The Online Books Page

Functions of real variables

See also what's at Wikipedia, your library, or elsewhere.

• Functions of complex variables

• Convex functions
• Functions of several real variables
• Vector valued functions

• Real variables
• Function of a real variable

• Real Variables With Basic Metric Space Topology (originally published 1993; this version c2007), by Robert B. Ash (PDF files at Wayback Machine)
• Basic Analysis: Introduction to Real Analysis (online edition, c2013), by Jiří Lebl (PDF with commentary at jirka.org)
• Real Analysis (second edition, 2008), by Brian S. Thomson, Judith B. Bruckner, and Andrew M. Bruckner (PDF at classicalrealanalysis.info)
• A Primer of Real Functions (Carus Mathematical Monograph #13; c1960), by Ralph P. Boas (page images at HathiTrust)
• Theory of Functions of a Real Variable (typescript notes by Kahane on lectures by Friedman, New York University, 1952-1953), by Bernard Friedman, ed. by Charles Kahane (page images at HathiTrust; US access only)
• Lectures on the Theory of Functions of Real Variables, by James Pierpont
  • volume 1: page images at Cornell
  • volume 2: page images at Cornell
• Vorlesungen Über Reelle Funktionen (in German; Leipzig and Berlin: B. G. Teubner, 1918), by Constantin Carathéodory
  • multiple formats at Google; US access only
  • multiple formats at archive.org
  • page images at HathiTrust; US access only

• Convex Functions and Dual Extremum Problems (Harvard dissertation, 1963), by R. Tyrrell Rockafellar (PDF at math.washington.edu)

• Vector Calculus (electronic edition, 2013 or later), by Michael Corral (PDF with commentary at mecmath.net)

• Vector Calculus (electronic edition, 2013 or later), by Michael Corral (PDF with commentary at mecmath.net)

Items below (if any) are from related and broader terms.

• A First Course in Complex Analysis (electronic edition, c2017), by Matthias Beck, Gerald Marchesi, Dennis Pixton, and Lucas Sabalka (PDF with commentary at sfsu.edu)
• Complex Variables (revised edition, c2004), by Robert B. Ash and W. Phil Novinger (PDF files at Wayback Machine)
• Convex Geometric Analysis (1999), ed. by Keith M. Ball and Vitali D. Milman (PDF files with commentary at msri.org)
• Current Topics in Complex Algebraic Geometry (1995), ed. by C. Herbert Clemens and János Kollár (PDF files with commentary at msri.org)
• Analytic Functions of a Complex Variable (Carus Mathematical Monograph #2; Chicago: Pub. for the Mathematical Association of America by the Open Court Pub. Co., c1926), by David Raymond Curtiss (page images at HathiTrust)
• Lectures Introductory to the Theory of Functions of Two Complex Variables, by Andrew Russell Forsyth (page images at Cornell)
• Fourier Transforms in the Complex Domain (American Mathematical Society Colloquium Publications v19, 1934), by Raymond E. A. C. Paley and Norbert Wiener (multiple formats at archive.org)
• Alignment Charts; The Teaching of the Calculus of Probability; On the Theory of Complex Functions (Notre Dame Mathematical Lectures #4; 1944), contrib. by Lester R. Ford, A. H. Copeland, and Emil Artin (PDF files at Project Euclid)

• Several Complex Variables (1999), ed. by Michael Schneider and Yum-Tong Siu (PDF files with commentary at msri.org)

• Complexity, Global Politics, and National Security (1997), ed. by David S. Alberts and Thomas J. Czerwinski (PDF at dtic.mil)

• Complex Analysis (c2001), by George L. Cain (PDF files with commentary at gatech.edu)

• Banach Modules and Functors on Categories of Banach Spaces (c1979), by Johann Cigler, Viktor Losert, and Peter W. Michor (PDF in Austria)
• Functors and Categories of Banach Spaces: Tensor Products, Operator Ideals, and Functors on Categories of Banach Spaces (c1978), by Peter W. Michor (PDF in Austria)

