welcome to egr 106 foundations of engineering ii course information today’s specific topics: –...
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Welcome to EGR 106 Foundations of Engineering II
Course information Today’s specific topics:
– Computation and algorithms– MATLAB
Basics Demonstrations
Material in textbook chapter 1
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Computation
What is computation?
Examples: 3 + 2
tan 40o
Computation = “transformation from one or more inputs to an output”
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Human Computation
“Simple” computations (trivial to us)– Adding 2 single digit numbers– Recognizing a letter of the alphabet– Comparing 2 numbers for <, =, >
“Harder” computations (based on simple)– Adding 3 or more numbers – Reading a word– Sorting a list of numbers
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Algorithms
Definition: “a set of directions for carrying out a computation in terms of other, simpler computations”
“Simpler computations” = ones that we already know how to do
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Example
Memorizing addition tables in grammar school
0 1 2 3 4 5 6 7 8 9
0 0 1 2 3 4 5 6 7 8 9
1 1 2 3 4 5 6 7 8 9 10
2 2 3 4 5 6 7 8 9 10 11
3 3 4 5 6 7 8 9 10 11 12
4 4 5 6 7 8 9 10 11 12 13
5 5 6 7 8 9 10 11 12 13 14
6 6 7 8 9 10 11 12 13 14 15
7 7 8 9 10 11 12 13 14 15 16
8 8 9 10 11 12 13 14 15 16 17
9 9 10 11 12 13 14 15 16 17 18
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Permits multi-digit addition
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Computer Computation
Very fast at arithmetic operations Algorithms = computer programs
– Need to understand what computations are “simple” for the computer
– Need to write a clear set of directions to be followed
– Build more complicated computations from intermediate ones
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Examples
Find the smallest in a list of number Sort a list of numbers Some for discussion/thought
(first two from Kaplan, Introduction to Scientific Computation and Programming)
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Find the Smallest of a List:
S et P =1, S =first num ber on list
S et S equal to the sm aller of S and theP th num ber on the list
Done withlist?
S top
no
yes
S tart with the list and 2 variab les, P and S
Increase P by 1
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Example: list = 7,1,5
Step P S
1 1 S = 7
2 2
3 S = smaller(7,1) = 1
4 3
5 S = smaller(1,5) = 1
6 stop
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Sort a List of Numbers:
S tart with your list and an em pty list
Let S = the sm allest num ber in the list
Done withlist?
S top
no
yes
Delete S from the old list;A ppend S to the new list
Note reuse!
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Example: list = 8,5,1,2
Step S Orig List New List
1 1
2 8,5,2 1
3 2
4 8,5 1,2
5 5
6 8 1,2,5
7 8
8 1,2,5,8
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Some Others….
Adding numbers expressed in Roman numerals
LXVI + XXXIV = ???
Find the 2nd smallest number in a list Convert the month/day into day of the year
Feb 15 = day 46
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MATLAB – What is it ?
Name is from matrix laboratory Powerful tool for
– Computation and visualization of engineering and science mathematics
– Communication of ideas– Programming:
Built-in editor, debugger, and help Many predefined functions (grouped in toolboxes) Interpreted or compiled programs
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Today is “beginning MATLAB”, sort of like “beginning French”:
– We start with basic terminology– We consider the simplest of computations– We do computation in interpreter mode (the
“enter” key invokes/runs/executes the operation requested)
Chapter 1 of Gilat– Pages 5-22
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The MATLAB Environment
Data represented in arrays– Organized by row and column indices– Use variable names for them
Multi-paned desktop: – Command window– Workspace browser– Current directory– Other windows: Figure, File Editor, Help, …..
More next week
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The Command Window
Command prompt >> Basic math operations are available:
addition + subtraction – division /
multiplication * exponentiation ^
“enter” key “executes” or “runs” or “invokes” the operation
Operator precedence: PEMDAS5 – 4 + 3 ^ 4 / ( 3 – 1 ) = ?
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Finite precision mathematics !!
By default, 5 significant digits are shown, with exponential notation as needed
Results of NaN, Inf, possible
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Allows Stored Variables
The equal sign is an assignment operator c = 7.5 bob3 = 3.7789
There are naming restrictions:Connected symbols, starting with a letter Make them unique Some are predefined for special values or
uses: pi inf flops j i ans for
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Combining Operations and =
Generally, computation requires 3 pieces of information:– The operator?– The inputs?– What to do with the output?
MATLAB storing the result in a variable Accomplished by the equal sign, =
Specified on the right hand side of an equal sign
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For these examples, 2 and 4 are the input and addition is the operation
No specification of the output; the default is to put it into the variable named ans
The output is assigned to the variable named bob
bob is again the destination of the result, we’ve just used functional style notation for the computation
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Note that = is not really an equal sign, but is an assignment operator
The computation on the right can be trivial
Here the computation is done using bob, then the result is put into variable bob
An error results since we’ve got things on the wrong sides of the assignment operator
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Other Useful Operations
abs(x) ceil(x) exp(x) fix(x) sign(x) floor(x) log(x) round(x) sqrt(x) conj(x) log10(x) rem(x,y) sin(x)sinh(x) tan(x) atan2(x,y) asin(x) acosh(x) atan(x) sec(x) sind(x) many more exist !!
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Examples
Square roots
Note that trig functions generally work in radians, not degrees
In general, all variables are complex numbers
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Bits and Pieces
Other useful system commands: – clear, clc – diary – help, lookfor – who, whos
Semicolon (;) suppresses the displaying of the result of a computation
Arrow keys allow for editing of prior commands PC version (network license) is available from ECC
help desk for $10
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Plotting Basics
Figure window commands:
figure, figure(3), clf, close plot(x,y) in which x and y are “arrays” Annotation commands:
title('the title goes here')
xlabel('the x axis label goes here')
ylabel('the y axis label goes here')
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Now for Some Demos!
Simple demos of variables and math “Demos” at the command line A simple gui of a bouncing ball