Mathematical Analysis

e-books in this category

A Course of Modern Analysis
by E. T. Whittaker, G. N. Watson - Cambridge University Press , 1927
This classic text is known to and used by thousands of mathematicians and students of mathematics throughout the world. It is the standard book of reference in English on the applications of analysis to the transcendental functions.
(5305 views)

A Course of Pure Mathematics
by G. H. Hardy , 1908
G. H. Hardy was one of the greatest mathematicians of the 20th century. When the first edition appeared in 1908, it was the only comprehensive introduction to analysis in the English language. It remains unsurpassed in that genre in any language.
(1257 views)

A First Course in Complex Analysis
by Matthias Beck, Gerald Marchesi, Dennis Pixton , 2007
These are the lecture notes of a one-semester undergraduate course: complex numbers, differentiation, functions, integration, Cauchy's theorem, harmonic functions, power series, Taylor and Laurent series, isolated singularities, etc.
(4371 views)

Advanced Calculus and Analysis
by Ian Craw - University of Aberdeen , 2000
Introductory calculus course, with some leanings to analysis. It covers sequences, monotone convergence, limits, continuity, differentiability, infinite series, power series, differentiation of functions of several variables, and multiple integrals.
(4260 views)

Analysis Tools with Applications
by Bruce K. Driver - Springer , 2003
These are lecture notes from Real analysis and PDE: Basic Topological, Metric and Banach Space Notions; Riemann Integral and ODE; Lebesbgue Integration; Hilbert Spaces and Spectral Theory of Compact Operators; Complex Variable Theory; etc.
(1276 views)

Analysis: An Introductory Course
by I. F. Wilde - King's College London , 2009
The material is intended to provide a gentle (but nonetheless serious) introduction to some of the concepts of analysis. Contents: Sets; The Real Numbers; Sequences; Series; Functions; Power Series; The elementary functions.
(2081 views)

Applied Analysis
by John Hunter, Bruno Nachtergaele - World Scientific Publishing Company , 2005
Introduces applied analysis at the graduate level, particularly those parts of analysis useful in graduate applications. Only a background in basic calculus, linear algebra and ordinary differential equations, and functions and sets is required.
(1287 views)

Basic Analysis: Introduction to Real Analysis
by Jiri Lebl - Lulu.com , 2009
This is a free online textbook for a first course in mathematical analysis. The text covers the real number system, sequences and series, continuous functions, the derivative, the Riemann integral, and sequences of functions.
(1466 views)

Basics of Algebra and Analysis For Computer Science
by Jean Gallier , 2007
From the table of contents: Linear Algebra; Determinants; Basics of Affine Geometry; Polynomials, PID's and UFD's; Topology; Differential Calculus; Zorn’s Lemma and Some Applications; Gaussian elimination, LU-factoring and Cholesky-factoring.
(3284 views)

Chebyshev and Fourier Spectral Methods
by John P. Boyd - Dover Publications , 2001
The text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, cardinal functions, etc.
(2728 views)

Complex Analysis
by George Cain , 2001
The textbook for an introductory course in complex analysis. It covers complex numbers and functions, integration, Cauchy's theorem, harmonic functions, Taylor and Laurent series, poles and residues, argument principle, and more.
(2427 views)

Complex Analysis on Riemann Surfaces
by Curtis McMullen - Harvard University , 2005
Contents: Maps between Riemann surfaces; Sheaves and analytic continuation; Algebraic functions; Holomorphic and harmonic forms; Cohomology of sheaves; Cohomology on a Riemann surface; Riemann-Roch; Serre duality; Maps to projective space; etc.
(895 views)

Complex Variables - Complex Analysis
by John H. Mathews - Cal State Fullerton , 2006
Analytic and Harmonic Functions; Sequences, Series, and Julia and Mandelbrot Sets; Complex Integration; Taylor and Laurent Series; Residue Theory; The z-Transforms and Applications; Conformal Mapping; Fourier Series and the Laplace Transform.
(2210 views)

Complex Variables: Second Edition
by R. B. Ash, W. P. Novinger - Dover Publications , 2007
The text for advanced undergraduates and graduates, it offers a concise treatment, explanations, problems and solutions. Topics include elementary theory, general Cauchy theorem and applications, analytic functions, and prime number theorem.
(2337 views)

Dynamics in One Complex Variable
by John Milnor - Princeton University Press , 1991
This text studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the case of rational maps of the Riemann sphere. The book introduces some key ideas in the field, and forms a basis for further study.
(2345 views)

Elliptic Functions
by Arthur Latham Baker - John Wiley & Sons , 1890
The author used only such methods as are familiar to the ordinary student of Calculus, avoiding those methods of discussion dependent upon the properties of double periodicity, and also those depending upon Functions of Complex Variables.
(257 views)

