Differential Equations in Engineering and Mechanics
2 volume set -- Theory and Applications
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These two volumes give comprehensive coverage of the essential differential equations students they are likely to encounter in solving engineering and mechanics problems. They cover a very broad range of theories related to solving differential equations, mathematical preliminaries, ODE (n-th order and system of 1st order ODE in matrix form), PDE (1st order, 2nd, and higher order including wave, diffusion, potential, biharmonic equations and more). Plus rarer material such as Green’s function, integrodifferential equations, asymptotic expansion and perturbation, calculus of variations, variational principles, finite difference method. And then a very broad range of problems, including beams and columns, plates, shells, structural dynamics, catenary and cable suspension bridge, nonlinear buckling, transports and waves in fluids, geophysical fluid flows, nonlinear waves and solitons, Maxwell equations, Schrodinger equations, celestial mechanics and fracture mechanics and dynamics. The focus is on the mathematical technique for solving the differential equations involved.
Table of Contents
Book 1 Theory. Mathematical Preliminaries. Introduction to Differential Equations. Ordinary Differential Equations. Series Solutions of 2nd Order ODE. System of First Order Differential Equations. First Order Partial Differential Equations. Higher Order Partial Differential Equations. Green’s Function. Wave, Diffusion and Potential Equations. Eigenfunction Expansions. Integral and Integro-Differential Equations. Asymptotic Expansion and Perturbation. Calculus of Variations. Variational Principles. Finite Difference Method. Appendices. Book 2 Applications. Theory of Beams and Columns. Theory of Plates. Theory of Shells. Structural Dynamics. Catenary and Cable Suspension Bridges. Nonlinear Buckling. Transports and Waves in Fluids. Geophysical Fluid Flows. Nonlinear Waves and Solitons. Mathematical Theory for Maxwell Equations. Quantum Mechanics and Schrodinger Equation. Celestial Mechanics. Fracture Mechanics and Dynamics.
Professor K.T. Chau is Chair Professor of Geotechnical Engineering and former Associate Dean (Research and Development) at the Hong Kong Polytechnic University, where he was awarded the “Teaching Excellence Award in 2012/2013” by the Department of Civil and Environmental Engineering. He is a Fellow of the Hong Kong Institution of Engineers and past President of the Hong Kong Society of Theoretical and Applied Mechanics. He is the Chairman of the Elasticity Committee of the Engineering Mechanics Division of ASCE, the Chairman of the TC103 Technical Committee of Numerical Methods on Geomechanics of International Society of Soil Mechanics and Geotechnical Engineering and the Chairman of the Geomechanics Committee of the Applied Mechanics Division of ASME. He is also the Vice President of the Hong Kong Institute of Science.
His book “Analytic Methods in Geomechanics” was published in 2013 by CRC Press, and it is the first book of its kind, covering, continuum mechanics, tensor analysis, 2-D elasticity, 3-D elasticity, plasticity, fracture mechanics, viscoelasticity, poroelasticity, and dynamics and waves in geomaterials. Since 2012, he has been teaching subjects called “Engineering Analysis” and “Engineering Analysis & Computation” at PolyU. They are mainly using differential equations in engineering analysis.