book consists of four parts: Analysis, Geometry, Perturbations and Applications. The first part shortly reviews of some background material and gives an introduction to PDEs. The second part is devoted to a short introduction to various aspects of differential geometry that will be needed later. The third part and heart of the book presents a systematic development of effective methods for various approximation schemes for parabolic differential equations. The last part is devoted to applications in financial mathematics, in particular, stochastic differential equations. Although this book is intended for advanced undergraduate or beginning graduate students in, it should also provide a useful reference for professional physicists, applied mathematicians as well as quantitative analysts with an interest in PDEs.
電子資源:	http://dx.doi.org/10.1007/978-3-319-26266-6

Heat kernel method and its applications[electronic resource] /
Avramidi, Ivan G.

Heat kernel method and its applications[electronic resource] /by Ivan G. Avramidi. - Cham :Springer International Publishing :2015. - xix, 390 p. :ill., digital ;24 cm.

Part I Analysis -- 1 Background in Analysis -- 2 Introduction to Partial Differential Equations -- Part II Geometry -- 3 Introduction to Differential Geometry -- Part III Perturbations -- 4 Singular Perturbations -- 5 Heat Kernel Asymptotics -- 6 Advanced Topics -- Part IV Applications -- 7 Stochastic Processes -- 8 Applications in Mathematical Finance -- Summary -- References -- Index.

The heart of the book is the development of a short-time asymptotic expansion for the heat kernel. This is explained in detail and explicit examples of some advanced calculations are given. In addition some advanced methods and extensions, including path integrals, jump diffusion and others are presented. The book consists of four parts: Analysis, Geometry, Perturbations and Applications. The first part shortly reviews of some background material and gives an introduction to PDEs. The second part is devoted to a short introduction to various aspects of differential geometry that will be needed later. The third part and heart of the book presents a systematic development of effective methods for various approximation schemes for parabolic differential equations. The last part is devoted to applications in financial mathematics, in particular, stochastic differential equations. Although this book is intended for advanced undergraduate or beginning graduate students in, it should also provide a useful reference for professional physicists, applied mathematicians as well as quantitative analysts with an interest in PDEs.

ISBN: 9783319262666

Standard No.: 10.1007/978-3-319-26266-6doiSubjects--Topical Terms:

389324
Differential equations, Partial.

LC Class. No.: QA374

Dewey Class. No.: 515.353

Heat kernel method and its applications[electronic resource] /
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