Book:Books/Analysis

The following books covered on $\mathsf{Pr} \infty \mathsf{fWiki}$ discuss analysis in its various forms.

For a comprehensive list of books referenced on $\mathsf{Pr} \infty \mathsf{fWiki}$ (and more), see Books.

Books

• 1591: Franciscus Vieta: In Artem Analyticam Isagoge ("Introduction to the Analytical Arts")
• 1711: Isaac Newton: Analysis per Quantitatem Series
• 1730: Jacobo Stirling: Methodus Differentialis
• 1748: Maria Gaëtana Agnesi: Instituzioni Analitiche ad uso della Gioventù Italiana
• 1748: Leonhard Paul Euler: Introductio in Analysin Infinitorum
• 1808: C. Kramp: Élémens d'arithmétique universelle
• 1821: Augustin Louis Cauchy: Cours d'analyse
• 1824: Niels Henrik Abel: Mémoire sur les équations algébriques ou on démontre l'impossibilité de la résolution de l'équation générale du cinquième degré
• 1882-87: Camille Jordan: Cours d'Analyse de l'École Polytechnique

• 1902: E.T. Whittaker: A Course of Modern Analysis
  • 1915: E.T. Whittaker and G.N. Watson: A Course of Modern Analysis (2nd ed.)
  • 1920: E.T. Whittaker and G.N. Watson: A Course of Modern Analysis (3rd ed.)
  • 1927: E.T. Whittaker and G.N. Watson: A Course of Modern Analysis (4th ed.)

• 1902: Édouard Goursat: Cours d'Analyse Mathématique: Volume $\text { 1 }$
  • 1904: Édouard Goursat: A Course in Mathematical Analysis: Volume $\text { 1 }$ (translated by Earle Raymond Hedrick) (translation of Cours d'Analyse Mathématique, Volume 1)
  • 1910 -- 1913: Édouard Goursat: Cours d'Analyse Mathématique: Volume $\text { 1 }$ (2nd ed.)
  • 1924: Édouard Goursat: Cours d'Analyse Mathématique: Volume $\text { 1 }$ (4th ed.)

• 1905: Édouard Goursat: Cours d'Analyse Mathématique: Volume $\text { 2 }$
  • 1910 -- 1913: Édouard Goursat: Cours d'Analyse Mathématique: Volume $\text { 2 }$ (2nd ed.)
    • 1916: Édouard Goursat: A Course in Mathematical Analysis: Volume $\text { 2 (Part 1) }$ (translated by Earle Raymond Hedrick and Otto Dunkel) (Part 1) (translation of Cours d'Analyse Mathématique, Volume 2)
    • 1917: Édouard Goursat: A Course in Mathematical Analysis: Volume $\text { 2 (Part 2) }$ (translated by Earle Raymond Hedrick and Otto Dunkel) (Part 2) (translation of Cours d'Analyse Mathématique, Volume 2)
  • 1925: Édouard Goursat: Cours d'Analyse Mathématique: Volume $\text { 2 }$ (4th ed.)

• 1910 -- 1913: Édouard Goursat: Cours d'Analyse Mathématique: Volume $\text { 3 }$ (2nd ed.)
  • 1923: Édouard Goursat: Cours d'Analyse Mathématique: Volume $\text { 3 }$ (3rd ed.)

• 1913: Hermann Weyl: The Concept of a Riemann Surface

• 1918: Hermann Weyl: The Continuum: A Critical Examination of the Foundation of Analysis

• 1925: George Pólya and Gábor Szegő: Problems and Theorems in Analysis I (translated by Dorothée Aeppli)
• 1925: George Pólya and Gábor Szegő: Problems and Theorems in Analysis II (translated by C.E. Billigheimer)

• 1930: Edmund Landau: Grundlagen der Analysis
  • 1951: Edmund Landau: Foundations of Analysis (translated by F. Steinhardt)

• 1931: Lawrence M. Graves: Theory of Functions of Real Variables

• 1938: C.V. Durell and Alan Robson: Shorter Advanced Trigonometry

• 1942: James M. Hyslop: Infinite Series
  • 1945: James M. Hyslop: Infinite Series (2nd ed.)
  • 1947: James M. Hyslop: Infinite Series (3rd ed.)

