Here is a list of online books about Applied Mathematics and Mathematical Physics in various formats available for free :
Advanced Analytic Methods in Science and Engineering
          by Hung Cheng, 2004, PDF
Advanced Graph Theory and Combinatorial Optimization
          by Alexander Schrijver, 64 pp, 430KB, PDF
Analytical Classical Dynamics: An intermediate level course
          by Richard Fitzpatrick, 2007, 315 pages, 3.1MB, PDF
Applications of global analysis in mathematical physics
          by Jerrold E. Marsden, 1974, 277 pages, 17MB, PDF
Applied Combinatorics
          by Mitchel T. Keller, William T. Trotter, 2013, 345 pp, 25MB, PDF
Applied Finite Mathematics
          by Rupinder Sekhon, 2011, 347 pp
Applied Mathematical Programming Using Algebraic Systems
          by Bruce A. McCarl, Thomas H. Spreen, 2011, 567 pages, 1.7MB, PDF
Applied Mathematics by Example: Theory
          by Jeremy Pickles, 2010, 134 pages, PDF
Applied Mathematics by Example: Exercises
          by Jeremy Pickles, 2010, 121 pages, PDF
The Basics of Financial Mathematics
          by Richard F. Bass, 2003, 106 pages, 0.5MB, PDF
The Chaos Hypertextbook
          by Glenn Elert, 2007
Combinatorics on Words: Christoffel Words and Repetition in Words
          by J. Berstel, A. Lauve, C. Reutenauer, F. Saliola, 2008, 202 pages, 2.6MB, PDF
The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy
          by John D. Williams, 1982, 286 pages, 7.9MB, PDF
Complex and Adaptive Dynamical Systems: A Primer
          by Claudius Gros, 2008, 276 pages, 4.2MB, PDF
Computable Integrability
          by Alexey Shabat, Elena Kartashova, 2011, 174 pp, 780KB, PDF
Computational Turbulent Incompressible Flow
          by Johan Hoffman, Claes Johnson, 2007, 415 pages, 22MB, PDF
Constrained mechanics and Lie theory
          by Robert Hermann, 1992
Constructive Nonlinear Control
          by R. Sepulchre, M. Jankovic, P. Kokotovic, 1996, 323 pages, 1.5MB, PDF
Convex Optimization
          by Stephen Boyd, Lieven Vandenberghe, 2004, 730 pages, 5.5MB, PDF
Cook-Book Of Mathematics
          by Viatcheslav Vinogradov, 1999, 116 pages, 700KB, PDF
A Course in Combinatorial Optimization
          by Alexander Schrijver, 2012, 221 pp, 1.4MB, PDF
Cryptography, A Study on Secret Writings
          by Andre Langie, 1922, 192 pages, 15MB, PDF
Derivations of Applied Mathematics
          by Thaddeus H. Black, 2008, 492 pages, 2.4MB, PDF
Design of Comparative Experiments
          by R. A. Bailey, 2008, 348 Pages, PDF
Digraphs: Theory, Algorithms and Applications
          by Jorgen Bang-Jensen, Gregory Gutin, 2002, 772 pages, 3.5MB, PDF
Discrete Dynamical Systems
          by Arild Wikan, 2013, 254 pp, 5.7MB, PDF
Discrete Mathematics with Algorithms
          by M. O. Albertson, J. P. Hutchinson, 1988, 560 pp, multiple PDF files
Discrete Optimization
          by Guido Schaefer, 2012, 97 pp, 690KB, PDF
Discrete Oscillation Theory
          by Ravi P. Agarwal, at al. 2005
Distributed-Parameter Port-Hamiltonian Systems
          by Hans Zwart, Birgit Jacob, 2009, 208 pages, 1.2MB, PDF
Doing Physics with Quaternions
          by Douglas B. Sweetser, 2005, 157 pages, 560KB, PDF
Dynamic Graphs, Quaternion Analysis, and Unified Field Theory
          by Douglas B. Sweetser, 2005, 76 pages, 1.3MB, PDF
Dynamic Systems
          by John Hassler, 87 pages, PDF
Dynamical Systems
          by Shlomo Sternberg, 2000, 151 pp, 1MB, PDF
Dynamics, Ergodic Theory, and Geometry
          by Boris Hasselblatt, 2007, 334 pages, PDF
Dynamics in One Complex Variable
          by John Milnor, 1991, 146 pages, PDF
Econometrics
          by Michael Creel, 2008, 376 pages, 2.6MB, PDF
Elementary catastrophe theory
          by Peter W. Michor, 1985, 9.9MB, PDF
Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists
          by W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral, 2007, 3.2MB, PDF
Elementary Symbolic Dynamics and Chaos in Dissipative Systems
          by Bai-Lin Hao, 1989, 475 pp, 20MB, PDF
An elementary treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics by William Elwood Byerly, 1893, 309 pages, 1.3MB, PDF
Elements for Physics: Quantities, Qualities, and Intrinsic Theories
          by Albert Tarantola, 2006, 280 pages, 3.7MB, PDF
Elements of Applied Mathematics
          by Cobb Herbert E. 1911
Encyclopedia of Dynamical Systems
          by D. Anosov, at al. 2009
Entropy and Partial Differential Equations
          by Lawrence C. Evans, 2003, 213 pages, 1MB, PDF
Ergodic Optimization, Zero Temperature Limits and the Max-plus Algebra
          by A. T. Baraviera, R. Leplaideur, A. O. Lopes, 2013, 106 pp, 1MB, PDF
Ergodic Theory of Differentiable Dynamical Systems
          by Lai-Sang Young, 2010, 48 pages, 430KB, PDF
Foundations of Cryptography
          by Oded Goldreich, 1998, PS
Functional and Structured Tensor Analysis for Engineers
          by R. M. Brannon, 2003, 323 pages, 3.6MB, PDF
Game Theory
          by Thomas S. Ferguson, 2008, PDF
Games, Fixed Points and Mathematical Economics
          by Christian-Oliver Ewald, 2007, 134 pages, 860KB, PDF
Games of No Chance 3
          by Michael H. Albert, Richard J. Nowakowski, 2009, 586 pages, PDF
Gauge theory for fiber bundles
          by Peter W. Michor, 1998, 106 pages, 600KB, PDF
Geometrical Theory of Dynamical Systems
          by Nils Berglund, 2001, 85 pages, 2.2MB, PDF
The Geometrization of Physics
          by Richard S. Palais, 1981, 107 pages, 630KB, PDF
Geometry and Quantum Field Theory
          by Pavel Etingof, MIT, 2002
Geometry in Physics
          by Alexander Altland, 2010, 79 pages, 3MB, PDF
Geometry, Topology and Physics, part 2
          by Maximilian Kreuzer, 2010, PDF
Graduate-Level Course in Game Theory
          by Jim Ratliff, 1997, PDF
Handbook of Applied Cryptography
          by Alfred Menezes, Paul van Oorschot, Scott Vanstone, 1996, 816 pages, PDF
Inside Out: Inverse Problems and Applications
          edited by Gunther Uhlmann, 2003, 400 pages, PDF
Integer Programming and Combinatorial Optimization
          by Dimitris Bertsimas, 2004, PDF
Introducing categories to the practicing physicist
          by Bob Coecke, 2008, 30 pages, 280KB, PDF
Introduction to Algebraic and Constructive Quantum Field Theory
          by John C. Baez, Irving E. Segal and Zhengfang Zhou, 1992
Introduction to Braided Geometry and q-Minkowski Space
          by Shahn Majid, 1994, 60 pages, 680KB, PDF
Introduction to Dynamical Systems: A Hands-on Approach with Maxima
          by Jaime E. Villate, 2006, 450KB, PDF
Introduction to Graphs
          by Alexander K. Hartmann, Martin Weigt, 2006, 45 pages, 340KB, PDF
Introduction to Groups, Invariants and Particles
          by Frank W. K. Firk, 2000, 162 pages, 0.4MB, PDF
An Introduction to Hyperbolic Analysis
          by Andrei Khrennikov, Gavriel Segre, 2005, 42 pages, 350KB, PDF
An Introduction to Mathematical Optimal Control Theory
          by Lawrence C. Evans, 2010, 126 pages, 690KB, PDF
Introduction to Non-Linear Algebra
          by V. Dolotin, A. Morozov, 2008, 141 pages, 1.8MB, PDF
Introduction to Physics
          by Igor Dolgachev, 1996, 286 pages, PDF
Introduction to Potential Theory via Applications
          by Christian Kuehn, 2008
An Introduction to Statistical Signal Processing
          by R. M. Gray, L. D. Davisson, 2005, 478 pages, 2.9MB, PDF
Introduction to Tensor Calculus and Continuum Mechanics
          by J. H. Heinbockel, 2001, 432 pages, 4MB, ZIP/PDF
Introduction to the Mathematics of Wavelets
          by Willard Miller, 2006, 294 pages, 1.3MB, PDF
