ISE 530 Optimization Methods for Analytics
Alp Ozkan
November 13, 2015
1
Transportation Problem
1.1
Mathematical Formulation
Given
1. the set of Supply Points (S),
2. the set of Demand Points (D),
the transportation problem is dened as nding the minimum c
VE320 Summer 2016
Introduction to Semiconductor Devices
Instructor: Yaping Dan
[email protected]
Lecture 13 Schottky Junction
Work function and electron affinity
Work function: energy different between the vacuum energy level and the Fermi level
Ele
VE320 Summer 2015
Introduction to Semiconductor Devices
Instructor: Yaping Dan
[email protected]
Lecture 18 Metal-Oxide-Semiconductor
CV difference between MIS and MOS
1.0
Flat band
C/C0
C/C0
1.0
Low f
Flat band
Low f
High f
High f
0
Vg= VT
Vg
0
Vg=
VE320 Summer 2016
Introduction to Semiconductor Devices
Instructor: Yaping Dan
[email protected]
Lecture 6 Dopants Ionization
E
Ionization of dopants
Ec
3kT
0.5
1
()
EF
Ev
Non-degenerate semiconductor
Boltzmann Distribution
2
E
E
Ionization of dopa
VE320 Summer 2016
Introduction to Semiconductor Devices
Instructor: Yaping Dan
[email protected]
Lecture 11 Ideal PN junction I-V behavior
From previous lecture
charge carrier transport: zero bias
E
Vb=0 N
D
NA
0 =
thermodynamic
electrostatic
E
0
Vv255
Dr Jing Liu
Question set 13
Summer, 2013
Evaluate the following integrals,
(Ex-1.1)
Z 3Z
4
(40 2xy) dx dy
2
1
(Ex-1.2)
Z 2Z
3
1
1
x y
+
y
x
dy dx
(Ex-1.3)
Z 1Z
1
sin(y 2 ) dy dx
x
0
(Ex-1.4)
Z 0Z
1
ZZ
(Ex-2.1) Evaluate
y
(x + y) dx dy
y
(x + 2y) dA,
Vv255
Dr Jing Liu
Question set 11
Summer, 2013
(Ex-1.1) Find the instantaneous rate of change z = 61 x2 + y 2 at (1, 0) in the direction given by v = h0, 1i.
(Ex-1.2) Find the instantaneous rate of change f (x, y, z) =
x2 +y 2
z2
at (1, 0, 1) in the direc
Vv255
Dr Jing Liu
Question set 10
Summer, 2013
Find the first partial derivatives of the function.
(Ex-1.1)
f (x, y) =
xy
x2 + y 2
f (x, y) =
ex
x + y2
(Ex-1.2)
(Ex-1.3)
f (x, y, z) = ln(x + 2y + 3z)
Find the equation of the tangent plane to the following
Vv255
Dr Jing Liu
Question set 9
Summer, 2013
For each of the following functions, find and sketch the natural domain.
(Ex-1.1)
f (x, y) =
x+y+1
x1
(Ex-1.2)
f (x, y) = x ln(y 2 x)
(Ex-1.3)
f (x, y) =
p
y + 1 + ln(x2 y)
(Ex-1.4)
f (x, y, z) =
p
1 x2 y 2 z
Vv255
Dr Jing Liu
Question set 12
Summer, 2013
Find all critical points and identify their nature for the following functions:
(Ex-1.1) f (x, y) = x2 + y 2 2x 6y + 14
(Ex-1.2) f (x, y) = 3x2 2xy + y 2 8y
(Ex-1.3) f (x, y) = x2 y 2
(Ex-1.4) f (x, y) = x4 +
Vv255 Lecture 1: Complex Number
Dr Jing Liu
May 14, 2013
1 / 43
Basics
L1.1 Complex number
C = cfw_x + yi : x, y R, i
z = x + yi = Re (z) = x;
2
= 1
Im (z) = y
L1.2 Addition, Subtraction
L1.3 Conjugate
L1.4 Modulus, Argument
L1.5 Principal value , Polar f
Vv255 Lecture 3 : Matrix algebra
Dr Jing Liu
May 21, 2013
1/8
Sums and Scalar Multiples
I
Recall that a matrix is a rectangular array of numbers, called entries or elements.