• 1953: Walter Rudin: Principles of Mathematical Analysis
  • 1964: Walter Rudin: Principles of Mathematical Analysis (2nd ed.)

• 1957: Tom M. Apostol: Mathematical Analysis
  • 1973: Tom M. Apostol: Mathematical Analysis (2nd ed.)

• 1958: N.G. de Bruijn: Asymptotic Methods in Analysis
  • 1961: N.G. de Bruijn: Asymptotic Methods in Analysis (2nd ed.)
  • 1970: N.G. de Bruijn: Asymptotic Methods in Analysis (3rd ed.)

• 1960: J. Dieudonné: Foundations of Modern Analysis
• 1965: Edwin Hewitt and Karl Stromberg: Real and Abstract Analysis

• 1966: Walter Rudin: Real and Complex Analysis
• 1967: Errett Bishop: Foundations of Constructive Analysis
• 1970: J.C. Burkill and H. Burkill: A Second Course in Mathematical Analysis
• 1970: Avner Friedman: Foundations of Modern Analysis
• 1970: R. Tyrell Rockafellar: Convex Analysis
• 1973: L.V. Ahlfors: Conformal Invariants: Topics in Geometric Function Theory

• 1989: James R. Kirkwood: An Introduction to Analysis
  • 1995: James R. Kirkwood: An Introduction to Analysis (2nd ed.)

• 1990: George Gasper and Mizan Rahman: Basic Hypergeometric Series
  • 2004: George Gasper and Mizan Rahman: Basic Hypergeometric Series (2nd ed.)

• 1993: Serge Lang: Real and Functional Analysis (3nd ed.)
• 1994: Brian S. Thomson: Symmetric Properties of Real Functions
• 1996: Eric Schechter: Handbook of Analysis and its Foundations
• 1997: Fernando Q. Gouvea: p-adic Numbers: An Introduction
• 1998: Ram Prakash Kanwal: Generalized Functions: Theory and Technique (2nd ed.)
• 2003: Charles C. Pugh: Real Mathematical Analysis (2nd ed.)
• 2005: G. Auliac and J.-Y. Caby: Mathématiques, Topologie et Analyse
• 2007: Svetlana Katok: p-adic Analysis Compared with Real
• 2011: Robert G. Bartle and Donald R. Sherbert: Introduction to Real Analysis (4th ed.)
• 2011: Graham R. Allan and H. Garth Dales: Introduction to Banach Spaces and Algebras
• 2014: Kenneth Falconer: Fractal Geometry: Mathematical Foundations and Applications (3rd ed.)

Logarithms

• 1614: John Napier: Mirifici Logarithmorum Canonis Descriptio

Analytical Geometry

• 1828: Julius Plücker: Analytisch-Geometrische Entwicklungen: Volume $\text { 1 }$ ("Developments in Analytic Geometry")
• 1831: Julius Plücker: Analytisch-Geometrische Entwicklungen: Volume $\text { 2 }$ ("Developments in Analytic Geometry")

• 1851: Elias Loomis: Elements of Analytical Geometry and of the Differential and Integral Calculus

• 1924: D.M.Y. Sommerville: Analytical Conics
  • 1929: D.M.Y. Sommerville: Analytical Conics (2nd ed.)
  • 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.)

Real Analysis

• 1908: G.H. Hardy: A Course of Pure Mathematics
  • 1952: G.H. Hardy: A Course of Pure Mathematics (10th ed.)

• 1926: J.E. Littlewood: Elements of the Theory of Real Functions

• 1930: E.G. Phillips: A Course of Analysis
  • 1939: E.G. Phillips: A Course of Analysis (2nd ed.)

