## subcategories

**Calculus** (32)

**Calculus of Variations** (6)

**Complex Analysis** (41)

**Differential Equations** (20)

**Functional Analysis** (34)

**Harmonic Analysis** (17)

**Numerical Analysis** (45)

**Real Analysis** (41)

**Tensor Calculus** (15)

**Vector Analysis** (13)

## see also

**Stochastic Calculus** (17)

**Wavelets** (8)

## e-books in Mathematical Analysis & Calculus category

**Measure Theory in Non-Smooth Spaces**

by

**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.

(

**5056**views)

**Applied Analysis**

by

**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.

(

**6695**views)

**An Introduction to Asymptotic Analysis**

by

**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.

(

**5426**views)

**Introduction to Analysis**

by

**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.

(

**7611**views)

**Introduction to Analysis**

by

**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.

(

**5927**views)

**Linear Mathematics In Infinite Dimensions**

by

**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 ...

(

**7591**views)

**Lecture Notes on the Theory of Distributions**

by

**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.

(

**7973**views)

**Bernoulli Polynomials and Applications**

by

**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.

(

**6474**views)

**A Course in Mathematical Analysis**

by

**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.

(

**8307**views)

**Set Theory and Topology: An Introduction to the Foundations of Analysis**

by

**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.

(

**10113**views)

**Multivector Differential Calculus**

by

**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.

(

**9078**views)

**Elementary Mathematical Analysis**

by

**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.

(

**9831**views)

**Orbital Integrals on Reductive Lie Groups and Their Algebras**

by

**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.

(

**8384**views)

**Calculus and Differential Equations**

by

**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.

(

**13380**views)

**Lectures on Disintegration of Measures**

by

**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.

(

**8635**views)

**Lectures on Topics in Analysis**

by

**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.

(

**9723**views)

**Special Functions and Their Symmetries: Postgraduate Course in Applied Analysis**

by

**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.

(

**13774**views)

**Nonstandard Analysis**

by

**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.

(

**10634**views)

**Reader-friendly Introduction to the Measure Theory**

by

**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.

(

**11017**views)

**Transmutations and Applications: a survey**

by

**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.

(

**8958**views)

**Semi-classical analysis**

by

**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.

(

**11177**views)

**Discrete Oscillation Theory**

by

**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.

(

**11127**views)

**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.

(

**24498**views)

**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.

(

**10739**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.

(

**13750**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.

(

**13854**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.

(

**27411**views)

**Mathematical Methods for Economic Theory: a tutorial**

by

**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.

(

**16132**views)

**Jacobi Operators and Complete Integrable Nonlinear Lattices**

by

**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.

(

**11572**views)

**Introduction to Methods of Applied Mathematics**

by

**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.

(

**16896**views)

**A Course of Modern Analysis**

by

**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.

(

**40300**views)