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Thursday 13 October 2011

CHAPTER 1: COMPUTER SYSTEM

Chapter 1: COMPUTER SYSTEM (WINDOWS)
1.1 Definition and Evolution of Computer
You must be using the computer so many times, don't you? But what do you know about its history? Do you know how computers evolved from being small calculators to becoming the intelligent machines that they are? Read on for information on the evolution of computers.
The term Computer, originally meant a person capable of performing numerical calculations with the help of a mechanical computing device. The evolution of computers started way back in the era before Christ. Binary arithmetic is at the core of computer systems. History of computers dates back to the invention of a mechanical adding machine in 1642. ABACUS, an early computing tool, the invention of logarithm by John Napier and the invention of slide rules by William Oughtred were significant events in the evolution of computers from these early computing devices. Here's introducing you to the ancestors of modern computers.
  • Abacus was invented in, as early as 2400 BC.
  • Pingala introduced the binary number system, which would later form the core of computing systems.
  • Later in 60 AD, Heron of Alexandria invented machines that could follow instructions. Who knew back then that this idea would evolve into intelligent machines!
  • The 1600s witnessed the invention of slide rules, the system of movable rods based on logarithms used to perform basic mathematical calculations, and a mechanical adding machine, which in some way, laid the foundation of modern-day calculating machines or computers.
1800s saw some remarkable feats in the history of computers. They included:
  • A punching card system was devised by Joseph Marie Jacquard in 1801.
  • Charles Babbage designed the first mechanical computer in 1822 and the Analytical Engine in 1834.
  • Morse code was invented in 1835 by Samuel Morse.
  • George Boole invented the Boolean algebra in 1848, which would later be at the heart of programming.
If you look at the timeline of the evolution of computers, you will notice that first generation computers made use of vacuum tubes. These computers were expensive and bulky. They used machine language for computing and could solve just one problem at a time. They did not support multitasking.
  • IBM, today a big name in the list of computer technology industries, was founded in 1911.
  • It was in 1937 that Alan Turing came up with the concept of a theoretical Turing machine. In the same year, John V. Atanasoff devised the first digital electronic computer. Atanasoff and Clifford Berry came up with the ABC prototype in the November of 1939. Its computations were based on a vacuum tube and it used regenerative capacitor memory.
  • Konrad Zuse’s electromechanical ‘Z Machines’, especially the Z3 of 1941 was a notable achievement in the evolution of computers. It was the first machine to include binary and floating-point arithmetic and a considerable amount of programmability. Since it was proved to be Turing complete in 1998, it is regarded as world’s first operational computer.
  • In 1943, the Colossus was secretly designed at Bletchley Park, Britain to decode German messages. The Harvard Mark I of 1944 was a large-scale electromechanical computer with less programmability. It was another step forward in the evolution of computers.
  • The U.S. Army's Ballistics Research Laboratory came up with the Electronic Numerical Integrator And Computer (ENIAC) in 1946. It came to be known as the first general purpose electronic computer. However, it was required to be rewired to change its programming thus making its architecture inflexible. Developers of ENIAC realized the flaws in the architecture and developed a better one. It was known as the stored program architecture or von Neumann Architecture. It got this name after John von Neumann, who for the first time described the architecture in 1945. All the projects of developing computers taken up thereafter have been using the von Neumann Architecture. All the computers use a ‘stored program architecture’, which is now a part of the definition of computers.
  • The U.S. National Bureau of Standards came up with Standards Electronic/Eastern Automatic Computer (SEAC) in 1950. Diodes handled all the logic making it the first computer to base its logic on solid devices.
  • American mathematician and engineer, known as the 'Father of Information Theory', Claude Shannon published a paper Programming a Computer for Playing Chess, wherein he wrote about a machine that could be made to play chess!
  • IBM announced the IBM 702 Electronic Data Processing Machine in 1953. It was developed for business use and could address scientific and engineering applications.
Till the 1950s all computers that were used were vacuum tube based. In the 1960s, transistor based computers replaced vacuum tubes. Transistors made computers smaller and cheaper. They made computers energy efficient. But transistors led to emission of large amounts of heat from the computer, which could damage them. The use of transistors marked the second generation of computers. Computers of this generation used punched cards for input. They used assembly language.
  • Stanford Research Institute brought out ERMA, Electronic Recording Machine Accounting Project, which dealt with automation of the process of bookkeeping in banking.
  • In 1959, General Electric Corporation delivered its ERMA computing system to the Bank of America in California.
The use of Integrated circuits ushered in the third generation of computers. Their use increased the speed and efficiency of computers. Operating systems were the human interface to computing operations and keyboards and monitors became the input-output devices. COBOL, one of the earliest computer languages, was developed in 1959-60. BASIC came out in 1964. It was designed by John George Kemeny and Thomas Eugene Kurtz. Douglas Engelbart invented the first mouse prototype in 1963. Computers used a video display terminal (VDT) in the early days. The invention of Color Graphics Adapter in 1981 and that of Enhanced Graphics Adapter in 1984, both by IBM added 'color' to computer displays. All through the 1990s, computer monitors used the CRT technology. LCD replaced it in the 2000s. Computer keyboards evolved from the early typewriters. The development of computer storage devices started with the invention of Floppy disks, by IBM again.
  • In 1968, DEC launched the first mini computer called the PDP-8.
  • In 1969, the development of ARPANET began with the financial backing of the Department Of Defense.
Thousands of integrated circuits placed onto a silicon chip made up a microprocessor. Introduction of microprocessors was the hallmark of fourth generation computers.
  • Intel produced large-scale integration circuits in 1971. During the same year, Micro Computer came up with the microprocessor and Ted Hoff, working for Intel introduced 4-bit 4004.
  • In 1972, Intel introduced the 8080 microprocessors.
  • In 1974, Xerox came up with Alto workstation at PARC. It consisted of a monitor, a graphical interface, a mouse, and an Ethernet card for networking.
  • Apple Computers brought out the Macintosh personal computer on January 24 1984.
  • By 1988, more than 45 million computers were in use in the United States. The number went up to a billion by 2002.
The fifth generation computers are in their development phase. They would be capable of massive parallel processing, support voice recognition and understand natural language. The current advancements in computer technology are likely to transform computing machines into intelligent ones that possess self organizing skills. The evolution of computers will continue, perhaps till the day their processing powers equal human intelligence.



Wednesday 12 October 2011


POLITEKNIK SULTAN SALAHUDDIN ABDUL AZIZ SHAH
JABATAN MATEMATIK, SAINS & KOMPUTER
BA101 – ENGINEERING MATHEMATICS 1

TOPICS :


  1. BASIC  ALGEBRA
  2. STANDARD FORM, INDEX & LOGARITHM
  3. TRIGONOMETRY
  4. GEOMETRY & MEASUREMENT
  5. COORDINATE GEOMETRY & GRAPH


1. Basic Definitions


Distance FormulaRecall Pythagoras' Theorem:
math expression
For a right-angled triangle with hypotenuse length c,
math expression
We use this to find the distance between any two points (x1,y1) and (x2y2) on the cartesian plane:

math expression
The point (x2y1) is at the right angle. We can see that:
  • The distance between the points (x1y1) and (x2y1) is simply x2 − x1 and
  • The distance between the points (x2y2) and (x2y1) is simply y2 − y1.
math expression
Using Pythagoras' Theorem we have the distance between (x1y1) and (x2y2) given by:
math expression

Example 1:

Find the distance between the points (3, -4) and (5, 7).
Here, x1 = 3 and y1 = -4x2 = 5 and y2 = 7
So the distance is given by:
math expression

Example 2:

Find the distance between the points (3, -1) and (-2, 5).
This time, x1 = 3 and y1 = -1x2 = -2 and y2 = 5
So the distance is given by:
math expression

Gradient (or slope)

The gradient of a line is defined as
math expression
math expression
In this triangle, the gradient of the line is given by: math expression


In general, for the line joining the points (x1y1and (x2y2):
math expression
We see from the diagram above, that the gradient (usually written m) is given by:
math expression

Example:

Find the slope of the line joining the points (-4, -1) and (2, -5).
These are the points involved:
graph
So the slope is:
math expression

Positive and Negative Slopes

In general, a positive slope indicates the value of the dependent variable increasesas we go left to right:
math expression
[The dependent variable in the above graph is the y-value.]

negative slope means that the value of the dependent variable is decreasing as we go left to right:
math expression


Inclination

math expression
We have a line with slope m and the angle that the line makes with the x-axis is α.
From trigonometry, we recall that the tan of angle αis given by:
tan
Now, since slope is also defined as opposite/adjacent, we have:
inclination
This gives us the result:
tan α = m
Then we can find angle α using
α = arctan m
(That is, α = tan-1m)
This angle α is called the inclination of the line.

Example 1:

Find the inclination of the line with slope 2.
math expression
Here, tan α = 2, so
math expression
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NOTE: The size of angle α is (by definition) only between 0° and 180°.

Example 2:

Find the slope of the line with inclination α = 137°.
The situation is as follows:
math
So the slope is:
= tan α
= tan 137°
= -0.933
Note that the slope is negative.
Easy to understand math videos: MathTutorDVD.com
Let's see Gradient and Inclination using LiveMath.

Parallel Lines

math expression
Lines which have the same slope are parallel.
If a line has slope m1 and another line has slope m2 then the lines are parallel if
m1 = m2

Here is a LiveMath animation showing that if the gradient stays the same and we only change the y-intercept, the lines are parallel.

Perpendicular Lines

math expression
If a line has slope m1 and another line has slope m2then the lines are perpendicular if
m1 × m2= -1

In the example at right, the slopes of the lines are 2 and -0.5 and we have:
2 × -0.5 = -1
So the lines are perpendicular.


Example:

A line has slope m = 4.
a) What is the slope of a line parallel to l?
b) What is the slope of a line perpendicular to l?
a) Since parallel lines have the same slope, the slope will be 4.
b) Using m1 × m2= -1, with m1 = 4, we obtain the value for m2:
math expression
Easy to understand math videos: MathTutorDVD.com

Special Cases

What if one of the lines is parallel to the y-axis?
For example, the line y = 3 is parallel to the x-axis and has slope 0. The line x = 3.6 is parallel to the y-axis and has an undefined slope.
The lines are clearly perpendicular, but we cannot find the product of their slopes. In such a case, we cannot draw a conclusion from the product of the slopes, but we can see immediately from the graph that the lines are perpendicular.
perpendicular lines
The same situation occurs with the x- and y-axes. They are perpendicular, but we cannot calculate the product of the 2 slopes, since the slope of the y-axis is undefined.

Exercises

(1) What is the distance between (-1, 3) and (-8, -4)?
math expression
(2) A line passes through (-3, 9) and (4, 4). Another line passes through (9, -1) and(4, -8). Are the lines parallel or perpendicular?
The line through (-3,9) and (4,4) has slope math expression
The line through (9,-1) and (4,-8) has slope math expression
Now
math expression
so the lines are perpendicular.
Note: We could have sketched the lines to determine whether they were parallel or perpendicular.
(3) Find k if the distance between (k,0) and (0, 2k) is 10 units.
This is the situation:
k0
Applying the distance formula, we have:
math expression
Now math expression so 5k2 = 100, giving:
k= 20
so
= ± √20 ≈ ± 4.472
We obtained 2 solutions, so there are 2 possible outcomes, as follows:
k02