• 1958: J.A. Green: Sequences and Series

• 1963: H.L. Royden: Real Analysis
  • 1968: H.L. Royden: Real Analysis (2nd ed.)
  • 1988: H.L. Royden: Real Analysis (3rd ed.)
  • 2010: H.L. Royden and P.M. Fitzpatrick: Real Analysis (4th ed.)

• 1964: Richard R. Goldberg: Methods of Real Analysis
  • 1976: Richard R. Goldberg: Methods of Real Analysis (2nd ed.)

• 1964: William K. Smith: Limits and Continuity

• 1965: Wendell Fleming: Functions of Several Variables
  • 1977: Wendell Fleming: Functions of Several Variables (2nd ed.)

• 1968: A.N. Kolmogorov and S.V. Fomin‎: Introductory Real Analysis (translated by Richard A. Silverman)
• 1969: R.P. Boas: A Primer of Real Functions
• 1973: C.R.J. Clapham: Introduction to Mathematical Analysis
• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach
• 1981: Charalambos D. Aliprantis and Owen Burkinshaw: Principles of Real Analysis
• 1981: Karl R. Stromberg: An Introduction to Classical Real Analysis
• 1989: R.M. Dudley: Real Analysis and Probability
• 1989: Elon Lages Lima: Análise Real 1
• 1981: Charalambos D. Aliprantis and Owen Burkinshaw: Principles of Real Analysis (3rd ed.)
• 2000: N.L. Carothers: Real Analysis
• 2000: Ebbe Thue Poulsen and Klaus Thomsen: Indledning til Matematisk Analyse 1a
• 2005: Elias M. Stein and Rami Shakarchi: Real Analysis: Measure Theory, Integration, and Hilbert Spaces
• 2007: Robert B. Ash: Real Variables with Basic Metric Space Topology

Calculus

• 1656: John Wallis: Arithmetica Infinitorum
• 1669: Isaac Newton: On Analysis by Means of Equations with an Infinite Number of Terms
• 1670: Isaac Barrow: Lectiones Geometricae
• 1696: Guillaume de l'Hôpital: L'Analyse des Infiniment Petits
• 1734: George Berkeley: The Analyst
• 1736: Isaac Newton: The Method of Fluxions and Infinite Series
• 1742: Colin MacLaurin: A Treatise of Fluxions
• 1755: Leonhard Paul Euler: Institutiones Calculi Differentialis
• 1768-94: Leonhard Paul Euler: Institutiones Calculi Integralis
• 1797: Lazare Carnot: Réflexions sur la métaphysique du calcul infinitésimal
• 1800: L.F.A. Arbogast: Du Calcul des Dérivations

• 1896: Joseph Edwards: Integral Calculus for Beginners: With an Introduction to the Study of Differential Equations

• 1897: Horace Lamb: An Elementary Course of Infinitesimal Calculus
  • 1902: Horace Lamb: An Elementary Course of Infinitesimal Calculus (2nd ed.)
  • 1919: Horace Lamb: An Elementary Course of Infinitesimal Calculus (3rd ed.)

• 1912: Edwin Bidwell Wilson: Advanced Calculus

• 1914: G.W. Caunt: Introduction to Infinitesimal Calculus

• 1933: C.V. Durell and A. Robson: Elementary Calculus: Volume $\text { I }$
• 1934: C.V. Durell and A. Robson: Elementary Calculus: Volume $\text { II }$

• 1934: Richard Courant: Differential and Integral Calculus: Volume $\text { I }$ (translated by E.J. McShane)
  • 1937: Richard Courant: Differential and Integral Calculus: Volume $\text { I }$ (2nd ed.) (translated by E.J. McShane)

• 1936: Richard Courant: Differential and Integral Calculus: Volume $\text { II }$ (translated by E.J. McShane)

• 1939: R.P. Gillespie: Integration
  • 1944: R.P. Gillespie: Integration (2nd ed.)

• 1946: P. Abbott: Teach Yourself Calculus

• 1947: David V. Widder: Advanced Calculus
  • 1961: David V. Widder: Advanced Calculus (2nd ed.)

• 1951: J.C. Burkill: The Lebesgue Integral

• 1951: George B. Thomas, Jr.: Calculus and Analytic Geometry
  • 1968: George B. Thomas, Jr.: Calculus and Analytic Geometry (4th ed.)
  • 1996: George B. Thomas, Jr. and Ross L. Finney: Calculus and Analytic Geometry (9th ed.)

• 1958: P.J. Hilton: Differential Calculus
• 1960: P.J. Hilton: Partial Derivatives

• 1963: Murray R. Spiegel: Theory and Problems of Advanced Calculus
  • 1974: Murray R. Spiegel: Theory and Problems of Advanced Calculus (SI ed.)

• 1964: Frank Ayres, Jr.: Theory and Problems of Differential and Integral Calculus (2nd ed.)
  • 1972: Frank Ayres, Jr. and J.C. Ault: Theory and Problems of Differential and Integral Calculus (SI ed.)

• 1966: Walter Ledermann: Multiple Integrals
• 1967: Tom M. Apostol: Calculus Volume 1
• 1967: Michael Spivak: Calculus (4th ed. 2008)

• 1968: Lynn H. Loomis and Shlomo Sternberg: Advanced Calculus
  • 1990: Lynn H. Loomis and Shlomo Sternberg: Advanced Calculus (2nd ed.)

• 1969: Tom M. Apostol: Calculus Volume 2
• 1971: Wilfred Kaplan and Donald J. Lewis: Calculus and Linear Algebra

• 1978: Roland E. Larson and Robert P. Hostetler: Calculus
  • 2001: Roland E. Larson, Robert P. Hostetler, Bruce H. Edwards and David E. Heyd: Calculus (7th ed.)
  • 2005: Roland E. Larson, Robert P. Hostetler and Bruce H. Edwards: Calculus (8th ed.)
  • 2009: Roland E. Larson and Bruce H. Edwards: Calculus (9th ed.)

• 1980: John C. Amazigo and Lester A. Rubenfeld: Advanced Calculus
• 1983: K.G. Binmore: Calculus
• 1997: H.A. Priestley: Introduction to Integration
• 2017: David Acheson: The Calculus Story

Complex Analysis

• 1806: Jean-Robert Argand: Essai sur une manière de représenter les quantités imaginaires dans les constructions géométriques
• 1935: E.T. Copson: An Introduction to the Theory of Functions of a Complex Variable

• 1940: E.G. Phillips: Functions of a Complex Variable
  • 1957: E.G. Phillips: Functions of a Complex Variable (8th ed.)

• 1953: Lars V. Ahlfors: Complex Analysis
  • 1966: Lars V. Ahlfors: Complex Analysis (2nd ed.)
  • 1979: Lars V. Ahlfors: Complex Analysis (3rd ed.)

• 1960: Walter Ledermann: Complex Numbers
• 1964: Murray R. Spiegel: Theory and Problems of Complex Variables

• 1973: John B. Conway: Functions of One Complex Variable
  • 1978: John B. Conway: Functions of One Complex Variable (2nd ed.)

• 1974: Peter Henrici: Applied and Computational Complex Analysis: Volume $\text { 1 }$
• 1977: Peter Henrici: Applied and Computational Complex Analysis: Volume $\text { 2 }$

• 1977: Serge Lang: Complex Analysis
• 1983: Ian Stewart and David Tall: Complex Analysis (The Hitchhiker's Guide to the Plane)

• 1985: H.A. Priestley: Introduction to Complex Analysis
  • 1990: H.A. Priestley: Introduction to Complex Analysis (revised ed.)

• 1986: Peter Henrici: Applied and Computational Complex Analysis: Volume $\text { 3 }$
• 1991: Reinhold Remmert: Theory of Complex Functions (2nd ed.)
• 1999: Jerrold E. Marsden and Michael J. Hoffman: Basic Complex Analysis (3rd ed.)
• 2001: Christian Berg: Kompleks funktionsteori
• 2002: Robert E. Greene and Steven G. Krantz: Function Theory of One Complex Variable
• 2004: James Ward Brown and Ruel V. Churchill: Complex Variables and Applications (7th ed.)
• 2005: Eberhard Freitag and Rolf Busam: Complex Analysis
• 2006: Robert E. Greene and Steven G. Krantz: Function Theory of One Complex Variable (3rd ed.)
• 2008: David C. Ullrich: Complex Made Simple
• 2009: Murray R. Spiegel, Seymour Lipschutz, John Schiller and Dennis Spellman: Complex Variables (2nd ed.)