I
A matrix with m rows and n columns is said to be size m n (read, m by n).
L3.1
Vv255 Lecture 13 : Functions of several variables
Dr Jing Liu
June 25, 2013
1/7
Notation and terminology
L13.1 A function f of two variables is a rule that assigns to each ordered pair of real
numbers (x, y ) in a set D a unique real number denoted by f (
Vv255 Lecture 12 : Arc length and curvature
Dr Jing Liu
June 20, 2013
1/5
Length of plane curves (Arc length)
I
I
I
Suppose that y = f (x) is a smooth curve on the interval [a, b].
q
q
Lk = (xk )2 + (yk )2 = (xk )2 + [f (xk ) f (xk1 ]2
f (x )f (x
)
k
k1
A
Vv255 Lecture 7 : Dot product and Orthogonality for Rn
Dr Jing Liu
June 1, 2013
1/4
Dot product (A.K.A inner product)
L7.1 If u and v are column vectors in Rn , then the product
uT v = u1 v1 + u2 v2 + + un vn
is called the inner (dot) product of u and v.
VE320 Summer 2016
Introduction to Semiconductor Devices
Instructor: Yaping Dan
[email protected]
Lecture 16 Metal-Insulator-Semiconductor
MIS structure: work function
Metal
SiO2
Metal
oxide
semiconductor
Vacuum level
Ws
Vg
p- Si
Wm
Vg = 0
eb
EF
Flat
VE320 Summer 2016
Introduction to Semiconductor Devices
Instructor: Yaping Dan
[email protected]
Lecture 17 Metal-Oxide-Semiconductor
MIS and MOS structure
Vg
Vg
Metal
Metal
SiO2
SiO2
n+
n+
p- Si
p- Si
Metal-insulator-semiconductor (MIS)
Metal-oxide
ISE 530 Optimization Methods for Analytics
September 10, 2015
1
AMPL and Linear Programming Softwares
AMPL is an optimization software that is able to handle all linear programs. It
has a demo version at
http:/ampl.com/try-ampl/download-a-demo-version/
De
Viterbi School of Engineering
Daniel J. Epstein Department of Industrial and Systems Engineering
ISE 330: Introduction to Operations Research
Fall 2006 (October 25): Midterm
1 hour 15 minutes
( 9 pages + 1 page extra graph paper + 1 page fun reading )
Que
University of Southern California
Daniel J. Epstein Department of Industrial and Systems Engineering
ISE 330: Introduction to Operations Research
Final Review
Minimum Spanning Tree Problem
Minimum Spanning Tree Problem and Shortest Path Problem
n start wi
University of Southern California
Daniel J. Epstein Department of Industrial and Systems Engineering
ISE 330: Introduction to Operations Research
Midterm Solution: prepared by Jie Liu
(a).
(b).
The optimal basic feasible solution is (11.67,1.67)
The defin
University of Southern California
Daniel J. Epstein Department of Industrial and Systems Engineering
ISE 330: Introduction to Operations Research
Instructor: Elaine Chew
Midterm
21 October 2003
1 hour 15 minutes
( 7 pages )
Question
Total
(a)
15
(b)
10
(c
ISE 330: Introduction to Operations Research
Fall 2006: Monday, December 11, 2PM-4PM
Instructor: Elaine Chew
Final Exam
Twenty pages total (last two are blank)
Two hours
Snape to Sirius: "Give me a reason," he whispered. "Give me a reason to do it,
and I
VE320 Summer 2016
Introduction to Semiconductor Devices
Instructor: Yaping Dan
[email protected]
Lecture 11 Non-ideal PN junction I-V behavior
G-R in depletion region at zero bias
E
Zero Bias Vb=0
ND
NA
0 =
thermodynamic
electrostatic
E
0
=
0 =
Ec
VE320 Summer 2016
Introduction to Semiconductor Devices
Instructor: Yaping Dan
[email protected]
Lecture 2 Quantum well and Energy Band
Outline
Electrons in an Infinite Quantum Well
Electrons in a Finite Quantum Well
Electrons in Periodic Finite