1. Welcome to EGR 106 Foundations of Engineering II Course information Today’s specific topics: – Computation and algorithms – M ATLAB Basics Demonstrations Material in textbook chapter 1

2. Computation What is computation? Examples:3 + 2 tan 40 o Computation = “transformation from one or more inputs to an output”

3. 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

4. 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

5. Example Memorizing addition tables in grammar school 0123456789 00123456789 112345678910 223456789 11 33456789101112 445678910111213 5567891011121314 66789101112131415 778910111213141516 8891011121314151617 99101112131415161718

6. Permits multi-digit addition

7. 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

8. 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)

9. Find the Smallest of a List:

10. Example: list = 7,1,5 StepPS 11S = 7 22 3S = smaller(7,1) = 1 43 5S = smaller(1,5) = 1 6stop

11. Sort a List of Numbers: Note reuse!

12. Example: list = 8,5,1,2 StepSOrig ListNew List 11 28,5,21 32 48,51,2 55 681,2,5 78 81,2,5,8

13. Some Others…. Adding numbers expressed in Roman numerals LXVI + XXXIV = ??? Find the 2 nd smallest number in a list Convert the month/day into day of the year Feb 15 = day 46

14. M ATLAB – 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

15. Today is “beginning M ATLAB ”, 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

16. The M ATLAB 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

18. 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: PEMDAS 5 – 4 + 3 ^ 4 / ( 3 – 1 ) = ?

20. Finite precision mathematics !! By default, 5 significant digits are shown, with exponential notation as needed Results of NaN, Inf, possible

21. Allows Stored Variables The equal sign is an assignment operator c = 7.5bob3 = 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

22. Combining Operations and = Generally, computation requires 3 pieces of information: – The operator? – The inputs? – What to do with the output? M ATLAB  storing the result in a variable Accomplished by the equal sign, = Specified on the right hand side of an equal sign

23. 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

24. 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

25. 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 !!

26. Examples Square roots Note that trig functions generally work in radians, not degrees In general, all variables are complex numbers

27. 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

28. 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')

29. Now for Some Demos! Simple demos of variables and math “Demos” at the command line A simple gui of a bouncing ball