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 vect∨The meaning of Christoffel symbols in covariant differentiation;How to derive the curvature tens∨How quaternions can be used to describe vector rotations in 3-D space.