1. 1 = MATLAB Mathematics + Laboratory + Dan Ophir, Ph.D. Cell.: 052-551359 e-Mail: comp_ophir@yahoo.com Civil Engineering =

2. 2 Requirements Tests: 1.Intermediate, 2.Final. Exercises in diskettes 1..rtf format (Office); 2..m,.mdl,.fig (Matlab) 75% Lectures + 25% Exercises Note = Tests + Exercises

3. 3 Students 8 7 6 5 4 3 2 1

4. 4 Files 1..m --- Script 2..mat --- Workspace 3..mdl --- Block program – Model (Simulink) User’s:

5. 5 Conventions 1)> - pressing on a menu, sub- menu, button 2)blue – link 3)red – a reserved word.

6. 6 Mode of Interaction Interpreter Compiler Interactive Batch: Script Program

7. 7 MATLAB - Potential Type: Demo

8. 8 Demo MATLAB>Matrices>graphs and matrices MATLAB>Numerics>2D-solutions MATLAB>Numerics>Command line demos>Run Command line demos >function plot MATLAB>Visualization>3D plots of comples functions>Run 3D plots of> Cube root

9. 9 Demo (2-cont.) MATLAB>Language/Graphics>3d surface plots> Run 3D surface plots>color map

10. 10 Work Environment Desktop FilesWork- Space Windows

11. 11 Windows User’s: 1.Script.m 2.Module.mdl 3.Figure.fig System’s: 1.Commands (history) 2.Variables 3.Help Window 4.Launch Pad 5.Workspace (variables) 6.Array Editor

12. 12 Getting Starting MATLAB: Command Window First commands: 1.helpwin – list of all.m files (scripts) included in the path (described in a help window) > tips (>See also, >Back, >Forward) 2. help - a help in the command window. 3. help debug – a help of special topics or command. lookfor conversion which fprintf

13. 13 Interactive Calculation Command window: x=5; y=x+2; disp(y); files.mat for workspace saving. MATLAB.mat – default file name who – the local variables values whos – the local variables data structure use : save / load – to treat with workspace file

14. 14 M-File Editor/Debugger window 1. Command window: setpath 2. Command window: open fibonaci.m file 3. Command window: fibonaci Input: Output: 1. Command window: Fibonacci series 2. Figure No. 1

15. 15 Fibonnacci 1 1 2 3 5 8 13 21… Converges to the golden ratio. A B C AB : CB = CB : AC

16. 16 Golden Ratio Parthenon

17. 17 Simulink window First step: 1)menu:file>new>model 2)or: >open>browsing.mdl gives the model specifications. 3) model - icon Second step: 1)menu: file>open 2)Browsing for.mdl C:\MATLAB_5\my_exampl es\mdl\MDL\Simple\INTEG RAL.MDL Modeling Programming Third step: (Integral window) 1.menu: simulation>start 2.Input & Integration windindows

18. 18 MATLAB as a Language Language : Syntax, Semantics

19. 19 Language Components script – function: f(a,b) command: x=y+5 variable: myBook_1 operator: + * constant: 3.27 special symbol: %, ; “ ( )

20. 20 Operations (operators) operationsymbolexample Addition+3+2 Subtraction-54.4 –25.3 Multiplication*3.15 * 6 Division/ or \23.4/8 Exponentiation^3^4 helpwin>matlab\ops>*

21. 21 Variables Naming rules: 1.letters, digits, _ 2.Case sensitive 3.Starting with a letter Reserved World List (17) for end if while function return elseif case otherwise switch continue else try catch global persistent break

22. 22 MATLAB special variables Special Variables

23. 23 Control Flow keywords % if - Conditionally execute statements. % else - IF statement condition. % elseif - IF statement condition. % end - Terminate scope of FOR, WHILE, SWITCH and IF statements. % for - Repeat statements a specific number of times. % while - Repeat statements an indefinite number of times. % break - Terminate execution of WHILE or FOR loop. help>manual>control flow help>else

24. 24 Functions Library Trigonometric : sin, cot Exponential : log, exp, ^, sqrt Complex : conj, real Rounding and remainder: fix, floor, mod Coordinate Transformation: carth2sph,pol2cart Number Theoretic: factor, isprime, gcd Specialized: besselj, legendre helpwin> matlab\elfun (topics elem. func) > tan

25. 25 Function Syntax Example: function [mean] = avg(x,n) mean = sum(x)/n; function [list of output arguments ] = name (input-arg.) commands…

26. 26 Command Command : collection of the following entities: variables, constants, calling functions, keywords (reserved words) and operators. Examples : x=23+10*sin(0.3); x

27. 27 Program Program: A collection of commands with some significance. >> % fibonnaci - sequence >> b(1)=1; b(2)=1; >> for I=3:5, b(I)=b(I-1)+b(I-2); end >> b >> who

28. 28 Example: FOR, matrix Command: >> for i=1:5, for j=1:4, a(i,j)=i+j; end >> a Output: 2 3 4 5 3 4 5 6 4 5 6 7 5 6 7 8 6 7 8 9 basewords: loop, matrix, index operators: >> :, () ; row column

29. 29 Simple for, if for I=1:5 I end 1 2 3 4 5 Code: Output: I=1; J=2; X=5; X=6; if x==5 I else J end 1212

30. 30 FAQ Frequently Asked Questions שאלות שכיחות >> If for … Previous command

31. 31 Language Manual MANUAL.M help manual

32. 32 Script, Program, Function Script, Program, Function : A collection of commands enclosed between two special commands (module) and having a special task.

33. 33 Exercise 1(list) Choose 8 Reserved words and explain their function in MATLAB and give examples of their usage. Use the help features of MATLAB and the manual.m file. Choose 5 operators not given in the lecture and explain their function

34. 34 Exercise 2 (Pitagoras) Input : Two perpendicular sides a,b of a right-angled triangle, Output : The length of the opposite side c. Do : To write commands to compute c. b a c c 2 = a 2 + b 2

35. 35 Simple Script – Sum_Arr 1. a=[1 2 3]; 2. n=3; 3. % function f=sum(a,n) 4. % Computing the sum of the elements of an array 5. sum1=0; 6. for i=1:n, 7. sum1=sum1+a(i); 8. end 9. f=sum1; 10. s=sprintf('sum:%d',sum1); 11. disp(s);

36. 36 Fibonacci Script (recursive) 1. % fibonaci.m (recusive algorithm) 2. %A script to calculate Fibonacci numbers 3. %first described by Leonardo of Pisa 4. f=[1 1]; n=1; 5. while f(n) + f(n+1) <100 6. f(n+2)=f(n)+f(n+1) 7. n=n+1; 8. end

37. 37 Exercise 3 (primes) 1.Write a script/function myPrime to print all the prime numbers less than n; 2.Take n=100. 3.Compare the results with those received by using the MATLAB original function.

38. 38 Line 2D

39. 39 Exercise 4: Triangle Draw (in the.m file) a triangle,whose vertices are at the points: (5,5), (0,10), (10,10) שרטט (קובץ.m) משולש שקודקודיו בנקודות הבאות: (5,5),(0,10),(10,10)