The use of actual observations to infer the properties of a model is an inverse problem, which are often difficult as they may not have a unique solution. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. …

## Derivations of Applied Mathematics

Free book Derivations of Applied Mathematics is a book of applied mathematical proofs. If you have seen a mathematical result, if you want to know why the result is so, you can look for the proof here. …

## Linear Algebra, Infinite Dimensions, and Maple

Linear Algebra, Infinite Dimensions, and Maple can be downloaded free of charge in pdf format. These notes evolved in the process of teaching a beginning graduate course in Hilbert Spaces. …

## Elements of Abstract and Linear Algebra

This is a foundational textbook on abstract algebra with emphasis on linear algebra. You may download parts of the book or the entire textbook. It is provided free online in pdf format. This book is a survey of abstract algebra with emphasis on linear algebra. It is intended for students in mathematics, computer science, and the physical sciences. …

## The Geometry and Topology of Three-Manifolds

This is an electronic edition of the 1980 lecture notes distributed by Princeton University. It is available in pdf and postscript formats. …

## Difference Equations to Differential Equations

Difference Equations to Differential Equations: An introduction to calculus by Dan Sloughter is available in pdf format for free. Thorough, relatively concise calculus text. Includes many examples, graphs, and problems. …

## The Calculus of Functions of Several Variables

The Calculus of Functions of Several Variables by Dan Sloughter is available in pdf format for free. In your first exposure to calculus, the primary focus of your attention was on functions involving a single independent variable and a single dependent variable. …

## Multivariable Calculus

Multivariable Calculus by George Cain & James Herod. Download it in pdf format. …

## Elementary Number Theory

Free eBook **“Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach”** by William Stein. This is a textbook about classical elementary number theory and elliptic curves. …

## Mathematics for the Physical Sciences

This free book offers advanced undergraduates and graduate students in physics, engineering, and other natural sciences a solid foundation in several fields of mathematics. …