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.
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.
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.
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.
An
elementary treatise on Fourier's series and spherical, cylindrical, and
ellipsoidal harmonics
by William Elwood Byerly
- Ginn and company , 1893
From
the table of contents: Development in Trigonometric Series; Convergence
of Fourier's Series; Solution of Problems in Physics by the Aid of
Fourier's Integrals and Fourier's Series; Zonal Harmonics; Spherical
Harmonics; Cylindrical Harmonics; ...
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Constructive
Real Numbers and Constructive Function Spaces
by N.
A. Sanin - American Mathematical Society , 1968
The
book is devoted to certain problems of constructive mathematical
analysis. The basic sections are devoted to the foundations of the
theory of constructive function spaces. The theory of constructive real
numbers is presented in the first chapter.
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.
Elementary
Real Analysis
by B. S. Thomson, J. B. Bruckner,
A. M. Bruckner - Prentice Hall , 2001
The
book is written in a rigorous, yet reader friendly style with
motivational and historical material that emphasizes the big picture and
makes proofs seem natural rather than mysterious. Introduces key
concepts such as point set theory and other.
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.
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.
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.
Functional
and Structured Tensor Analysis for Engineers
by R.
M. Brannon - The University of Utah , 2003
A
step-by-step introduction to tensor analysis that assumes you know
nothing but basic calculus. Considerable emphasis is placed on a
notation style that works well for applications in materials modeling,
but other notation styles are also reviewed.
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.
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.
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.
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.
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.
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.
Hyperbolic
Functions
by James McMahon - John
Wiley & Sons , 1906
College
students who wish to know something of the hyperbolic trigonometry,
will find it presented in a simple and comprehensive way in the first
half of the work. Readers are then introduced to the more general
trigonometry of the complex plane.
Integral
Operators
by Leif Mejlbro - BookBoon
, 2009
Examples
of Hilbert-Smith operators and other types of integral operators,
Hilbert Schmidt norm, Volterra integral operator, Cauchy-Schwarz
inequality, Hoelder inequality, iterated kernels, Hermitian kernel, and
much more.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Notes
on Automorphic Functions
by Anders Thorup
- Kobenhavns Universitet , 1995
In
mathematics, the notion of factor of automorphy arises for a group
acting on a complex-analytic manifold. From the contents: Moebius
transformations; Discrete subgroups; Modular groups; Automorphic forms;
Poincare Series and Eisenstein Series.
Problems
in Mathematical Analysis
by B. P. Demidovich
- MIR Publishers
This
collection of problems and exercises in mathematical analysis covers
the maximum requirements of general courses in higher mathematics for
higher technical schools. It contains over 3,000 problems covering all
branches of higher mathematics.
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.
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.
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.
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.
Short
introduction to Nonstandard Analysis
by E. E.
Rosinger - arXiv , 2004
These
notes offer a short and rigorous introduction to Nostandard Analysis,
mainly aimed to reach to a presentation of the basics of Loeb
integration, and in particular, Loeb measures. The Abraham Robinson
version of Nostandard Analysis is pursued.
Spectral
Theory
by Leif Mejlbro - BookBoon
, 2009
Spectral
Theory - Functional Analysis Examples. Contents: Spectrum and
resolvent; The adjoint of a bounded operator; Self adjoint operator;
Isometric operators; Unitary and normal operators; Positive operators
and projections; Compact operators.
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.
The
Continuum and Other Types of Serial Order
by Edward
V. Huntington - Dover Publications , 1917
This
classic of mathematics presents the best systematic elementary account
of the modern theory of the continuum as a type of serial order. Based
on the Dedekind-Cantor ordinal theory, it requires no knowledge of
higher mathematics.
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.
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.
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.
Vector
Analysis and Quaternions
by Alexander
Macfarlane - John Wiley & Sons , 1906
Contents:
Addition of Coplanar Vectors; Products of Coplanar Vectors; Coaxial
Quaternions; Addition of Vectors in Space; Product of Two Vectors;
Product of Three Vectors; Composition of Quantities; Spherical
Trigonometry; Composition of Rotations.
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.
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