Notation and colours

The book follows the notation of Favata’s notes throughout. Where Gurtin’s An Introduction to Continuum Mechanics, the course’s other reference, differs, the second column says how.

Symbols

Symbol	Meaning	Gurtin
$E$ , $V$	Euclidean point space, its translation (vector) space	same
$u \cdot v$ , $u \times v$	scalar and vector product	same
$u \cdot v \times w$	$u \cdot (v \times w)$ , the scalar triple product	same
${e_{i}}$	a fixed right-handed orthonormal basis	same
$u_{i}$ , $A_{ij}$	components, with summation over repeated indices	same
$δ_{ij}$ , $ϵ_{ijk}$	Kronecker delta, Ricci (permutation) symbol	same
$Lin$	second-order tensors, linear maps $V \to V$	same
$Sym$ , $Skw$	symmetric and skew tensors	same
$Orth$ , $Rot$	orthogonal tensors, rotations ( $det = 1$ )	$Orth^{+}$ for rotations
$a \otimes b$	dyad: $(a \otimes b) v = (b \cdot v) a$	same
$A \cdot B$	$tr (A^{⊤} B)$ , scalar product of tensors	same; others write $A : B$
$A^{*}$	cofactor, $(det A) A^{- ⊤}$	same
$x$	reference position	$X$
$f$	deformation	$χ$
$f (x)$	current position	$x$
$F = \nabla f$	deformation gradient	same
$f_{i, j}$	$\partial f_{i} / \partial x_{j}$	same
$u$ , $H$	displacement, displacement gradient $F - I$	same
$det F$	volume ratio	$J$
$C$ , $U$	right Cauchy–Green and right stretch tensors	same
$R$	the rotation of the polar decomposition	same
$d ℓ_{0}$ , $d a_{0}$ , $d v_{0}$	reference length, area, volume elements	$d X$ , …
$n_{ref}$ , $n_{cur}$	reference and current normals	$n_{R}$ , $n$

Colours

Colours carry meaning, and the same colour means the same thing in the text and in the demos, in both themes.

	Colour	Used for
$e_{1}$ , $e_{2}$ , $e_{3}$	red, green, blue	the family $i = 1, 2, 3$ : basis vectors, the columns $A e_{i}$ , the terms of a sum
$x$	violet	an input vector you drag
$Ax$	darker violet	its image
$a$	orange	eigenvectors, principal directions
$reference$	grey, dashed	the reference configuration, what was there before
$current$	teal	the current configuration, what is there after
$n$	pink	normals
red shading		something gone wrong: orientation flipped, $det \leq 0$

Marks

Essential: one of the few definitions everything else is built on (Index of terms).
beyond the notes: added for this book: a proof the notes skip, an example, a result from the syllabus the notes have not reached yet. Everything unmarked is in Favata’s notes.
Proofs, solutions and asides are folded; click to open them. A link with a dotted underline opens what it names in place; click it again to close.