In this comprehensive monograph, the authors apply modern mathematical methods to the study of mechanical and physical phenomena or techniques in acoustics, optics, and electrostatics, where classical mathematical tools fail. They present a general method of approaching problems, pointing out different aspects and difficulties that may occur. With respect to the theory of distributions, only the results and the principle theorems are given as well as some mathematical results. The book also systematically deals with a large number of applications to problems of general Newtonian mechanics, as well as to problems pertaining to the mechanics of deformable solids and physics. Special attention is placed upon the introduction of corresponding mathematical models. Addressed to a wide circle of readers who use mathematical methods in their work: applied mathematicians, engineers in various branches, as well as physicists, while also benefiting students in various fields.

A much-needed guide on how to use numerical methods to solve practical engineering problems

Bridging the gap between mathematics and engineering, "Numerical Analysis with Applications in Mechanics and Engineering" arms readers with powerful tools for solving real-world problems in mechanics, physics, and civil and mechanical engineering. Unlike most books on numerical analysis, this outstanding work links theory and application, explains the mathematics in simple engineering terms, and clearly demonstrates how to use numerical methods to obtain solutions and interpret results.

Each chapter is devoted to a unique analytical methodology, including a detailed theoretical presentation and emphasis on practical computation. Ample numerical examples and applications round out the discussion, illustrating how to work out specific problems of mechanics, physics, or engineering. Readers will learn the core purpose of each technique, develop hands-on problem-solving skills, and get a complete picture of the studied phenomenon. Coverage includes: How to deal with errors in numerical analysisApproaches for solving problems in linear and nonlinear systemsMethods of interpolation and approximation of functionsFormulas and calculations for numerical differentiation and integrationIntegration of ordinary and partial differential equationsOptimization methods and solutions for programming problems

"Numerical Analysis with Applications in Mechanics and Engineering "is a one-of-a-kind guide for engineers using mathematical models and methods, as well as for physicists and mathematicians interested in engineering problems.