The material presented in this book is suited for a first course in Functional Analysis which can be followed by masters students. While covering all the standard material expected of such a course, efforts have been made to illustrate the use of various theorems via examples taken from differential equations and the calculus of variations, either through brief sections or through exercises. In fact, this book will be particularly useful for students who would like to pursue a research career in the applications of mathematics. The book includes a chapter on weak and weak*topologies and their applications to the notions of reflexivity, separability and uniform convexity. The chapter on the Lebesgue spaces also presents the theory of one of the simplest classes of Sobolev spaces. The book includes a chapter on compact operators and the spectral theory for compact self-adjoint operators on a Hilbert space. Each chapter has large collection of exercises at the end. These illustrate the results of the text, show the optimality of the hypotheses of various theorems via examples or counterexamples, or develop simple versions of theories not elaborated upon in the text.

El calculo diferencial e integral es facil y sencillo La finalidad de realizar el presente material de calculo diferencial e integral paso a paso, es con el objeto de proporcionar un apoyo tanto a los alumnos como profesores van a desarrollar el programa a nivel bachillerato. Dicho trabajo esta disenado en unidades, he seleccionado el material considerado la dificultad de los ejercicios, procesos algebraicos y matematicos necesarios para su solucion. Es recomendable para los alumnos que adeudan la materia asi como los que la cursan por primera ocasion, puede considerarse como un material de apoyo o complementario; Para el profesor se considera como un material fundamental en el desarrollo de su programa, por la serie de ejercicios resueltos y propuestos los cuales se encuentran en forma gradual partiendo del mas sencillo al mas complejo.

This brief monograph by a distinguished professor is based on a mathematics course offered at the California Institute of Technology. The majority of students taking this course were advanced undergraduates and graduate students of engineering. A solid background in advanced calculus is a prerequisite.
Topics include elementary and convergence theories of convolution quotients, differential equations involving operator functions, and exponential functions of operators. Tools developed in the preceding chapters are then applied to problems in partial differential equations. Solutions to selected problems appear at the end of the book.

This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important contributions to their respective topics. This volume is the first of its kind that covers such a comprehensive range of topics in fractional dynamics. It will point out to advanced undergraduate and graduate students, and young researchers the possible directions of research in this subject.

In addition to those who intend to work in this field and those already in the field, this volume will also be useful for researchers not directly involved in the field, but want to know the current status and trends of development in this subject. This latter group includes theoretical chemists, mathematical biologists and engineers.

This textbook for the basic lecture course of the same name deals with selected topics of multidimensional analysis. It is also an introduction to the theory of ordinary differential equations and the Fourier theory, of importance in the application of image processing and acoustics.

Publisher's Note: Products purchased from Third Party sellers are not guaranteed by the publisher for quality, authenticity, or access to any online entitlements included with the product. Your INTEGRAL tool for mastering ADVANCED CALCULUS Interested in going further in calculus but don't where to begin? No problem! With Advanced Calculus Demystified, there's no limit to how much you will learn. Beginning with an overview of functions of multiple variables and their graphs, this book covers the fundamentals, without spending too much time on rigorous proofs. Then you will move through more complex topics including partial derivatives, multiple integrals, parameterizations, vectors, and gradients, so you'll be able to solve difficult problems with ease. And, you can test yourself at the end of every chapter for calculated proof that you're mastering this subject, which is the gateway to many exciting areas of mathematics, science, and engineering. This fast and easy guide offers: Numerous detailed examples to illustrate basic concepts Geometric interpretations of vector operations such as div, grad, and curl Coverage of key integration theorems including Green's, Stokes', and Gauss' Quizzes at the end of each chapter to reinforce learning A time-saving approach to performing better on an exam or at work Simple enough for a beginner, but challenging enough for a more advanced student, Advanced Calculus Demystified is one book you won't want to function without!