The Online Books Page

Geometry, Infinitesimal

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

• Geometry

• Calculus

• Calculus of tensors

• Infinitesimal geometry

• Tensor and Vector Analysis, With Applications to Differential Geometry (New York: Ronald Press Co., 1962), by C. E. Springer (page images at HathiTrust)
• Lezioni di Calcolo Differenziale Assoluto (in Italian; Rome: A. Stock, 1925), by Tullio Levi-Civita, ed. by Enrico Persico
  • PDF at Chicago
  • page images at HathiTrust; US access only
• Vector and Tensor Analysis (New York: J. Wiley and Sons; London: Chapman and Hall, c1947), by Louis Brand (page images at HathiTrust)
• Tensor Analysis of Networks (New York: J. Wiley and Sons; London: Chapman and Hall, 1939), by Gabriel Kron (page images at HathiTrust)
• The Application of Tensors to the Analysis of Rotating Electrical Machinery (first edition (16 parts); Schenectady, NY: General Electric Review, c1938), by Gabriel Kron (page images at HathiTrust)
• Diakoptics: Piecewise Solution of Large-Scale Systems (21 chapters in 3 volumes; 1957-1958), by Gabriel Kron (page images at HathiTrust)

• Linear Algebra Done Right (current online edition, 2025), by Sheldon Jay Axler (multiple formats with commentary at axler.net)
• Linear Algebra (first edition; 2013), by David Cherney, Tom Denton, and Andrew Waldron, ed. by Rohit Thomas (PDF with commentary at UC Davis)
• Elementary Linear Algebra (online CC-BY edition, 2012), by Kenneth Kuttler
  • main text: PDF at saylor.org
  • solutions manual: PDF at saylor.org
• Elementary Linear Algebra (second online edition, 1998), by Keith Robert Matthews (PDF files with commentary at numbertheory.org)
• A First Course in Linear Algebra (electronic edition), by Robert A. Beezer (HTML and PDF with commentary at linear.ups.edu)
• Modern Multidimensional Calculus (Reading, MA, et al: Addison-Wesley Pub. Co., c1963), by M. Evans Munroe (page images at HathiTrust)
• Elements of Abstract and Linear Algebra, by Edwin H. Connell (PDF and Postscript at Miami)
• Elementary Divisors and Some Properties of the Lyapunov Mapping X to AX + XA* (Argonne, IL: Argonne National Laboratory, 1961), by Wallace Givens (page images at HathiTrust)

• The Electronic Journal of Linear Algebra (1996-) (full serial archives)

• Linear Algebra (third edition, 2017), by Jim Hefferon (PDF with commentary at smcvt.edu)

• Ends of Complexes (1996), by Bruce Hughes and Andrew Ranicki (PDF in the UK)
• A Treatise on the Line Complex, by C. M. Jessop (page images at Cornell)

• The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds (ca. 1996), ed. by Andrew Ranicki (PDF in the UK)

• Algebraic L-Theory and Topological Manifolds (electronic edition, 2011), by Andrew Ranicki (PDF in the UK)

• Lie Algebras In Particle Physics: From Isospin To Unified Theories (second edition; Boca Raton et al: CRC Press, c2021), by Howard Georgi (PDF with commentary at OAPEN)

• The Octonions (prepublication version, 2001, with links to related materials), by John C. Baez (illustrated HTML at ucr.edu)

• Homogeneous Linear Substitutions, by Harold Hilton (page images at Cornell)
• Determinants, by Laenas Gifford Weld (page images at Cornell)
• A Short Course in the Theory of Determinants, by Laenas Gifford Weld (page images at Cornell)

• 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)

• Operator Algebras and Quantum Statistical Mechanics, by Ola Bratteli and Derek W. Robinson
  • volume I: PDF in Norway
  • volume II: PDF in Norway

