This gives comprehensive coverage of the essential differential equations students they are likely to encounter in solving engineering and mechanics problems across the field -- alongside a more advance volume on applications.
This first volume covers 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 more advanced topics such as Green’s function method, integral and integro-differential equations, asymptotic expansion and perturbation, calculus of variations, variational and related methods, finite difference and numerical methods.
All readers who are concerned with and interested in engineering mechanics problems, climate change, and nanotechnology will find topics covered in these books providing valuable information and mathematics background for their multi-disciplinary research and education.
Table of Contents
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.
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.
"A very unique and useful book, with elaborate formulations, applications and examples; comprehensive and rigorous."
-- Ken P. Chong, George Washington University
"I am delighted to recommend this highly readable book by Professor K. T. Chau (of Hong Kong Polytechnical University) on differential equations as they arise in mechanics and allied areas of the engineering and physical sciences... Chau’s book is essentially encyclopedic, but it is consistently and successfully pedagogic."
-- James Rice, Harvard University in Pure and Applied Geophysics
"An impressive piece of work, including material not just on differential equations but on other elementary and advanced topics, valuable to both students and researchers."
-- John Rudnicki, Northwestern University