## Peter Monk

Print publication date: 2003

Print ISBN-13: 9780198508885

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198508885.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use.  Subscriber: null; date: 17 September 2019

# (p.427) Appendix B Vector and Differential Identities

Source:
Finite Element Methods for Maxwell's Equations
Publisher:
Oxford University Press

# B.1 Vector identities

1. (1) a x b = -b x a.

2. (2) a · (b x c = (a x b) · c = (c x a) · b.

# B.2 Differential identities

These differential identities are valid for smooth functions/vector functions:

(B.1)
$Display mathematics$
(B.2)
$Display mathematics$
(B.3)
$Display mathematics$
(B.4)
$Display mathematics$
(B.5)
$Display mathematics$
(B.6)
$Display mathematics$
(B.7)
$Display mathematics$
(B.8)
$Display mathematics$
In the (B.6) and (B.8), ▵u = (▵u1, ▵u2, ▵u3) in Cartesian coordinates only.

# B.3 Differential identities on a surface

Let S be a smooth surface with unit normal υ‎ and let v and p be smooth functions defined a neighborhood of S. The following identities hold:

$Display mathematics$
The differntial equalities in this and the previous subsection can be extended to less smooth functions as discussed in the text.