Introduction to Vertex Algebras
          by Christophe Nozaradan, 2008, 94 pages, 700KB, PDF
Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem
          by Peter B. Gilkey, 1984, DVI/PS
Inverse Problem Theory and Methods for Model Parameter Estimation
          by Albert Tarantola, 2004, 358 pages, 20MB, PDF
Invitation to Dynamical Systems
          by Edward R. Scheinerman, 1995, 384 pages, 3.3MB, PDF, book and solution guide
Isometrica: A Geometrical Introduction to Planar Crystallographic Groups
          by George Baloglou, 2007, 473 pages, 7.3MB, PDF
Iterative Methods for Optimization
          by C.T. Kelley, 1987, 188 pp, 1.4MB, PDF
Iterative Methods in Combinatorial Optimization
          by Lap Chi Lau, R. Ravi, M. Singh, 2011, 229 pp, 1MB, PDF
Lecture Notes on Non-Cooperative Game Theory
          by Tamer Basar, 2010, 142 pages, 700KB, PDF
Lectures on Classical Mechanics
          by John C. Baez, 2005, 76 pages, 500KB, PDF
Lectures on complex geometry, Calabi-Yau manifolds and toric geometry
          by Vincent Bouchard, 2007, 63 pages, 530KB, PDF
Lectures On Approximation By Polynomials
          by J.G. Burkill, 1959, 75 pp, 310KB, PDF
Lectures on Optimization: Theory and Algorithms
          by John Cea, 1978, 237 pp, 1.1MB, PDF
Lectures on Topics In One-Parameter Bifurcation Problems
          by P. Rabier, 1985, 238 pp, 1.3MB, PDF
Lie Theory and Special Functions
          by Willard Miller, 1968, 338 pages, PDF
Linear Methods of Applied Mathematics
          by Evans M. Harrell II, James V. Herod, 2000
Linear Systems Theory and Introductory Algebraic Geometry
          by Robert Hermann, 1974
Math in Society
          by David Lippman, 2011, 214 pp, 3.7MB, PDF
Mathematical Control Theory: Deterministic Finite Dimensional Systems
          by Eduardo D. Sontag, 1998, 544 pages, 2.4MB, PDF
Mathematical Methods
          by Mihir Sen, Joseph M. Powers, 2010, 432 pages, 3.8MB, PDF
Mathematical Methods for Economic Theory: a tutorial
          by Martin J. Osborne, 2007
Mathematical Methods in Quantum Mechanics
          by Gerald Teschl, 2009, 317 pages, 1.8MB, PDF
Mathematical Methods of Engineering Analysis
          by Erhan Cinlar, Robert J. Vanderbei, 2000, 119 pages, 480KB, PDF
Mathematical Population Genetics
          by Warren J Ewens, 2006, 85 pages, 410KB, PDF
Mathematical Tools for Physics
          by James Nearing, 2006, 569 pages, 3.8MB, PDF
Mathematics and Biology: The Interface, Challenges, and Opportunities
          edited by Simon A. Levin, 2009
Mathematics for Algorithm and Systems Analysis
          by Edward A. Bender, S. Gill Williamson, 2005, 256 pages, PDF
Mathematics of Cartography
          by Cynthia Lanius, 2003
Mathematics of Human Motion: from Animation towards Simulation
          by A.I. Zhmakin, 2011, 91 pages, 740KB, PDF
The Mathematics of Investment
          by William L. Hart, 1924
Mathematics of the Discrete Fourier Transform (DFT): with Audio Applications
          by Julius O. Smith III, 2007, 322 pages
Matroid Decomposition
          by Klaus Truemper, 1998, PS
More Games of No Chance
          edited by Richard J. Nowakowski, 2002, PS/PDF
Music and Mathematics
          by Thomas M. Fiore, 2009, 36 pages, 250KB, PDF
Noncommutative Geometry, Quantum Fields and Motives
          by Alain Connes, Matilde Marcolli, 2007, 705 pages, 6.4MB, PDF
Nonlinear Programming
          by Robert Freund, 2004, PDF
Notes on Optimization
          by Pravin Varaiya, 1972, 140 pages, 760KB, PDF
The Octonions
          by John C. Baez, 2001, 56 pages, 420KB, PDF
On 2D Inverse Problems
          Wikibooks, 2013, online html
Optimization Algorithms on Matrix Manifolds
          by P.-A. Absil, R. Mahony, R. Sepulchre, 2007, 240 pages, PDF
Optimization and Dynamical Systems
