Mathematical Nomenclature and Symbols Physical Units

"What's in a name?" Shakespeare: Romeo and Juliet, ii, 2

A few general rules are observed: vectors are marked as bold characters, e.g., x, n, or r. The product a ■ b of two vectors a, b e IRn is always understood as the scalar product aTb = Xn=1 aibi. Matrices are indicated with sans serif font, e.g., A. The list below gives our mathematical symbols and operators.

IRn the n-dimensional vector space of real (column) vectors with n components

V gradient operator V :=Vx = = >•••> dr) applied to a scalar-valued function f := defines the quantity on the left side of an equation by the term on the right side of the equation = quantity on the left side of the equation is set identically to the term on the right side of the equation = indicates a first-order Taylor series expansion xT the transposed vector, xT := (x1xn) is a row vector e; unit vector associated with the i th coordinate axis

1l identity matrix of appropriate dimension

M(m, n) set of matrices with m rows and n columns

Superscripts indicate attributes of a quantity, e.g., Ltol, a bolometric luminosity. Subscripts are used for indexing and counting. The subscript j is always used to refer to one of the binary components. To avoid confusion with the symbols R and L, the radii and luminosities of the binary components are written in calligraphic style R and L if they are in absolute (or solar) units. Symbols used in this book are listed in Appendix F.

Throughout this book we mostly use SI units. However, when referring to original papers or figures, CGS or even special units such as A cannot be avoided. Where possible we give only generic physical dimensions of quantities, such as mass, length, time, energy.

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