Trigonometric Series

• 1906: H.S. Carslaw: Introduction to the Theory of Fourier's Series and Integrals
  • 1921: H.S. Carslaw: Introduction to the Theory of Fourier's Series and Integrals (2nd ed.)
  • 1930: H.S. Carslaw: Introduction to the Theory of Fourier's Series and Integrals (3rd ed.)

• 1935: Antoni Zygmund: Trigonometrical Series
• 1961: I.N. Sneddon: Fourier Series

• 1965: Ronald N. Bracewell: The Fourier Transform and its Applications
  • 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.)

• 1968: Peter D. Robinson: Fourier and Laplace Transforms
• 1981: H.J. Nussbaumer: Fast Fourier Transform and Convolution Algorithms

• 2004: Loukas Grafakos: Classical Fourier Analysis
  • 2008: Loukas Grafakos: Classical Fourier Analysis (2nd ed.)
  • 2014: Loukas Grafakos: Classical Fourier Analysis (3rd ed.)

Laplace Transforms

• 1965: Murray R. Spiegel: Theory and Problems of Laplace Transforms

Functional Analysis

• 1927: A.R. Forsyth: Calculus of Variations
• 1946: Gilbert A. Bliss: Lectures on the Calculus of Variations

• 1948: E. Hille and R.S. Phillips: Functional Analysis and Semi-Groups
  • 1957: E. Hille and R.S. Phillips: Functional Analysis and Semi-Groups (2nd ed.)
  • 1996: E. Hille and R.S. Phillips: Functional Analysis and Semi-Groups (Revised ed.)

• 1950: Charles Fox: An Introduction to the Calculus of Variations
  • 1963: Charles Fox: An Introduction to the Calculus of Variations (2nd ed.)

• 1957: A.N. Kolmogorov and S.V. Fomin: Elements of the Theory of Functions and Functional Analysis: Volume $\text { 1 }$ (translated by Leo F. Boron)
• 1961: A.N. Kolmogorov and S.V. Fomin: Elements of the Theory of Functions and Functional Analysis: Volume $\text { 2 }$ (translated by Leo F. Boron)
• 1962: N.I. Akhiezer: The Calculus of Variations (translated by Aline H. Frink)
• 1963: I.M. Gelfand and S.V. Fomin: Calculus of Variations (translated by Richard A. Silverman)

• 1967: Paul R. Halmos: A Hilbert Space Problem Book
  • 1982: Paul R. Halmos: A Hilbert Space Problem Book (2nd ed.)

• 1978: Erwin Kreyszig: Introductory Functional Analysis with Applications
  • 1989: Erwin Kreyszig: Introductory Functional Analysis with Applications (2nd ed.)

• 1980: Kösaku Yosida: Functional Analysis (6th ed.)

