Edward B. Magrab – författare

Advanced Engineering Mathematics with Mathematica® presents advanced analytical solution methods that are used to solve boundary-value problems in engineering and integrates these methods with Mathematica® procedures. It emphasizes the Sturm–Liouville system and the generation and application of orthogonal functions, which are used by the separation of variables method to solve partial differential equations. It introduces the relevant aspects of complex variables, matrices and determinants, Fourier series and transforms, solution techniques for ordinary differential equations, the Laplace transform, and procedures to make ordinary and partial differential equations used in engineering non-dimensional. To show the diverse applications of the material, numerous and widely varied solved boundary value problems are presented.

Advanced Engineering Mathematics with Mathematica® presents advanced analytical solution methods that are used to solve boundary-value problems in engineering and integrates these methods with Mathematica® procedures. It emphasizes the Sturm–Liouville system and the generation and application of orthogonal functions, which are used by the separation of variables method to solve partial differential equations. It introduces the relevant aspects of complex variables, matrices and determinants, Fourier series and transforms, solution techniques for ordinary differential equations, the Laplace transform, and procedures to make ordinary and partial differential equations used in engineering non-dimensional. To show the diverse applications of the material, numerous and widely varied solved boundary value problems are presented.

Free Mathematica 10 Update Included! Now available from www.wiley.com/go/magrab

Updated material includes:- Creating regions and volumes of arbitrary shape and determining their properties: arc length, area, centroid, and area moment of inertia- Performing integrations, solving equations, and determining the maximum and minimum values over regions of arbitrary shape- Solving numerically a class of linear second order partial differential equations in regions of arbitrary shape using finite elements

The first part of the book introduces Mathematica''s syntax and commands useful in solving engineering problems. Tables are used extensively to illustrate families of commands and the effects that different options have on their output. From these tables, one can easily determine which options will satisfy one''s current needs. The order of the material is introduced so that the engineering applicability of the examples increases as one progresses through the chapters. The second part of the book obtains solutions to representative classes of problems in a wide range of engineering specialties. Here, the majority of the solutions are presented as interactive graphics so that the results can be explored parametrically.

Key features:

An Engineer''s Guide to Mathematica is a must-have reference for practitioners, and graduate and undergraduate students who want to learn how to solve engineering problems with Mathematica.

Free Mathematica 10 Update Included! Now available from www.wiley.com/go/magrab

Updated material includes:- Creating regions and volumes of arbitrary shape and determining their properties: arc length, area, centroid, and area moment of inertia- Performing integrations, solving equations, and determining the maximum and minimum values over regions of arbitrary shape- Solving numerically a class of linear second order partial differential equations in regions of arbitrary shape using finite elements

The first part of the book introduces Mathematica''s syntax and commands useful in solving engineering problems. Tables are used extensively to illustrate families of commands and the effects that different options have on their output. From these tables, one can easily determine which options will satisfy one''s current needs. The order of the material is introduced so that the engineering applicability of the examples increases as one progresses through the chapters. The second part of the book obtains solutions to representative classes of problems in a wide range of engineering specialties. Here, the majority of the solutions are presented as interactive graphics so that the results can be explored parametrically.

Key features:

An Engineer''s Guide to Mathematica is a must-have reference for practitioners, and graduate and undergraduate students who want to learn how to solve engineering problems with Mathematica.

Created specifically forthe book are 16 interactive graphics (IGs) that can be used to replicate all numerical calculations appearing in the book and many of its figures, numerically evaluate all formulas appearing in tables, solve all exercises, and determine probabilities and critical values for commonly used probability distributions. After downloading a free program, the IGs are ready to use and are self-explanatory in the context of the material.

This book presents new topics such as Inerters in spring-mass models and attached to beams; fluid loading on beams, plates, and shells; bio-inspired vibration isolation and absorption; coupled bending and torsion of beams; beams with functionally graded materials; as well as a new chapter on the Mindlin/Timoshenko plate theory: rectangular and circular. New applications and enhancements to the previous edition include moving mass on beams; thin beams with attached pendulum; transient response of beams with in-span attachments; and shells to model blood flow in arteries.

This work presents a unified approach to the vibrations of elastic systems as applied to MEMS devices, mechanical components, and civil structures.

Applications include atomic force microscopes, energy harvesters, and carbon nanotubes and consider such complicating effects as squeeze film damping, viscous fluid loading, in-plane forces, and proof mass interactions with their elastic supports. These effects are analyzed as single degree-of-freedom models and as more realistic elastic structures. The governing equations and boundary conditions for beams, plates, and shells with interior and boundary attachments are derived by applying variational calculus to an expression describing the energy of the system. The advantages of this approach regarding the generation of orthogonal functions and the Rayleigh-Ritz method are demonstrated.

A large number of graphs and tables are given to show the impact of various factors on the systems’ natural frequencies, mode shapes, and responses.