Mathematical Models in Applied Mechanics
Mathematical Models in Applied Mechanics is perfectly designed for final year undergraduate and graduate students. This textbook utilizes the power of mathematics in solving practical, scientific and technical problems through mathematical modeling techniques. Taken from real-life situations, the text includes twenty-one ordered problems, which gives students the ability to develop the skills necessary to create new situational models.
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Mathematical Models in Applied Mechanics is perfectly designed for final year undergraduate and graduate students. This textbook utilizes the power of mathematics in solving practical, scientific and technical problems through mathematical modeling techniques. Taken from real-life situations, the text includes twenty-one ordered problems, which gives students the ability to develop the skills necessary to create new situational models. Booknews This book, designed for final year undergraduate and graduate students, demonstrates the power of mathematics in solving practical, scientific, and technical problems through mathematical modeling techniques, and develops the theory and methods of partial differential equations. Chapters cover problem formulation, wave motion, elliptic problems, diffusion, and asymptotic methods for non- linear problems. The text includes 21 problems taken from real situations, and students are encouraged to develop the skill of constructing their own models of new situations. Some background in applied analysis and mechanics is assumed. Annotation c. Book News, Inc., Portland, OR (booknews.com)
1Problem Formulation1.1Introduction11.2Normalization of the problem21.3Perturbation procedures51.4Analytical methods for ordinary differential equations91.5Classical analogies212Wave Motion2.1Transverse waves on a stretched string372.2Second-order hyperbolic equations and weak solutions452.3Linear hyperbolic systems in two independent variables532.4Multiple reflections and use of transforms592.5Wave motion with two or more space variables652.6Waveguides and dispersion742.7Quasi-linear systems813Elliptic Problems3.1Potential theory953.2Variational methods and variational inequalities1023.3Free-boundary problems1073.4Application of complex variable methods1163.5Quasi-static continuum models1284Diffusion4.1The diffusion equation1454.2Stefan problems1544.3Weak solutions1644.4Diffusion and convection1754.5Non-linear diffusion1865Asymptotic Methods for Non-Linear Problems5.1Non-linear ordinary differential equations2035.2Thin layers and lubrication theory2195.3Boundary layers2335.4Far-field solutions249Bibliography269Index273
\ From The CriticsThis book, designed for final year undergraduate and graduate students, demonstrates the power of mathematics in solving practical, scientific, and technical problems through mathematical modeling techniques, and develops the theory and methods of partial differential equations. Chapters cover problem formulation, wave motion, elliptic problems, diffusion, and asymptotic methods for non- linear problems. The text includes 21 problems taken from real situations, and students are encouraged to develop the skill of constructing their own models of new situations. Some background in applied analysis and mechanics is assumed. Annotation c. Book News, Inc., Portland, OR (booknews.com)\ \
