Mathematics for Physics

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Untangling Complex Systems: A Grand Challenge for Science

Pier Luigi Gentili
August 10, 2018

Complex Systems are natural systems that science is unable to describe exhaustively. Examples of Complex Systems are both unicellular and multicellular living beings; human brains; human immune systems; ecosystems; human societies; the global economy; the climate and geology of our planet. This...

Complex Analysis and Special Functions with Mathematical Software Tools

A. Swaminathan
July 15, 2018

This text emphasizes the special functions that are used in complex analysis. Starting with the algebraic system of complex numbers, it offers an entry-level course on complex analysis of one variable. It presents the study of analytic functions, conformal mapping, analysis of singularities, and...

Ordinary Differential Equations: Applications, Models, and Computing

Charles Roberts
June 15, 2018

In the traditional curriculum, students rarely study nonlinear differential equations and nonlinear systems due to the difficulty or impossibility of computing explicit solutions manually. Although the theory associated with nonlinear systems is advanced, generating a numerical solution with a...

Computational Problems for Physics: With Guided Solutions Using Python

Rubin H. Landau, Manuel José Páez
June 04, 2018

Our future scientists and professionals must be conversant in computational techniques. In order to facilitate integration of computer methods into existing physics courses, this textbook offers a large number of worked examples and problems with fully guided solutions in Python as well as other...

Difference Equations: Theory, Applications and Advanced Topics, Third Edition

Ronald E. Mickens
April 09, 2018

Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of...

Knot Theory: Second Edition

Vassily Olegovich Manturov
March 29, 2018

Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the...

Elastic Waves: High Frequency Theory

Vassily Babich, Aleksei Kiselev
March 27, 2018

Elastic Waves: High Frequency Theory is concerned with mathematical aspects of the theory of high-frequency elastic waves, which is based on the ray method. The foundations of elastodynamics are presented along with the basic theory of plane and spherical waves. The ray method is then described in...

Concise Optics: Concepts, Examples, and Problems

Ajawad I. Haija, M. Z. Numan, W. Larry Freeman
March 01, 2018

This introductory text is a reader friendly treatment of geometrical and physical optics emphasizing problems and solved examples with detailed analysis and helpful commentary. The authors are seasoned educators with decades of experience teaching optics. Their approach is to gradually present...

The Second-Order Adjoint Sensitivity Analysis Methodology

Dan Gabriel Cacuci
February 28, 2018

The Second-Order Adjoint Sensitivity Analysis Methodology generalizes the First-Order Theory presented in the author’s previous books published by CRC Press. This breakthrough has many applications in sensitivity and uncertainty analysis, optimization, data assimilation, model calibration, and...

Applied Functional Analysis

J. Tinsley Oden, Leszek Demkowicz
January 16, 2018

Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject. It motivates students to study functional analysis by providing many contemporary applications and examples drawn from mechanics and science. This well-received textbook starts with a thorough...

Mathematical Methods for Physics and Engineering

Mattias Blennow
December 18, 2017

Suitable for advanced undergraduate and graduate students, this new textbook contains an introduction to the mathematical concepts used in physics and engineering. The entire book is unique in that it draws upon applications from physics, rather than mathematical examples, to ensure students are...

Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems

Andrei D. Polyanin, Valentin F. Zaitsev
November 03, 2017

The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field...