ABSTRACT

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.

chapter 1|81 pages

Mathematical Preliminaries

chapter 2|30 pages

Introduction to Differential Equations

chapter 3|114 pages

Ordinary Differential Equations

chapter 4|94 pages

Series Solutions of Second Order ODEs

chapter 5|-154 pages

Systems of first order differential equations

chapter 8|46 pages

Green’s Function Method

chapter 9|69 pages

Wave, Diffusion and Potential Equations

chapter 10|36 pages

Eigenfunction Expansions

chapter 11|62 pages

Integral and Integro-Differential Equations

chapter 12|66 pages

Asymptotic Expansion and Perturbation

chapter 13|44 pages

Calculus of Variations

chapter 14|34 pages

Variational and Related Methods

chapter 15|50 pages

Finite Difference and Numerical Methods