Transformations

Transition Mathematics

Metric Spaces: Iteration and Application

Here is an introductory text on metric spaces that is the first to be written for students who are as interested in the applications as in the theory. Knowledge of metric spaces is fundamental to understanding numerical methods (for example for solving differential equations) as well as analysis, yet most books at this level emphasise just the abstraction and theory. Dr Bryant uses applications to provide motivation and to sustain the development and discusses numerical procedures where appropriate. The reader is expected to have had some exposure to elementary analysis, but the author provides examples throughout to refresh the student's memory and to test and extend understanding. In short, this is an introductory textbook that will appeal to students of mathematics and engineering and will give them the required background for more advanced courses in both analysis and numerical analysis.

An introduction to metric spaces for those interested in the applications as well as theory.

An Introduction to Hilbert Space

This textbook is an introduction to the theory of Hilbert spaces and its applications. The notion of a Hilbert space is a central idea in functional analysis and can be used in numerous branches of pure and applied mathematics. Dr. Young stresses these applications particularly for the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. The book is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). The book will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.

The notion of a Hilbert space is a central idea in functional analysis and this text demonstrates its applications in numerous branches of pure and applied mathematics.

Transform Linear Algebra

This book encourages readers to develop an intuitive understanding of the foundations of Linear Algebra. An emphasis on the concepts of Linear Algebra and Matrix Theory conveys the structure and nature of Linear Spaces and of Linear Transformations. Almost every chapter has three sections: a lecture followed by problems, theoretical and mathematical enrichment, and applications to and from Linear Algebra. Specific chapter topics cover linear transformations; row reduction; linear equations; subspaces; linear dependence, bases, and dimension; composition of maps, matrix inverse and transpose; coordinate vectors, basis change; determinants, …l-matrices; matrix eigenvalues; orthogonal bases and orthogonal matrices; symmetric and normal matrix eigenvalues; singular values; and basic numerical linear algebra techniques. For individuals in fields related to economics, engineering, science, or mathematics.

Non-Linear Elastic Deformations

Theory of Linear Operators in Hilbert Space

Stability Theory of Differential Equations

Introduction To Fourier Optics

The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the field. All the material has been update and several new sections explore the recent progress made in the areas of wavelength modulation, analog information processing, and holography. The book also explores Fourier analysis applications and emphasizes those applications to diffraction, imaging, optical data processing, and holography.

A Hilbert Space Problem Book (Graduate Texts in Mathematics)

A Short Course on Banach Space Theory (London Mathematical Society Student Texts)

This short course on classical Banach space theory is a natural follow-up to a first course on functional analysis. The topics covered have proven useful in many contemporary research arenas, such as harmonic analysis, the theory of frames and wavelets, signal processing, economics, and physics. The book is intended for use in an advanced topics course or seminar, or for independent study. It offers a more user-friendly introduction than can be found in the existing literature and includes references to expository articles and suggestions for further reading.

This is a short course on classical Banach space theory. It is a natural follow-up to a first course on functional analysis. The topics covered have proven useful in many contemporary research arenas such as harmonic analysis, the theory of frames and wavelets, signal processing, economics, and physics. The book is intended for use as in an advanced topics course or seminar, or for independent study. It offers a gentler introduction than can be found in the existing literature, even including elementary exercises. In addition, the text includes references to expository articles and suggestions for further reading.

This is a short course on Banach space theory with special emphasis on certain aspects of the classical theory. In particular, the course focuses on three major topics: The elementary theory of Schauder bases, an introduction to Lp spaces, and an introduction to C(K) spaces. While these topics can be traced back to Banach himself, our primary interest is in the postwar renaissance of Banach space theory brought about by James, Lindenstrauss, Mazur, Namioka, Pelczynski, and others. Their elegant and insightful results are useful in many contemporary research endeavors and deserve greater publicity. By way of prerequisites, the reader will need an elementary understanding of functional analysis and at least a passing familiarity with abstract measure theory. An introductory course in topology would also be helpful; however, the text includes a brief appendix on the topology needed for the course.