Fourier Series and Systems of Differential Equations and Eigenvalue Problems
by Leif Mejlbro - BookBoon , 2007
This volume gives some guidelines for solving problems in the theories of Fourier series and Systems of Differential Equations and eigenvalue problems. It can be used as a supplement to the textbooks in which one can find all the necessary proofs.
(1191 views)

Functional Analysis Lecture Notes
by T. B. Ward - University of East Anglia , 2003
By the end of the course, you should have a good understanding of normed vector spaces, Hilbert and Banach spaces, fixed point theorems and examples of function spaces. These ideas will be illustrated with applications to differential equations.
(2089 views)

Fundamentals of Analysis
by W W L Chen - Macquarie University , 2008
Set of notes suitable for an introduction to the basic ideas in analysis: the number system, sequences and limits, series, functions and continuity, differentiation, the Riemann integral, further treatment of limits, and uniform convergence.
(1967 views)

Global Analysis: Functional Analysis Examples
by Leif Mejlbro - BookBoon , 2009
From the table of contents: Metric spaces; Topology; Continuous mappings; Sequences; Semi-continuity; Connected sets, differentiation; Normed vector spaces and integral operators; Differentiable mappings; Complete metric spaces; and more.
(249 views)

Harmonic Function Theory
by Sheldon Axler, Paul Bourdon, Wade Ramey - Springer , 2001
A book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the text. The authors have taken care to motivate concepts and simplify proofs.
(1506 views)

Hilbert Spaces and Operators on Hilbert Spaces
by Leif Mejlbro - BookBoon , 2009
Functional analysis examples. From the table of contents: Hilbert spaces; Fourier series; Construction of Hilbert spaces; Orthogonal projections and complements; Weak convergence; Operators on Hilbert spaces, general; Closed operations.
(36 views)

Holomorphic Spaces
by S. Axler, J. McCarthy, D. Sarason - Cambridge University Press , 1998
This volume consists of expository articles on holomorphic spaces. Topics covered are Hardy spaces, Bergman spaces, Dirichlet spaces, Hankel and Toeplitz operators, and a sampling of the role these objects play in modern analysis.
(370 views)

Homeomorphisms in Analysis
by Casper Goffman, at al. - American Mathematical Society , 1997
This book features the interplay of two main branches of mathematics: topology and real analysis. The text covers Lebesgue measurability, Baire classes of functions, differentiability, the Blumberg theorem, various theorems on Fourier series, etc.
(1443 views)

Interactive Real Analysis
by Bert G. Wachsmuth - Seton Hall University , 2007
Interactive Real Analysis is an online, interactive textbook for Real Analysis or Advanced Calculus in one real variable. It deals with sets, sequences, series, continuity, differentiability, integrability, topology, power series, and more.
(1930 views)

Introduction to Complex Analysis
by W W L Chen - Macquarie University , 2008
Introduction to some of the basic ideas in complex analysis: complex numbers; foundations of complex analysis; complex differentiation; complex integrals; Cauchy's integral theorem; Cauchy's integral formula; Taylor series; Laurent series; etc.
(1738 views)

Introduction to Infinitesimal Analysis Functions of One Real Variable
by N. J. Lennes - John Wiley & Sons , 1907
This volume is designed as a reference book for a course dealing with the fundamental theorems of infinitesimal calculus in a rigorous manner. The book may also be used as a basis for a rather short theoretical course on real functions.
(1296 views)

Introduction to Lebesgue Integration
by W W L Chen - Macquarie University , 1996
An introduction to some of the basic ideas in Lebesgue integration with the minimal use of measure theory. Contents: the real numbers and countability, the Riemann integral, point sets, the Lebesgue integral, monotone convergence theorem, etc.
(1739 views)

Introduction to Methods of Applied Mathematics
by Sean Mauch , 2004
Advanced mathematical methods for scientists and engineers, it contains material on calculus, functions of a complex variable, ordinary differential equations, partial differential equations and the calculus of variations.
(4668 views)

Introduction to Real Analysis
by William F. Trench - Prentice Hall , 2003
This book introduces readers to a rigorous understanding of mathematical analysis and presents challenging concepts as clearly as possible. Written for those who want to gain an understanding of mathematical analysis and challenging concepts.
(2585 views)

Introduction to the Elementary Functions
by Raymond Benedict McClenon - Ginn and company , 1918
The book covers some parts of plane trigonometry and analytic geometry, followed by an introduction to the differential calculus, including differentiation of simpler algebraic functions and applications to problems of rates and maxima and minima.
(2055 views)

Introduction to Vectors and Tensors Volume 1: Linear and Multilinear Algebra
by Ray M. Bowen, C.-C.Wang - Springer , 2008
This book presents the basics of vector and tensor analysis for science and engineering students. Volume 1 covers algebraic structures and a modern introduction to the algebra of vectors and tensors. Clear presentation of mathematical concepts.
(4580 views)