• Noncommutative Geometry, Quantum Fields and Motives (prepublication version, ca. 2008), by Alain Connes and Matilde Marcolli (PDF at alainconnes.org)
• Lectures on Graded Differential Algebras and Noncommutative Geometry, by Michel DuBois-Violette (PDF at arxiv.org)

• Journal of Noncommutative Geometry (partial serial archives)

• 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)

• 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)

• Comparison Geometry (1997), ed. by Karsten Grove and Peter Petersen (PDF files with commentary at msri.org)

• Thèses Presentées a la Faculté des Sciences de Paris, Pour Obtenier le Grade de Docteur ès Sciences Mathématiques: Sur le Cercle Considéré Comme Élément Générateur de L'espace; Propositions Données par la Faculté (dissertation in French; Paris: Gauthier-Villars et fils, 1889), by E. Cosserat (Javascript-dependent page images in France)

• Real Variables With Basic Metric Space Topology (originally published 1993; this version c2007), by Robert B. Ash (PDF files at Wayback Machine)

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

• Elementary Calculus: An Infinitesimal Approach (electronic edition; last revised 2022), by H. Jerome Keisler (PDF files at Wisconsin)
• Community Calculus (various electronic editions, c2014), by David Guichard, contrib. by Neal Koblitz and H. Jerome Keisler (PDF and HTML files at whitman.edu)
• Active Calculus (electronic edition, c2013), by Matthew R. Boelkins, contrib. by David Austin and Steven Schlicker (PDF files with commentary at gvsu.edu)
• Calculus for the Life Sciences: A Modeling Approach (2 volumes, intended for different audiences; c2011-2013), by James L. Cornette and Ralph A. Ackerman (PDF files with commentary at Iowa States)
• Calculus I (electronic edition, c2007), by Paul Dawkins (illustrated HTML and PDF with commentary at lamar.edu)
• Calculus II (electronic edition, c2007), by Paul Dawkins (illustrated HTML and PDF with commentary at lamar.edu)
• Calculus III (electronic edition, c2007), by Paul Dawkins (illustrated HTML and PDF with commentary at lamar.edu)
• Calculus (c2002), by Kenneth E. Iverson (PDF at jsoftware.com)
• The Calculus of Functions of Several Variables (electronic edition, c2001), by Dan Sloughter (PDF files at synechism.org)
• Advanced Calculus (revised edition; Boston and London: Jones and Bartlett, c1990), by Lynn H. Loomis and Shlomo Sternberg (PDF at Harvard; 58 MB)
• Calculus I, II, and III (second edition, with student guides and errata corrections; 6 volumes originally published New York: Springer-Verlag, 1985), by Jerrold E. Marsden and Alan Weinstein, contrib. by Frederick H. Soon (PDF files at Caltech)
• An Introduction to Proofs and the Mathematical Vernacular (2015), by Martin V. Day (PDF with commentary at vt.edu)
• Student's Guide to Calculus by J. Marsden and A. Weinstein (3 volumes originally published New York: Springer-Verlag, 1985), by Frederick H. Soon, contrib. by Jerrold E. Marsden and Alan Weinstein
  • Volume I: PDF files at Caltech
  • Volume II: PDF files at Caltech
  • Volume III: PDF files at Caltech
• Calculus Unlimited (c1981), by Jerrold E. Marsden and Alan Weinstein (PDF files at Caltech)
• Calculus (New York et al.: McGraw-Hill, c1963), by Lester R. Ford and L. R. Ford (page images at HathiTrust)
• Calculus and Analytic Geometry (2 volumes; Englewood Cliffs, NJ: Prentice-Hall, 1963), by Melcher P. Fobes and Ruth B. Smyth (page images at HathiTrust)
• Advanced Calculus (Princeton, NJ et al.: D. Van Nostrand Co., c1959), by H. K. Nickerson, D. C. Spencer, and Norman Earl Steenrod (page images at HathiTrust)
