Petre P. Teodorescu

Numerical Analysis with Applications in Mechanics and Engineering: Teodorescu/Numerical Analysis with Applications in Mechanics and Engineering

A much-needed guide on how to use numerical methods to solve practical engineering problemsBridging 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 problemsNumerical 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.

Numerical Differentiation and Integration

This chapter gives introduction to numerical differentiation by means of an expansion into a Taylor series and interpolation polynomials, and numerical integration. The numerical integration formulas include the Newton-C??Tes quadrature formulae, the trapezoid formula, Simpsons formula, Eulers and Gregorys formulae, Rombergs formula, and Chebyshevs quadrature formulae. In addition, the chapter considers quadrature formulae of Gauss type obtained by orthogonal polynomials, calculation of improper integrals, Kantorovichs method, and the Monte Carlo method for calculation of definite integrals. These are followed by applications.

Solution of Algebraic Equations

This chapter deals with the determination of limits of the roots of polynomials, including their separation. Three methods are considered, namely, Lagranges method, the Lobachevski-Graeffe method, and Bernoullis method. In addition, the chapter talks about Bierge-Viete method and Lin methods. These are followed by applications.