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