Basic Concepts of Mathematics
- http://www.trillia.com/zakon1.html
- This text by Elias Zakon helps the student complete the transition from purely manipulative to rigorous mathematics. Chapters cover Set Theory, the Real Numbers, and n-dimensional Geometry.
Dynamics and Chaos
- http://www.mathphysics.com/dynam/
- Class notes by Evans M. Harrell II for an introductory course on dynamical systems and chaos, taken by mathematicians, engineers, and physicists. This text concentrates on models rather than proofs in order to bring out the concepts of dynamics and chaos. Theorems are carefully stated, though only occasionally proved.
Global Analysis
- http://www.ams.org/online_bks/surv53/
- "The Convenient Setting of Global Analysis" - foundations of differential calculus in infinite dimensions with applications to differential geometry and global analysis by Andreas Kriegl and Peter W. Michor published by AMS in 1997. Whole book or chapters in crosslinked PDF.
Linear Methods of Applied Mathematics
- http://www.mathphysics.com/pde/
- Textbook suitable for a first course on partial differential equations, Fourier series and special functions, and integral equations by Evans M. Harrell II and James V. Herod. HTML, RTF and PDF with Maple and Mathematica worksheets.
Numerics - Interactive
- http://www.weblearn.hs-bremen.de/risse/MAI/docs/numerics.pdf
- In this book by Thomas Risse, basic numerical algorithms are presented and implemented in order to determine the precision of computation, to solve systems of linear equations, to evaluate elementary functions, to find zeros, to integrate and to solve ordinary differential equations numerically. The performance of different algorithms can be compared.
Plane Geometry
- http://www.math.rutgers.edu/~zeilberg/GT.html
- Shalosh B. Ekhad XIV. A fully illustrated and completely self-contained Elementary Geometry textbook (ca. 2050), downloaded from the future by Doron Zeilberger. Entirely written in Maple.
Potential Theory
- http://www.geocities.com/fabrikant_books/
- Two texts by V.I. Fabrikant: Applications of Potential Theory in Mechanics, Selection of New Results (1989); Mixed Boundary Value Problems of Potential Theory and their Applications in Engineering (1991). Text in PDF with figures separately in JPG.
Stochastic Calculus
- http://www.chiark.greenend.org.uk/~alanb/
- A fairly complete elementary introduction to the basics of stochastic integration with respect to continuous semimartingales by Alan Bain. All the theory usually needed for basic mathematical finance. Sixty pages in DVI, postscript, and PDF.