Vectors and Tensors by Example

If you have been confused by vectors, vector calculus, tensor analysis, or quaternions, this book is for you. Packed with examples, including Matlab examples, this book will show you: How to use Matlab to calculate dot and cross products, and solve linear equations; How to prove any vector identity using Cartesian tensors; How to derive the expressions for gradient, divergence, Laplacian, and curl in any curvilinear coordinate system; How to understand covariant and contravariant components of a vector; The meaning of Christoffel symbols in covariant differentiation; How to derive the curvature tensor; How quaternions can be used to describe vector rotations in 3-D space.