When is a vector field uniquely specified?
F
is specified.
Suppose
A=
?
Can we solve for F
NO.
' =F
+
F
Suppose
NO.
f(x,y,z) is any scalar field
will give same result.
. F is specified.
=
' =F
+
F
B
B(x,y,z) is any vector field
will give same r
Miller Indexing
Points, Directions and Planes in a crystal structure
Required for properly knowing the location of different
kinds of atoms, vacancies or defects etc in a solid
Crystallographic Points
Point coordinates for unit cell
center are
z
111
a/2,
SEGMENTATION
AND
TARGETING IN
MARKETING
Prof. Sameer Mathur,
Ph.D.
Agenda
What is Segmentation
Segmentation Bases
Target Marketing Strategies
Sameer Mathur
BuddingMarkets.com
Indian Institute of Management,
Lucknow
Marketing Professor 2013
Marketing Prof
Outline of the week
1
Rank and solvabilty of homogeneous and inhomogeneous systems(lec
4)
2
Rn , Subspaces, Linear spans (lec 5)
3
Linear dependence/independence, basis and dimension (lec 5)
4
Row/Column ranks of a matrix, equality (lec 6)
5
Rank-nullity
Bonding and material properties
ISSUES TO ADDRESS.
How bonding occurs?
Types of bonds
Properties inferred from bonding
Stable Electron Configurations
Stable electron configurations.
have complete s and p subshells
tend to be unreactive.
Adapted from
MA 106: Linear Algebra
Instructors: Prof. Akhil Ranjan and Prof. S. Krishnan
January 5, 2017
1 / 42
Text and references
Main Text:
E. Kreyszig, Advanced Engineering Mathematics, 8th ed. (Chapters 6 and
7)
Additional references:
1) Notes by Prof. I.K. Rana
Outline of the week
1
Rank and solvabilty (lec 4)
2
Rn , Subspaces, Linear spans (lec 5)
3
Linear dependence/independence, basis and dimension (lec 5)
4
Row/Column ranks of a matrix, equality (lec 6)
5
Homogeneous/Inhomogeneous linear systems (lec 6)
()
J
Outline of the week
1
Gram-Schmidt process(Lec 10)
2
Eigenvalue problem (Lec 10)
3
Diagonalization (Lec11)
January 23, 2017
1/1
Gram-Schmidt process
We noted that expanding vectors in an orthogonal/orthonormal basis is a
simple matter.
Question: How to fi
MM 152: Materials and Technology
Spring 2016
Dipti Gupta
Department of Metallurgical Engineering and Materials Science
Indian Institute of Technology - Bombay
Course Material:
Materials Science and Engineering: An Introduction
W.D. Callister, Jr., 8th ed
5 Definitions of
Marketing
Prof. Sameer Mathur,
Ph.D.
Agenda
Sameer Mathur
BuddingMarkets.com
Indian Institute of Management,
Lucknow
Marketing Professor 2013
Marketing Professor 2009 2013
Ph.D. and M.S. (Marketing) 2003 2009
st
1 iton
n
defn
http:/www.m