          by U. Helmke, J. B. Moore, 1996, 414 pages, 2.8MB, PDF
Partial Differential Equations for Finance
          by Robert V. Kohn, 2003, PDF/PS
Partial Differential Equations of Mathematical Physics
          by William W. Symes, 2006, 105 pages, 490KB, PDF
Perturbation theory of dynamical systems
          by Nils Berglund, 2001, 111 pages, 4.8MB, PDF
Physics, Topology, Logic and Computation: A Rosetta Stone
          by John C. Baez, Mike Stay, 2009, 73 pages, 780KB, PDF
A Primer of Quaternions
          by Arthur S. Hathaway, 2006, 70 pages, 570KB, PDF
Probability for Finance
          by Patrick Roger, 2010, 115 pages, 4.3MB, PDF
Queueing Theory
          by Ivo Adan, Jacques Resing, 2002, 180 pages, 810KB, PDF
Random Matrix Models and Their Applications
          edited by Pavel Bleher, Alexander Its, 2001, 438 pages, PS/PDF
Robust Optimization
          by A. Ben-Tal, L. El Ghaoui, A. Nemirovski, 2009, 564 pp, PDF
A Short Course on Approximation Theory
          by N. L. Carothers, 2009, 159 pp, 780KB, PDF
Singularities of Transition Processes in Dynamical Systems
          by Alexander N. Gorban, 2004, 55 pp, 760KB, PDF
Special Fuzzy Matrices for Social Scientists
          by W. B. V. Kandasamy, F. Smarandache, K. Ilanthenral, 2007, 2MB, PDF
Statistical Mechanics of Nonequilibrium Liquids
          by Denis J. Evans, Gary P. Morriss, 2007, 318 pages, 15MB, PDF
Statistical Method in Economics
          by Victor Chernozhukov, 2006, 63 pages, 670KB, PDF
Statistical Tools for Economists
          by Daniel McFadden, 2001, PDF
Statistical Treatment of Experimental Data
          by Hugh D. Young, 1962, PDF
Statistics, Probability, and Game Theory: papers in honor of David Blackwell
          by David Blackwell, at al. 1996
Stochastic Control for Economic Models
          by David A. Kendrick, 2002, 297 pages, 1.9MB, PDF
Stochastic Processes for Finance
          by Patrick Roger, 2010, 104 pages, 4.2MB, PDF
Structural Analysis of Discrete Data with Econometric Applications
          by Charles F. Manski, Daniel McFadden, 1981, 504 pages, 17MB, ZIP/PDF
Substitutions in Dynamics, Arithmetics, and Combinatorics
          by Pierre Arnoux, et al. 2002, PS
Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists
          by W. B. V. Kandasamy, F. Smarandache, K. Amal, 2008, 280 pages, 900KB, PDF
Synchronization and Linearity: An Algebra for Discrete Event Systems
          by F. Baccelli, G. Cohen, G. J. Olsder, J. Quadrat, 1993, 501 pages, 4.1MB, PDF
Techniques of Applied Mathematics
          by Andrew Fowler, 2005, 141 pages, 1.8MB, PDF
Topics in Combinatorial Optimization
          by Michel Goemans, 2004, PDF
Topics in dynamics I: Flows
          by Edward Nelson, 1969, 122 pages, 2.7MB, PDF
Topics in the Geometric Theory of Integrable Mechanical Systems
          by Robert Hermann, 1984
Topics in the Geometric Theory of Linear Systems
          by Robert Hermann, 1984
Traveling Wave Solutions of Parabolic Systems
          by A. Volpert, V. Volpert, V. Volpert, 2000, 448 pages, 3MB, PDF
Unsolved Problems in Mathematical Systems and Control Theory
          by Vincent D. Blondel, Alexandre Megretski, 2004, 350 pages, 1.4MB, PDF
Vector Analysis and Quaternions
          by Alexander Macfarlane, 1906, 65 pages, 460KB, PDF
Vector Bundles and an Introduction to Gauge Theory
          by Steven Bradlow, 1998, PDF/DVI/TeX/PS
Von Neumann Algebras and Local Quantum Theory
          by I. F. Wilde, 2009, 88 pages, 460KB, PDF
Voting, Arbitration & Fair Division: Mathematics of Social Choice
          by Marcus Pivato, 2007, 181 pages, 3MB, PDF
Why the Boundary of a Round Drop Becomes a Curve of Order Four
          by A. N. Varchenko and P. I. Etingof, 1992, 72 pages, 4.5MB, PDF
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