1. Fundamentals of Programming 20-ENFD-112 Sections 001 to 007 Instructor: Prof. Dieter Schmidt Lecture: Monday, Wednesday 3:00-3:50 Web page http://www.blackboard.uc.eduhttp://www.blackboard.uc.edu

2. Overview of MATLAB MATLAB Computer Algebra Program for solving mathematical problems in engineering MATLAB like a scientific calculator – but much much more. Other Computer Algebra Programs Mathematica, Maple, Magma, and others Difference to MATLAB: These programs do most of their calculations in “symbolic” form and usually use exact “integer arithmetic” MATLAB uses “floating point arithmetic”

3. Availability of Computer Algebra Programs at UC Mathematica Site license for entire campus Available in all labs Individual copies can be bought in computer store Used by Department of Mathematics in Computer Lab for calculus MATLAB Site license only for College of Engineering Available only in labs (and classrooms) of College of Engineering under folder Mathematics Individual student version can be bought for $100 Used in several courses in CoE

4. Student version of MATLAB Same capabilities as full version Prompt is EDU>> instead of >> Restriction: no commercial use Full version of MATLAB is expensive It has many modules for different fields, the first two come with student version of MATLAB, others have to be bought Simulink Mathematics toolbox Bioinformatics toolbox Data Acquisition toolbox Financial toolbox Statistics toolbox and others

5. Starting MATLAB MATLAB has to be installed Double click on icon For student version CD of MATLAB has to be in CD drive. MATLAB desktop Command Window Command History Window Current Directory Window

6. Arithmetic Operations Lowest precedence +Addition:a+b -Subtraction:a-b Next higher precedence *Multiplication:a*b /right division:a/b \left division:a\b same as b/a good for matrix operations, avoid otherwise Highest precedence ^ exponentiation:a^b Evaluation from left to right for equal precedence Use parentheses to change order

7. Format statements, for display of results format shortdisplays up to 6 decimal digits 1.6667 format longdisplays up to 16 decimal digits 1.666666666666667 format short e base 10 notation 1.2345e+002 format long e base 10 notation 16 digits format banktwo decimal digits 123.45 format +displays only +,-, or blank (of limited use) format ratdisplays rational approximation format compactsuppresses some line feeds format looseundoes format compact Internal representation: roughly 15-16 decimal digits accuracy depends on computer usually 64 bit binary floating point numbers, IEEE format

8. Predefined values ansalways the result of the previous execution epsaccuracy of floating point numbers, that is, last binary digit (bit) that can not be stored Infnumbers ≥ 2 1024  10 308 NaN not a number i.e. 0/0 piNote with format rat: pi=355/113 i,j imaginary unit sqrt(-1) Watch out, these values can be redefined This may lead to unexpected results i,j are less of a problem, when correct format for complex numbers are used.

9. Available Mathematical Functions exp(x) sqrt(x) log(x) natural logarithm, base e log10(x)base 10 cos(x) sin(x) tan(x) acos(x)cos -1 (x) asin(x) atan(x) and others

10. Help within Matlab In command window help function helpwin topic lookfor topic type filename doc function or use menu bar

11. Plotting of functions x = [ -10 : 0.1 : 10 ]; y = sin(x) ; plot( x, y), xlabel('x'), ylabel('y')

12. Arrays x=[-10 : 0.1 : 10] x is an array of 201 values -10,-9.9,-9.8,…,9.8,9.9,10.0 x(1),x(2),x(3),…,x(199),x(200),x(201) [start : increment : stop] Note ":" with "," it would only be an array with three elements: x=[-10, 0.1, 10] gives x(1)=-10, x(2)=0.1, x(3)=10 x(4) and others are now undefined

13. Functions of arrays Most built-in functions produce desired result y = sin(x) produces array y of same length as x plot(x,y) requires two arrays of same length y = x^2 will not work, nor does y=x * x for Matlab x is a matrix (array) rules for matrix multiplication are different to tell Matlab to do element by element operation need to write y = x.^2 or y =x. * x