Chapter 7
Multicores, Multiprocessors,
and Clusters
Goal: connecting multiple computers
to get higher performance
Job-level (process-level) parallelism
High throughput for independent jobs
Parallel processing program
Multiprocessors
Scalability, availabil
Intervals of Increase and Decrease
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Inc/Dec Test
10/16/2009
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Rolles Theorem
Let us rst review what we did last time.
Theorem (Rolles Theorem)
Suppose f satises the foll
Section 3.4 Curve Sketching
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3.4 Curve Sketching
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Review
y
y
B
B
Concave Upward
Concave Downward
A
A
x
Math 1850 (University of Toledo)
3.4 Curve Sketching
x
2
Section 5.4 The General Exponential and Logarithmic
Functions
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General Log and Exp
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Review: the Natural Exponential Function
We have seen the natural exponential function f (x ) =
Section 4.1 Areas and Distances
Section 4.2 The Denite Integral
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Areas, Distances and Denite Integrals
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Area of geometric gure
From geometry, we know how to co
Section 3.3 Intervals of Concavity and Points of
Inection
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Review
Last time I covered Increasing/Decreasing Test (to determine the
Maxwells Equations for Time-Varying Fields
The understanding of time-varying EM phenomena (the dynamic case) requires the
use of Maxwells equations as an integrated unit.
The coupling that exists between electric and magnetic fields in the dynamic case is
Magnetostatics
For steady (time-independent, /t = 0) currents, the magnetic fields in a medium
with
are described by the 2nd pair of Maxwells equations:
.B=0
(5.1a)
x H = J (5.1b)
where J is the current density. We also have the relation: B = H (5.2)
0
fo
Electromagnetism: Maxwells Equations
The fundamental relations in electromagnetism (4 coupled PDEs!):
.D=
(4.1a)
V
x E = -B/t
(4.1b)
.B=0
(4.1c)
x H = J + D/t
(4.1d)
Electric field quantities
Magnetic field quantities
E electric field intensity
B magnetic
Section 5.1 Inverse Functions
Section 5.2 The Natural Logarithmic Function
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LN and Inverse Functions
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Denition
The natural logarithmic function is dened by the formula
x
ln(x ) =
Section 5.6 Inverse Trigonometric Functions
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Inverse Trig Functions
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Review
Last time we studied general exponential functions y = ax and logarithmic
functions y = loga x . These
Section 5.3 The Natural Exponential Function
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Natural Exponential Function
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Inverse Functions
A function f is one-to-one if for any x1 = x2 in the domain D (f ), we have
f (x1 ) =
Chapter 6
Storage and Other I/O Topics
I/O devices can be characterized by
Behaviour: input, output, storage
Partner: human or machine
Data rate: bytes/sec, transfers/sec
I/O bus connections
Chapter 6 Storage and Other I/O Topics 2
6.1 Introduction
Introd
Chapter 5
Large and Fast: Exploiting
Memory Hierarchy
Static RAM (SRAM)
Dynamic RAM (DRAM)
50ns 70ns, $20 $75 per GB
Magnetic disk
0.5ns 2.5ns, $2000 $5000 per GB
5.1 Introduction
Memory Technology
5ms 20ms, $0.20 $2 per GB
Ideal memory
Access time of SRA
Chapter 3
Arithmetic for Computers
Operations on integers
Addition and subtraction
Multiplication and division
Dealing with overflow
Floating-point real numbers
Representation and operations
Chapter 3 Arithmetic for Computers 2
3.1 Introduction
Arithmetic
Chapter 2
Instructions: Language of the
Computer
The repertoire of instructions of a
computer
Different computers have different
instruction sets
Early computers had very simple
instruction sets
But with many aspects in common
Simplified implementation
Ma
Chapter 1
Computer Abstractions and
Technology
Progress in computer technology
Makes novel applications feasible
Underpinned by Moores Law
Computers in automobiles
Cell phones
Human genome project
World Wide Web
Search Engines
Computers are pervasive
Chap
MATH 1850 FALL 2009
OPTIMIZATION PROBLEMS
Remember to verify that the answer you get is in fact the required maximum
or minimum value. Points will be taken o if you do not do that. You can verify
the answer by many ways: computing the values at the endpoi
Section 3.5 Optimization Problems
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Introduction
In many practical problems, we would like to know optimal solutions, that
is, soluti
Basic Laws of Vector Algebra
Scalars: m or T
Vectors: E, H, v
Vector algebra governs the laws of:
- addition
- subtraction
- multiplication
of vectors in any given coordinate systems
Also:
- vector representation and transformations in different coordin
Transmission Lines
Most generally, any structure or medium that serves to transfer energy or
information (which also requires energy) between 2 points can be considered a
transmission line.
We focus on transmission lines used for guiding EM signals:
- tel
Physics 2140 Homework #9
7 problems, due March 30
1. A human being can be electrocuted if a current as small as 50 mA passes near the heart. An electrician
working with sweaty hands makes good contact with the two conductors he is holding, one in each han
Physics 2140 Homework #8
6 problems, March 22
1. Two metal plates with area A = 0.1 m2 are 1 cm apart. The plates are connected by a 9 V battery.
(a) What is the capacitance of these plates?
(b) What is the charge on the positive plate?
(c) If the plates
Physics 2140 Homework #7
5 problems, due March 2
q
q
1. The gure shows four equal negative charges, q = 3 C, positioned on the
corners of a square with side a = 1 m. Find the potential at the center of the square.
(Careful: this does require a little calc
Physics 2140 Homework #6
5 problems, due February 23
1. Consider a point charge with Q = 1 mC sitting at the origin. If the potential 1 meter from the point charge
is 10 V, what is the potential 0.5 m from the point charge?
2. When an electron moves from
Physics 2140 Homework #5
7 problems, due February 16
2c
m
2 cm
10 cm
1.
The gure shows an oddly shaped pipe, which is 2 cm thick
everywhere. Water ows in from the left, moving at 10 m/s. Twice
as much water exits the pipe through the bottom branch as thro
Physics 2140 Homework #4
4 problems, due February 9
1. Find the electric eld of a ring with radius R and charge density
, a distance h above the center of the ring.
h
!
R
2. The gure shows a one-dimensional semicircle with radius R and
total charge Q. Fin
Physics 2140 Homework #3
6 problems, due February 2
This is a bit of a grab bag, because I wanted to save most of the integration problems for next week, after the
exam and after weve had more time to talk about it in class. Hope its interesting. Problem
Physics 2140 Homework #2
7 problems, due January 26
1. A uniform electric eld (that is, E is the same at every point) exists in a region between oppositely charged
plates. An electron is released from rest at the surface of the negatively charged plate an