Appendix A Notation
The following table defines the notation used in this book. Page numbers or references refer to the first appearance of each symbol.
| Symbol | Description | Location |
|---|---|---|
| \(\vect x\cdot\vect y\) | scalar product of two vectors \(\vect x,\vect y\in\mathbb R^N\) | Definition 1.4 |
| \(\lVert\vect x\rVert\) | norm (or length or magnitude) of a vector \(\vect x\in\mathbb R^N\) | Paragraph |
| \(\vect x\times\vect y\) | cross product of two vectors \(\vect x,\vect y\in\mathbb R^3\) | Definition 1.20 |
| \(\frac{\partial f}{\partial x_i}\) | partial derivative with respect to \(x_i\) | Definition 4.2 |
| \(\grad(f)\) | gradient of a scalar valued function | Definition 4.4 |
| \(\nabla f\) | gradient of a scalar valued function | Definition 4.4 |
| \(J_{\vect f}(x)\) | Jacobian matrix | Definition 4.18 |
| \(\frac{\partial}{\partial\vect v}f(\vect a)\) | directional derivative | Definition 4.25 |
| \(\curl(\vect f)\) | curl of a vector field \(\vect f\) on a subset of \(\mathbb R^3\) | Definition 8.14 |
| \(\nabla\times\vect f\) | curl of a vector field \(\vect f\) on a subset of \(\mathbb R^3\) | Definition 8.14 |
| \(\nabla=\left(\frac{\partial}{\partial x_1},\dots,\frac{\partial}{\partial x_N}\right)\) | Nabla operator | Definition 8.15 |
| \(\Delta u=\sum_{k=1}^N\frac{\partial^2 u}{\partial x_k^2}\) | Laplace operator | Definition 12.6 |