• 1981: George Leitmann: The Calculus of Variations and Optimal Control
• 1981: Michael Reed and Barry Simon: Methods of Modern Mathematical Physics I: Functional Analysis (Revised ed.)
• 1990: Nino Boccara: Functional Analysis: An Introduction for Physicists
• 1990: John B. Conway: A Course in Functional Analysis
• 1990: Frigyes Riesz and Béla Sz.-Nagy: Functional Analysis (translated by Leo F. Boron)
• 1991: Walter Rudin: Functional Analysis (2nd ed.)
• 1992: Hans Sagan: Introduction to the Calculus of Variations
• 1995: Gert K. Pedersen: Analysis Now (2nd ed.)
• 1996: Georgi E. Shilov: Elementary Functional Analysis
• 1996: Mariano Giaquinta and Stefan Hildebrandt: Calculus of Variations I: The Lagrangian Formalism
• 1996: Mariano Giaquinta and Stefan Hildebrandt: Calculus of Variations II: The Hamiltonian Formalism
• 1997: Reinhold Meise and Dietmar Vogt: Introduction to Functional Analysis
• 1998: George Bachman and Lawrence Narici: Functional Analysis
• 1998: Ram Prakash Kanwal: Generalized Functions: Theory and Technique (2nd ed.)
• 2001: Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos Santalucía, Jan Pelant and Václav Zizler: Functional Analysis and Infinite-Dimensional Geometry
• 2002: Peter D. Lax: Functional Analysis
• 2002: Martin Schechter: Principles of Functional Analysis (2nd ed.)
• 2004: Bruce van Brunt: The Calculus of Variations
• 2004: Yuli Eidelman, Vitali Milman and Antonis Tsolomitis: Functional Analysis: An Introduction
• 2004: John A. Burns: Introduction to The Calculus of Variations and Control with Modern Applications
• 2009: Srinivasan Kesavan: Functional Analysis
• 2009: Barbara D. MacCluer: Elementary Functional Analysis
• 2010: Haïm Brezis: Functional Analysis, Sobolev Spaces and Partial Differential Equations
• 2011: Elias M. Stein and Rami Shakarchi: Functional Analysis: An Introduction to Further Topics in Analysis
• 2012: Alberto Bressan: Lecture Notes on Functional Analysis: With Applications to Linear Partial Differential Equations
• 2013: Philippe G. Ciarlet: Linear and Nonlinear Functional Analysis with Applications
• 2013: Francis Clarke: Functional Analysis, Calculus of Variations and Optimal Control
• 2014: Mark Kot: A First Course in the Calculus of Variations
• 2014: Joseph Muscat: Functional Analysis: An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras
• 2017: Manfred Einsiedler and Thomas Ward: Functional Analysis, Spectral Theory, and Applications
• 2017: Amol Sasane: A Friendly Approach to Functional Analysis
• 2018: Theo Bühler and Dietmar A. Salamon: Functional Analysis
• 2020: James C. Robinson: Introduction to Functional Analysis

Measure Theory

• 1950: Paul R. Halmos: Measure Theory
• 1953: Marshall E. Munroe: Introduction to Measure and Integration

• 1980: Donald L. Cohn: Measure Theory
  • 2013: Donald L. Cohn: Measure Theory (2nd ed.)

• 1981: G. de Barra: Measure Theory and Integration
• 1992: Lawrence C. Evans and Ronald F. Gariepy: Measure Theory and Fine Properties of Functions
• 2001: Christian Berg and Tage Gutmann Madsen: Mål- og integralteori
• 2005: René L. Schilling: Measures, Integrals and Martingales

Dynamical Systems Theory

• 1999: Clark Robinson: Dynamical Systems: Stability, Symbolic Dynamics, and Chaos
• 2002: Michael Brin and Garrett Stuck: Introduction to Dynamical Systems

Special Functions

• 1829: Carl Jacobi: Fundamenta Nova Theoriae Functionum Ellipticarum

• 1895: Andrew Gray and G.B. Mathews: A Treatise on Bessel Functions
  • 1922: Andrew Gray and G.B. Mathews: A Treatise on Bessel Functions (2nd ed.) (with T.M. MacRobert)

• 1916: J.L. Jensen: An Elementary Exposition of the Theory of the Gamma Function

• 1946: F.E. Relton: Applied Bessel Functions

• 1981: Leonard Lewin: Polylogarithms and Associated Functions

• 1985: Aleksandar Ivić: The Riemann Zeta-Function

• 1986: Larry C. Andrews: Special Functions for Engineers and Applied Mathematicians
  • 1992: Larry C. Andrews: Special Functions of Mathematics for Engineers (second edition of Special Functions for Engineers and Applied Mathematicians from 1985)

• 1999: George E. Andrews, Richard Askey and Ranjan Roy: Special Functions