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 pr
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 ti
Section 3.4 Curve Sketching
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Review
y
y
B
B
Concave Upward
Concave Downward
A
A
x
M
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
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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Section 3.3 Intervals of Concavity and Points of
Inection
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Review
Last time
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 betw
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 curre
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
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 l
Section 5.6 Inverse Trigonometric Functions
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Inverse Trig Functions
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Review
Last time we studied general exponential functio
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
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
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
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 w
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
Wor
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
Section 3.5 Optimization Problems
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Introduction
In many practical problems, w
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
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 o
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
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
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 o
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
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
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-dimen
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
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