Fundamentals of Programming20-ENFD-112

Sections 001 to 007

Instructor: Prof. Dieter SchmidtLecture: Monday, Wednesday 3:00-

3:50Web page

http://www.blackboard.uc.edu

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”

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

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

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

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

Format statements, for display of results

format short displays up to 6 decimal digits 1.6667 format long displays 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 bank two decimal digits 123.45 format + displays only +,-, or blank (of limited

use) format rat displays rational approximation format compact suppresses some line feeds format loose undoes format compact

Internal representation: roughly 15-16 decimal digits accuracy

depends on computer usually 64 bit binary floating point numbers, IEEE format

Predefined values ans always the result of the previous

execution eps accuracy of floating point numbers,

that is, last binary digit (bit) that can not be stored Inf numbers ≥ 21024 10308

NaN not a number i.e. 0/0 pi Note 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.

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

Help within Matlab

In command window help function helpwin topic lookfor topic type filename doc function

or use menu bar

Plotting of functions

x = [ -10 : 0.1 : 10 ]; y = sin(x) ; plot( x, y), xlabel('x'), ylabel('y')

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

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