• Banach Modules and Functors on Categories of Banach Spaces (c1979), by Johann Cigler, Viktor Losert, and Peter W. Michor (PDF in Austria)

• Harmonic Analysis and the Theory of Probability (Berkeley and Los Angeles: University of California Press, 1955), by S. Bochner (page images at HathiTrust)
• Mathematical Dissertations, For the Use of Students in the Modern Analysis, by J. R. Young (page images at Cornell)
• A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With an Account of The Principal Transcendental Functions (second edition; Cambridge, UK: At the University Press, 1915), by E. T. Whittaker and G. N. Watson (multiple formats at archive.org)

• A Presentation of the Theory of Hermite's Form of Lamé's Equation, by J. Brace Chittenden (page images at Cornell)

• An Elementary Treatise on Spherical Harmonics and Subjects Connected With Them, by N. M. Ferrers (page images at Cornell)

• Grassmann's Space Analysis, by E. W. Hyde (page images at Cornell)

• The Contraction Mapping Principle and Some Applications (EJDE monograph #9, 2009), by R. M. Brooks and Klaus Schmitt (PDF with commentary at ams.org)
• Periodic Solutions for Evolution Equations (EJDE monograph #3, 2002), by Mihai Bostan (PDF with commentary at ams.org)
• Hilbert Space Methods for Partial Differential Equations, by R. E. Showalter (PDF files at ams.org)

• Precise Spectral Asymptotics for Elliptic Operators Acting in Fiberings over Manifolds With Boundary (1984), by Victor Ivrii (DjVu at Toronto)
• Chebyshev and Fourier Spectral Methods (second edition), by John P. Boyd (PDF with commentary at Citeseer)

• Journal of Spectral Theory (partial serial archives)

• Elementary Differential Equations With Boundary Value Problems (free online edition, 2013), by William F. Trench (PDF and LaTeX at trinity.edu)
• Notes on Diffy Qs: Differential Equations for Engineers (online edition, c2013), by Jiří Lebl (illustrated HTML and PDF with commentary at jirka.org)
• Student Solutions Manual for Elementary Differential Equations and Elementary Differential Equations With Boundary Value Problems (free online edition, originally published 2000), by William F. Trench (PDF at trinity.edu)
• Precise Spectral Asymptotics for Elliptic Operators Acting in Fiberings over Manifolds With Boundary (1984), by Victor Ivrii (DjVu at Toronto)

• Interfaces and Free Boundaries (partial serial archives)

• Flavors of Geometry (1997), ed. by Silvio Levy (PDF files with commentary at msri.org)

• Holomorphic Spaces (1998), ed. by Sheldon Jay Axler, John E. McCarthy, and Donald Sarason (PDF files with commentary at msri.org)

• Abel's Theorem and the Allied Theory, Including the Theory of the Theta Functions, by H. F. Baker (page images at Cornell)

• Applications of Global Analysis in Mathematical Physics (1974), by Jerrold E. Marsden (PDF files at Caltech)
• The Convenient Setting of Global Analysis, by Andreas Kriegl and Peter W. Michor (PDF in Austria)

• Singularities of Transition Processes in Dynamical Systems: Qualitative Theory of Critical Delays (EJDE monograph #5, 2004), by A. N. Gorban' (PDF with commentary at ams.org)
• Exploring Discrete Dynamics: The DDLab Manual (Frome, UK: Luniver Press, c2011), by Andrew Wuensche (PDF and page images with commentary in the UK)
• Flavors of Geometry (1997), ed. by Silvio Levy (PDF files with commentary at msri.org)
• The Hopf Bifurcation and Its Applications (1976), by Jerrold E. Marsden and Marjorie McCracken (PDF files at Caltech)
• Jacobi Operators and Completely Integrable Nonlinear Lattices, by Gerald Teschl (PDF and other formats in Austria)

More items available under broader and related terms at left.