# Mathematical Analysis & Calculus

## subcategories

Stochastic Calculus (18)
Wavelets (8)

## e-books in Mathematical Analysis & Calculus category

Measure Theory in Non-Smooth Spaces
by - De Gruyter Open ,
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.
(3841 views)
Applied Analysis
by - University of Toronto ,
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.
(5487 views)
An Introduction to Asymptotic Analysis
by - Heriot-Watt University ,
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.
(4441 views)
Introduction to Analysis
by - Purdue University ,
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.
(5999 views)

Introduction to Analysis
by - Reed College ,
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.
(4847 views)
Linear Mathematics In Infinite Dimensions
by - The Ohio State University ,
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 ...
(6422 views)
Special Functions, a Review
by - viXra ,
The present document is concerned with the review of the most frequently special functions applied in scientific fields. We review their principal properties and their interactions with different branches especially in mathematics ...
(5543 views)
Lecture Notes on the Theory of Distributions
by - Universitaet Wien ,
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.
(6801 views)
Bernoulli Polynomials and Applications
by - arXiv ,
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.
(5298 views)
A Course in Mathematical Analysis
by - Ginn & company ,
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.
(7002 views)
Multivector Differential Calculus
by - arXiv ,
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.
(8014 views)
Elementary Mathematical Analysis
by - The Macmillan Company ,
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.
(8812 views)
Orbital Integrals on Reductive Lie Groups and Their Algebras
by - InTech ,
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.
(7481 views)
Calculus and Differential Equations
by - Learning Development Institute ,
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.
(12026 views)
Lectures on Disintegration of Measures
by - Tata Institute of Fundamental Research ,
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.
(7466 views)
Lectures on Topics in Analysis
by - Tata Institute of Fundamental Research ,
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.
(8691 views)
Nonstandard Analysis
by ,
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.
(9450 views)
Reader-friendly Introduction to the Measure Theory
by - Yetanotherquant.de ,
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.
(9496 views)
Transmutations and Applications: a survey
by - arXiv ,
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.
(7898 views)
Semi-classical analysis
by - Harvard University ,
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.
(10087 views)
Discrete Oscillation Theory
by - Hindawi Publishing Corporation ,
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.
(10111 views)
Problems in Mathematical Analysis
by - 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.
(23076 views)
Short introduction to Nonstandard Analysis
by - arXiv ,
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.
(9469 views)
Theory of the Integral
by - Polish Mathematical Society ,
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.
(12281 views)
Real Numbers and Fascinating Fractions
by ,
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.
(12829 views)
by - University of Aberdeen ,
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.
(25998 views)
Mathematical Methods for Economic Theory: a tutorial
by - University of Toronto ,
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.
(14401 views)
Jacobi Operators and Complete Integrable Nonlinear Lattices
by - American Mathematical Society ,
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.
(10568 views)
Introduction to Methods of Applied Mathematics
by - Caltech ,
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.
(15516 views)
A Course of Modern Analysis
by - Cambridge University Press ,
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.
(38660 views)