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.