subcategories
Calculus (31)
Calculus of Variations (6)
Complex Analysis (42)
Differential Equations (20)
Functional Analysis (35)
Harmonic Analysis (17)
Numerical Analysis (45)
Real Analysis (40)
Tensor Calculus (12)
Vector Analysis (12)
see also
Stochastic Calculus (18)
Wavelets (8)
e-books in Mathematical Analysis & Calculus category
Measure Theory in Non-Smooth Spacesby Nicola Gigli - De Gruyter Open , 2017
The aim of this book, which gathers contributions from specialists with different backgrounds, is that of creating a collection of various aspects of measure theory occurring in recent research, increasing interactions between different fields.
(7106 views)
Applied Analysisby I.M. Sigal, M. Merkli - University of Toronto , 2001
In this course, we deal with modern analysis. Properties of functions are studied as much as they are needed for understanding maps. More specifically, our emphasis is on applications of modern analysis and the material is selected accordingly.
(8650 views)
An Introduction to Asymptotic Analysisby Simon J.A. Malham - Heriot-Watt University , 2010
From the table of contents: Order notation; Perturbation methods; Asymptotic series; Laplace integrals (Laplace's method, Watson's lemma); Method of stationary phase; Method of steepest descents; Bibliography; Notes; Exam formula sheet; etc.
(7667 views)
Introduction to Analysisby Irena Swanson - Purdue University , 2020
Students learn to write proofs while at the same time learning about binary operations, orders, fields, ordered fields, complete fields, complex numbers, sequences, and series. We also review limits, continuity, differentiation, and integration.
(10967 views)
Introduction to Analysisby Ray Mayer - Reed College , 2006
Contents: Notation, Undefined Concepts, Examples; Fields; Induction and Integers; Complexification of a Field; Real Numbers; Complex Numbers; Complex Sequences; Continuity; Properties of Continuous Functions; Derivative; Infinite Series; etc.
(8027 views)
Linear Mathematics In Infinite Dimensionsby U. H. Gerlach - The Ohio State University , 2015
Contents: Infinite Dimensional Vector Spaces; Fourier Theory; Sturm-Liouville Theory; Green's Function Theory; Special Function Theory; Partial Differential Equations; System of Partial Differential Equations: How to Solve Maxwell's Equations ...
(9963 views)
Lecture Notes on the Theory of Distributionsby Guenther Hoermann, Roland Steinbauer - Universitaet Wien , 2009
From the table of contents: 1. Test Functions and Distributions; 2. Differentiation, Differential Operators; 3. Basic Constructions; 4. Convolution; 5. Fourier Transform and Temperate Distributions; 6. Regularity; 7. Fundamental Solutions.
(10277 views)
Bernoulli Polynomials and Applicationsby Omran Kouba - arXiv , 2013
In these notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications are presented.
(8492 views)
A Course in Mathematical Analysisby E. Goursat, O. Dunkel, E.R. Hedrick - Ginn & company , 1904
Goursat's three-volume 'A Course in Mathematical Analysis' remains a classic study and a thorough treatment of the fundamentals of calculus. As an advanced text for students with one year of calculus, it offers an exceptionally lucid exposition.
(11486 views)
Set Theory and Topology: An Introduction to the Foundations of Analysisby Felix Nagel - arXiv , 2013
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. The exposition in this first part includes relation and order theory as well as a construction of number systems.
(12658 views)
Multivector Differential Calculusby Eckhard Hitzer - arXiv , 2013
This paper treats the fundamentals of the multivector differential calculus part of geometric calculus. The multivector differential is introduced, followed by the multivector derivative and the adjoint of multivector functions.
(11289 views)
Elementary Mathematical Analysisby J.W. Young, F.M. Morgan - The Macmillan Company , 1917
The book presents a course suitable for students in the first year of our colleges, universities, and technical schools. It presupposes on the part of the student only the usual minimum entrance requirements in elementary algebra and plane geometry.
(12206 views)
Orbital Integrals on Reductive Lie Groups and Their Algebrasby Francisco Bulnes - InTech , 2013
The purpose is to present a complete course on global analysis topics and establish some orbital applications of the integration on topological groups and their algebras to harmonic analysis and induced representations in representation theory.
(10259 views)
Calculus and Differential Equationsby John Avery - Learning Development Institute , 2010
The book places emphasis on Mathematics as a human activity and on the people who made it. From the table of contents: Historical background; Differential calculus; Integral calculus; Differential equations; Solutions to the problems.
(15960 views)
Lectures on Disintegration of Measuresby L. Schwartz - Tata Institute of Fundamental Research , 1976
These Notes cover I) disintegration of a measure with respect to a single sigma-algebra, and in part II, measure valued supermartingales and regular disintegration of a measure with respect to an increasing right continuous family of sigma-algebras.
(10861 views)
Lectures on Topics in Analysisby Raghavan Narasimhan - Tata Institute of Fundamental Research , 1965
Topics covered: Differentiable functions in Rn; Manifolds; Vector bundles; Linear differential operators; Cauchy Kovalevski Theorem; Fourier transforms, Plancherel's theorem; Sobolev spaces Hm,p; Elliptic differential operators; etc.
(11996 views)
Special Functions and Their Symmetries: Postgraduate Course in Applied Analysisby Vadim Kuznetsov, Vladimir Kisil - University of Leeds , 2003
This text presents fundamentals of special functions theory and its applications in partial differential equations of mathematical physics. The course covers topics in harmonic, classical and functional analysis, and combinatorics.
(16165 views)
Nonstandard Analysisby J. Ponstein , 2002
This book is concerned with an attempt to introduce the infinitesimals and the other 'nonstandard' numbers in a naive, simpleminded way. Nevertheless, the resulting theory is hoped to be mathematically sound, and to be complete within obvious limits.
(13160 views)
Reader-friendly Introduction to the Measure Theoryby Vasily Nekrasov - Yetanotherquant.de , 2009
This is a very clear and user-friendly introduction to the Lebesgue measure theory. After reading these notes, you will be able to read any book on Real Analysis and will easily understand Lebesgue integral and other advanced topics.
(13569 views)
Transmutations and Applications: a surveyby Sergei M. Sitnik - arXiv , 2010
We consider main transmutation theory topics with many applications, including author's own results. The topics covered are: transmutations for Sturm-Liouville operators, Vekua-Erdelyi-Lowndes transmutations, Sonine and Poisson transmutations, etc.
(10941 views)
Semi-classical analysisby Victor Guillemin, Shlomo Sternberg - Harvard University , 2012
In semi-classical analysis many of the basic results involve asymptotic expansions in which the terms can by computed by symbolic techniques and the focus of these lecture notes will be the 'symbol calculus' that this creates.
(13301 views)
Discrete Oscillation Theoryby Ravi P. Agarwal, at al. - Hindawi Publishing Corporation , 2005
This book is devoted to a rapidly developing branch of the qualitative theory of difference equations with or without delays. It presents the theory of oscillation of difference equations, exhibiting classical as well as recent results in that area.
(13291 views)
Problems in Mathematical Analysisby 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.
(27357 views)
Short introduction to Nonstandard Analysisby 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.
(13239 views)
Theory of the Integralby 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.
(16889 views)
Real Numbers and Fascinating Fractionsby 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.
(15885 views)
Advanced Calculus and Analysisby 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.
(30055 views)
Mathematical Methods for Economic Theory: a tutorialby Martin J. Osborne - University of Toronto , 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.
(19597 views)
Jacobi Operators and Complete Integrable Nonlinear Latticesby Gerald Teschl - American Mathematical Society , 1999
Introduction and a reference to spectral and inverse spectral theory of Jacobi operators and applications of these theories to the Toda and Kac-van Moerbeke hierarchy. It covers second order difference equations, self-adjoint operators, etc.
(13534 views)
Introduction to Methods of Applied Mathematicsby Sean Mauch - Caltech , 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.
(19888 views)
A Course of Modern Analysisby E. T. Whittaker, G. N. Watson - Cambridge University Press , 1920
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.
(43301 views)