• Advanced Calculus (first edition; New York: Prentice-Hall, 1947), by D. V. Widder (page images at HathiTrust)
• Analytical Geometry and Calculus (Cambridge, MA: Addison-Wesley Press, 1942), by H. B. Phillips (page images at HathiTrust)
• Calculus (New York: Prentice-Hall, 1942), by G. E. F. Sherwood and Angus E. Taylor (page images at HathiTrust)
• Calculus for Practical Engineers in a Simple, Quick Engineering Way (Austin, TX: Steck Co., c1942), by Alois Cibulka (page images at HathiTrust; US access only)
• Analytic Geometry and Calculus (second edition; Boston: D. C. Heath and Co., 1963), by William L. Hart (page images at HathiTrust)
• Modern Multidimensional Calculus (Reading, MA, et al: Addison-Wesley Pub. Co., c1963), by M. Evans Munroe (page images at HathiTrust)
• Advanced Calculus, by Edwin Bidwell Wilson (page images at Cornell)
• Calculus (1991; with instructor's manual and study guide), by Gilbert Strang (PDF files at MIT)
• The Calculus for Engineers (London and New York: Edward Arnold, 1897), by John Perry (page images at Google)
• Calculus Made Easy: Being a Very-Simplest Introduction to Those Beautiful Methods Which are Generally Called by the Terrifying Names of the Differential Calculus and the Integral Calculus (second edition, enlarged; London: Macmillan and Co., 1914), by Silvanus P. Thompson (TeX and PDF at Gutenberg)
• Cours d'Analyse de l'École Polytechnique ("premiere partie" only part published; in French; Paris: Gauthier-Villars, 1873), by Charles Hermite (page images at HathiTrust)
• The Differential and Integral Calculus (London: R. Baldwin, ca. 1842), by Augustus De Morgan
  • page images at HathiTrust
  • multiple formats at archive.org
• Differential and Integral Calculus, by Daniel A. Murray (page images at Cornell)
• Differential and Integral Calculus, by Virgil Snyder and John Irwin Hutchinson (page images at Cornell)
• Elementary Calculus: An Approach Using Infinitesimals (electronic edition; based on the 1986 print edition), by H. Jerome Kiesler (PDF files at Wisconsin)
• Elementary Illustrations of the Differential and Integral Calculus, by Augustus De Morgan (page images at Cornell)
• Elementary Textbook on the Calculus, by Virgil Snyder and John Irwin Hutchinson (page images at Cornell)
• Elements of the Differential and Integral Calculus (revised edition; Boston: Ginn and Co., c1911), by William Anthony Granville, ed. by Percey F. Smith (PDF at djm.cc)
• Introduction to Infinitesimal Analysis, by Oswald Veblen and N. J. Lennes (page images at Cornell)
• An Introduction to Mathematical Analysis (Boston et al.: Houghton Mifflin Co., c1921), by Frank Loxley Griffin
  • multiple formats at archive.org
  • page images at HathiTrust; US access only
• An Introduction to the Differential and Integral Calculus (second edition, 1849), by James B. Thomson (page images at Cornell)
• An Introduction to the Study of the Elements of the Differential and Integral Calculus, by Axel Harnack, trans. by George L. Cathcart (page images at Cornell)
• Mathematical Dissertations, For the Use of Students in the Modern Analysis, by J. R. Young (page images at Cornell)
• The Principles of Analytical Calculation (Cambridge, UK: Printed at the University Press, 1803), by Robert Woodhouse (page images at HathiTrust)
• A Defence of Free-Thinking in Mathematics, by George Berkeley (in Ireland)
• An Elementary Treatise on Curves, Functions, and Forces, by Benjamin Peirce
  • volume 1: page images at Cornell
  • volume 2: page images at Cornell
• Vector Calculus (electronic edition, 2013 or later), by Michael Corral (PDF with commentary at mecmath.net)

More items available under broader and related terms at left.