Theory of Differential Equations in Engineering and Mechanics

Description

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. Content: 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.