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Introduction to Real Analysis

This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.

This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.

An Introduction to Real Analysis

The Commonwealth and International Library: Mathematical Topics

An Introduction to Real Analysis presents the concepts of real analysis and highlights the problems which necessitate the introduction of these concepts. Topics range from sets, relations, and functions to numbers, sequences, series, derivatives, and the Riemann integral. This volume begins with an introduction to some of the problems which are met in the use of numbers for measuring, and which provide motivation for the creation of real analysis. Attention then turns to real numbers that are built up from natural numbers, with emphasis on integers, rationals, and irrationals. The chapters that follow explore the conditions under which sequences have limits and derive the limits of many important sequences, along with functions of a real variable, Rolle's theorem and the nature of the derivative, and the theory of infinite series and how the concepts may be applied to decimal representation. The book also discusses some important functions and expansions before concluding with a chapter on the Riemann integral and the problem of area and its measurement. Throughout the text the stress has been upon concepts and interesting results rather than upon techniques. Each chapter contains exercises meant to facilitate understanding of the subject matter. This book is intended for students in colleges of education and others with similar needs.

Each chapter contains exercises meant to facilitate understanding of the subject matter. This book is intended for students in colleges of education and others with similar needs.

Introduction to Applied Mathematics for Environmental Science

This book teaches mathematical structures and how they can be applied in environmental science. Each chapter presents story problems with an emphasis on derivation. For each of these, the discussion follows the pattern of first presenting an example of a type of structure as applied to environmental science. The definition of the structure is presented, followed by additional examples using MATLAB, and analytic methods of solving and learning from the structure.

This book teaches mathematical structures and how they can be applied in environmental science.

An Introduction to the Theory of Ordinary Differential Equations from the Standpoint of the Theory of Transformation Groups of One Parameter

Introduction to Perturbation Methods

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics.

Introduction to the Theory of Differential Inclusions

Differential inclusions play an important role as a tool in the study of various dynamical processes described by equations with a discontinuous or multivalued right-hand side. This text acts as an introduction to the subject.

Differential inclusions play an important role as a tool in the study of various dynamical processes described by equations with a discontinuous or multivalued right-hand side. This text acts as an introduction to the subject.

Differential Equations, Dynamical Systems, and an Introduction to Chaos

This text is about the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It is an update of one of Academic Press's most successful mathematics texts ever published, which has become the standard textbook for graduate courses in this area. The authors are tops in the field of advanced mathematics. Steve Smale is a Field's Medalist, which equates to being a Nobel prize winner in mathematics. Bob Devaney has authored several leading books in this subject area. Linear algebra prerequisites toned down from first edition Inclusion of analysis of examples of chaotic systems, including Lorenz, Rosssler, and Shilnikov systems Bifurcation theory included throughout.

This text is about the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics.