Calculus and mathematical analysis Books

The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's...

A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful...

The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex ...

This book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical, way and is mainly addressed to non-specialists in the subject. It is based on lectures...

From the reviews: "[...] the interested reader will find in Bremaud's book an invaluable reference because of its coverage, scope and style, as well as of the unified treatment it offers of (signal processing oriented) Fourier...

This well-written book contains the analytical tools, concepts, and viewpoints needed for modern applied mathematics. It treats various practical methods for solving problems such as differential equations, boundary value...

Several natural Lp spaces of analytic functions have been widely studied in the past few decades, including Hardy spaces, Bergman spaces, and Fock spaces. The terms "Hardy spaces" and "Bergman spaces" are by now standard and well established. But the...

This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a reasonable background in ordinary differential equations and who would like to get to the...

For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written textbook provides an introduction to many of the important topics associated with...

The Second Edition of this acclaimed text helps you apply theory to real-world applications in mathematics, physics, and engineering. It easily guides you through complex analysis with its excellent coverage of topics such as...

For readers with some competence in PDE solution properties, this book offers an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere...

During the 90s robust control theory has seen major advances and achieved a new maturity, centered around the notion of convexity. The goal of this book is to give a graduate-level course on this theory that emphasizes these...

This book explores connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations, and in particular...

Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra,...

This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for independent study. It includes...

This textbook gives an introduction to distribution theory with emphasis on applications using functional analysis. In more advanced parts of the book, pseudodi?erential methods are introduced. Distributiontheoryhasbeen...

Fractal Examples.- Metric Topology.- Topological Dimension.- Self-Similarity.- Measure Theory.- Fractal Dimension.- Additional Topics.

General Theory of Banach Algebras.- Gelfand Theory.- Functional Calculus, Shilov Boundary, and Applications.- Regularity and Related Properties.- Spectral Synthesis and Ideal Theory.

An Introduction to Classical Dynamics.- Dynamics over Local Fields: Good Reduction.- Dynamics over Global Fields.- Families of Dynamical Systems.- Dynamics over Local Fields: Bad Reduction.- Dynamics Associated to Algebraic Groups.- Dynamics in Dimension...

Measure Theory and Lp Spaces.- Measures.- Lp Spaces.- The Direct Method and Lower Semicontinuity.- The Direct Method and Lower Semicontinuity.- ConvexAnalysis.- Functionals Defined on Lp.- Integrands f = f (z).- Integrands f = f (x, z).- Integrands f = f...

This book is an account of the theory of Hardy spaces in one dimension, with emphasis on some of the exciting developments of the past two decades or so. The last seven of the ten chapters are devoted in the main to these...

Fundamentals of Imaging.- Case Examples of Imaging.- Image and Noise Models.- Regularization.- Variational Regularization Methods for the Solution of Inverse Problems.- Convex Regularization Methods for Denoising.- Variational Calculus for Non-convex...

The content of this book is multidisciplinary by nature. It uses mathematical tools from the theories of probability and stochastic processes, partial differential equations, and asymptotic analysis, combined with the physics...

Bases and Basic Sequences.- The classical sequence spaces.- Special types of bases.- Spaces of continuous functions.- L_1(\mu)-spaces and C(K)-spaces.- L_p(\mu)-spaces, 1 \leq p < \infty.- Factorization Theory.- Absolutely Summing Operators.-...

Convex sets and convex functions: the fundamentals.- Continuity and ?(X).- The derivatives and the subdifferential.- Minima and quasi minima.- The Fenchel conjugate.- Duality.- Linear programming and game theory.- Hypertopologies, hyperconvergences.-...

Observation, Control, and Stabilization.- Well-Posedness in a Riesz Basis Setting.- Observability of Strings.- Observability of Beams.- Vector Sum Estimates.- Problems on Spherical Domains.- Multidimensional Ingham-Type Theorems.- A General Ingham-Type...

The great response to the publication of the book Classical and Modern Fourier Analysishasbeenverygratifying.IamdelightedthatSpringerhasofferedtopublish the second edition of this book in two volumes: Classical Fourier...

A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited...

Squares.- Numbers, Numbers Everywhere.- Fibonacci Numbers.- Prime Numbers.- Choice and Chance.- Geometrical Constructions.- The Algebra of Group.

An Elementary Treatise On The Calculus: With Illustrations From Geometry, Mechanics And Physics is a book written by George Alexander Gibson in 1901. The book is a comprehensive guide to calculus, a branch of mathematics that deals with rates of change...

An Elementary Treatise On Conic Sections is a book written by Charles Smith in 1883. The book is a comprehensive guide to the study of conic sections, which are curves that result from the intersection of a plane and a cone. The book covers the history...

""An Elementary Treatise On Analytic Mechanics: With Numerous Examples"" is a book written by Edward Albert Bowser and first published in 1884. The book is aimed at students and professionals in the field of mechanics who are interested in learning about...

""An Elementary Treatise On The Calculus, For Engineering Students: With Numerous Examples And Problems Worked Out"" is a book written by John Graham and published in 1896. The book is aimed at engineering students and provides a comprehensive...

""An Elementary Treatise On Spherical Harmonics: And Subjects Connected With Them"" is a book written by Norman Macleod Ferrers in 1877. The book is an introduction to the mathematical concept of spherical harmonics and other related subjects. The author...

""An Elementary Treatise On Curves, Functions, And Forces V2: Containing Calculus Of Imaginary Quantities, Residual Calculus, And Integral Calculus"" is a book written by Benjamin Peirce and originally published in 1846. This book is focused on the study...

""A Scrapbook of Elementary Mathematics"" is a book written by William Frank White and first published in 1908. The book covers a wide range of topics in elementary mathematics, including arithmetic, algebra, geometry, and trigonometry. It is designed to...

In the last century many problems which arose in the science, engineer­ ing and technology literature involved nonlinear complex phenomena. In many situations these natural phenomena give rise to (i). ordinary differ­ ential...

This book is the first monograph in the field of uniqueness theory of meromorphic functions dealing with conditions under which there is the unique function satisfying given hypotheses. Developed by R. Nevanlinna, a Finnish...

These proceedings comprise a large part of the papers presented at the In­ ternational Conference Factorization, Singular Operators and related problems, which was held from January 28 to February 1, 2002, at the University of...

It is generally acknowledged that deterministic formulations of dy­ namical phenomena in the social sciences need to be treated differently from similar formulations in the natural sciences. Social science phe­ nomena typically...

Preface Constructing nonlinear parameter-dependent mathematical models is essential in modeling in many scientific research fields. The investigation of branching (bifurcating) solutions of such equations is one of the most...

Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected...

For many, modern functional analysis dates back to Banach's book [Ba32]. Here, such powerful results as the Hahn-Banach theorem, the open-mapping theorem and the uniform boundedness principle were developed in the setting of...

It was noted in the preface of the book "Inequalities Involving Functions and Their Integrals and Derivatives", Kluwer Academic Publishers, 1991, by D.S. Mitrinovic, J.E. Pecaric and A.M. Fink; since the writing of the...

Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then It is that they can't see the problem. one day, perhaps you will find the final question. G.K. Chesterton...