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Fundamentals of Programming 20-ENFD-112 Sections 001 to 007

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.edu. Overview of MATLAB. MATLAB Computer Algebra Program for solving mathematical problems in engineering

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Fundamentals of Programming 20-ENFD-112 Sections 001 to 007

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  1. Fundamentals of Programming20-ENFD-112 Sections 001 to 007 Instructor: Prof. Dieter Schmidt Lecture: Monday, Wednesday 3:00-3:50 Web page http://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 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

  8. 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.

  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

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