Introduction to Vectors and Tensors Volume 2: Vector and Tensor Analysis
by Ray M. Bowen, C.-C. Wang , 2008
The textbook presents introductory concepts of vector and tensor analysis, suitable for a one-semester course. Volume II discusses Euclidean Manifolds followed by the analytical and geometrical aspects of vector and tensor fields.
(3305 views)

Lectures on Entire Functions
by B. Ya. Levin - American Mathematical Society , 1996
This monograph aims to expose the main facts of the theory of entire functions and to give their applications in real and functional analysis. The general theory starts with the fundamental results on the growth of entire functions of finite order.
(1347 views)

Linear Functional Analysis
by W W L Chen - Macquarie University , 2008
An introduction to the basic ideas in linear functional analysis: metric spaces; connectedness, completeness and compactness; normed vector spaces; inner product spaces; orthogonal expansions; linear functionals; linear transformations; etc.
(1705 views)

Mathematical Analysis I
by Elias Zakon - The Trillia Group , 2004
Topics include metric spaces, convergent sequences, open and closed sets, function limits and continuity, sequences and series of functions, compact sets, power series, Taylor's theorem, differentiation and integration, total variation, and more.
(2153 views)

Mathematical Analysis II
by Elias Zakon - The TrilliaGroup , 2009
This book follows the release of the author's Mathematical Analysis I and completes the material on Real Analysis that is the foundation for later courses. The text is appropriate for any second course in real analysis or mathematical analysis.
(1059 views)

Mathematical Methods for Economic Theory: a tutorial
by Martin J. Osborne , 2007
This tutorial covers the basic mathematical tools used in economic theory. The main topics are multivariate calculus, concavity and convexity, optimization theory, differential and difference equations. Knowledge of elementary calculus is assumed.
(3245 views)

Monotone Operators in Banach Space and Nonlinear Partial Differential Equations
by R. E. Showalter - American Mathematical Society , 1997
This monograph presents some topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial-boundary-value problems for partial differential equations.
(2316 views)

Multivariable and Vector Analysis
by W W L Chen - Macquarie University , 2008
Introduction to multivariable and vector analysis: functions of several variables, differentiation, implicit and inverse function theorems, higher order derivatives, double and triple integrals, vector fields, integrals over paths, etc.
(2800 views)

Real Numbers and Fascinating Fractions
by N. M. Beskin , 1986
This text introduces the interesting and valuable concept of continued fractions. Contents: Two Historical Puzzles; Formation of Continued Fractions; Convergents; Non-terminating Continued Fractions; Approximation of Real Numbers.
(1190 views)

Real Variables: With Basic Metric Space Topology
by Robert B. Ash - Institute of Electrical & Electronics Engineering , 2007
A text for a first course in real variables for students of engineering, physics, and economics, who need to know real analysis in order to cope with the professional literature. The subject matter is fundamental for more advanced mathematical work.
(1971 views)

Set Theoretic Real Analysis
by Krzysztof Ciesielski - Heldermann Verlag , 1997
This text surveys the recent results that concern real functions whose statements involve the use of set theory. The choice of the topics follows the author's personal interest in the subject. Most of the results are left without the proofs.
(1658 views)

Several Complex Variables
by Michael Schneider, Yum-Tong Siu - Cambridge University Press , 1999
Several Complex Variables is a central area of mathematics with interactions with partial differential equations, algebraic geometry and differential geometry. This text emphasizes these interactions and concentrates on problems of current interest.
(661 views)

Stochastic Analysis - Notes
by I. F. Wilde , 2009
A gentle introduction to the mathematics of Stochastic Analysis. From the table of contents: Introduction; Conditional expectation; Martingales; Stochastic integration - informally; Wiener process; Ito's formula; Bibliography.
(2265 views)

Theory of functions of a real variable
by Shlomo Sternberg , 2005
The topology of metric spaces, Hilbert spaces and compact operators, the Fourier transform, measure theory, the Lebesgue integral, the Daniell integral, Wiener measure, Brownian motion and white noise, Haar measure, Banach algebras, etc.
(1822 views)

Theory of the Integral
by Stanislaw Saks - Polish Mathematical Society , 1937
Covering all the standard topics, the author begins with a discussion of the integral in an abstract space, additive classes of sets, measurable functions, and integration of sequences of functions. Succeeding chapters cover Caratheodory measure.
(412 views)

Treatise on Analysis Volume II
by Jean A. Dieudonne - Academic Pr , 1976
Elements of the theory of sets, real numbers, additional properties of the real line, metric spaces, normed spaces, spaces of continuous functions, Hilbert spaces, differential calculus, analytic functions, existence theorems, etc.
(1882 views)

Why the Boundary of a Round Drop Becomes a Curve of Order Four
by A. N. Varchenko, P. I. Etingof - American Mathematical Society , 1992
This book concerns the problem of evolution of a round oil spot surrounded by water when oil is extracted from a well inside the spot. It turns out that the boundary of the spot remains an algebraic curve of degree four in the course of evolution.
(3307 views)