Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Suitable for both senior undergraduate and graduate students, this is a self-contained book dealing with the classical theory of the partial differential equations through a modern approach; requiring minimal previous knowledge. It represents the solutions to three important equations of mathematical physics - Laplace and Poisson equations, Heat or diffusion equation, and wave equations in one and more space dimensions. Keen readers will benefit from more advanced topics and many references cited at the end of each chapter. In addition, the book covers advanced topics such as Conservation Laws and Hamilton-Jacobi Equation. Numerous real-life applications are interspersed throughout the book to retain readers' interest.

Differential equations, Partial

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

When one has to deal with fluid flows, magnetic fields or heat transfer in stars, one faces the partial differential equations that govern these processes. These phenomena are naturally multi-dimensional and their study requires new and sophisticated models. This volume gathers the lecture notes which summarize the essence of the lectures and conferences given by world experts in the field of multi-dimensional modelling of stars, during the 2018 Evry Schatzman School held in Roscoff, France. It gives the present status of our understanding of several processes that occur in stars, like thermal convection, double-diffusive convection, dynamo effect or baroclinic flows. Every subject is discussed under the light of the most recent results of nowadays research and is made accessible to all newcomers, either students or researchers who wish to join the field.

Differential equations, Partial

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Nonlinear wave equations --- Équations d'onde non linéaires --- Differential equations, Partial. --- Équations aux dérivées partielles --- Équations d'onde --- Wave equation --- Differential equations, Partial --- Équations d'onde --- Asymptotic theory --- Théorie asymptotique

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solitons, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements. Peter J. Olver is professor of mathematics at the University of Minnesota. His wide-ranging research interests are centered on the development of symmetry-based methods for differential equations and their manifold applications. He is the author of over 130 papers published in major scientific research journals as well as 4 other books, including the definitive Springer graduate text, Applications of Lie Groups to Differential Equations, and another undergraduate text, Applied Linear Algebra. A Solutions Manual for instrucors is available by clicking on "Selected Solutions Manual" under the Additional Information section on the right-hand side of this page. .

Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematics. --- Fourier analysis. --- Partial differential equations. --- System theory. --- Partial Differential Equations. --- Complex Systems. --- Fourier Analysis. --- Differential equations, Partial. --- Partial differential equations --- Differential equations, partial. --- Analysis, Fourier --- Mathematical analysis --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Differential equations, Partial --- Fourier analysis --- Asymptotic theory. --- Asymptotic theory in partial differential equations --- Asymptotic expansions

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book presents a concise introduction to a unified Hilbert space approach to the mathematical modelling of physical phenomena which has been developed over recent years by Picard and his co-workers. The main focus is on time-dependent partial differential equations with a particular structure in the Hilbert space setting that ensures well-posedness and causality, two essential properties of any reasonable model in mathematical physics or engineering. As a unique feature, this powerful tool for tackling time-dependent partial differential equations is subsequently applied to many equations. By means of illustrative examples, from the straightforward to the more complex, the authors show that many of the classical models in mathematical physics as well as more recent models of novel materials and interactions are covered, or can be restructured to be covered, by this unified Hilbert space approach. The reader should require only a basic foundation in the theory of Hilbert spaces and operators therein. For convenience, however, some of the more technical background requirements are covered in detail in the appendix. The theory is kept as elementary as possible, making the material suitable for a senior undergraduate or master’s level course. In addition, researchers in a variety of fields whose work involves partial differential equations and applied operator theory will also greatly benefit from this approach to structuring their mathematical models in order that the general theory can be applied to ensure the essential properties of well-posedness and causality.

Differential equations, Partial. --- Hilbert space. --- Mathematical physics. --- Physical mathematics --- Physics --- Banach spaces --- Hyperspace --- Inner product spaces --- Partial differential equations --- Mathematics --- Partial differential equations. --- Partial Differential Equations.