Advanced Mathematics For Physicists And Engineers

The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer­ ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before.

Two prominent specialists team up to explore this exciting new frontier in Introduction to Nanotechnology: The New Science of Small. In 24 accessible and visually rich half-hour lectures, you get an in-depth explanation of nanotechnology and how it is possible to work in a domain that is nine orders of magnitude smaller than humans—comparable to the difference in scale between you and the sun.

This book is a significant contribution towards the development of the knowledge for all advanced undergraduate, graduate level students, researchers, and professional engineers leading in the fields of nanotechnology, nanochemistry, macromolecular science and those who have interest in energy and environmental science.

This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered.