Differential Operators in Vector Analysis and the
Laplacian of a Vector in the Curvilinear
Orthogonal System
C.T. Tai, Radiation Laboratory, Department of Electrical
Engineering and Computer Science, The University of Michigan,
Ann Arbor, Michigan 48109-2

V15.1 Del Operator
1. Symbolic notation: the del operator
To have a compact notation, wide use is made of the symbolic operator del (some call
it nabla):
(1)
=
i+
j+
k
x
y
z
M
Recall that the product of
and the function M (x, y, z) is understood to be
.

Using the Del operator
Let us introduce the real valued vector function (or 3 variable scalar function)
type F : V3 ! R, for which F (hx; y; zi) = F (x; y; z) 2 R, and the vector
valued vector function (shortly vector function) type !
w : V3 ! V3 , for wh

Electromagnetic Theory
Prof. D.K. Ghosh
Department of Physics
Indian Institute of Technology, Bombay
Lecture - 5
Laplacian
In the last lecture we had talked about the curl of a vector field. Before that we
introduced the ideas about a divergence of a vect

2
1
Maxwells Equations
1. Maxwells Equations
the receiving antennas. Away from the sources, that is, in source-free regions of space,
Maxwells equations take the simpler form:
E=
H=
B
t
D
t
(source-free Maxwells equations)
(1.1.2)
D=0
B=0
The qualitative

Chapter 6
Maxwells Equations for
Electromagnetic Waves
6.1
Vector Operations
Any physical or mathematical quantity whose amplitude may be decomposed into
directional components often is represented conveniently as a vector. In this discussion, vectors are

Electromagnetism - Lecture 2
Electric Fields
Review of Vector Calculus
Differential form of Gausss Law
Poissons and Laplaces Equations
Solutions of Poissons Equation
Methods of Calculating Electric Fields
Examples of Electric Fields
1
Vector Calculu

Basic Mathematics
The Laplacian
R Horan & M Lavelle
The aim of this package is to provide a short self
assessment programme for students who want to
apply the Laplacian operator.
c 2005 rhoran@plymouth.ac.uk , mlavelle@plymouth.ac.uk
Copyright
Last Revis