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Mathematical Analysis & Calculus
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e-books in this category
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.
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.
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.
Calculus of Variations
by Erich Miersemann - Leipzig University , 2012
These notes are intended as a straightforward introduction to the calculus of variations which can serve as a textbook for undergraduate and beginning graduate students. The text covers functions of n variables and ordinary differential equations.
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.
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.
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.
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.
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.
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.
Selected Chapters in the Calculus of Variations
by Jürgen Moser - Birkhäuser , 2003
These notes describe the Aubry-Mather-Theory within the calculus of variations. The text consists of the original lectures of Juergen Moser and a bibliographic appendix with comments on the current state of the art in this field of interest.
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.
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.
by Lance Miller , 2005
Contents: Riemann Integration; Algebras of Sets and sigma-Algebras; Measures; Construction of Lebesgue Measure on R; Measureable Functions; Littlewood Principles; Lebesgue Integral and Convergence Theorems; General Mesaure; etc.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.