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Engineering Analysis – Fall 2009

Engineering Analysis – Fall 2009. Dan C. Marinescu Office: HEC 439 B Office hours: Tu-Th 11:00-12:00. Lecture 3. Last time - Analytical and Numerical Methods for Model Solving Today: - Overview of Matlab - Laplace Transform

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Engineering Analysis – Fall 2009

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  1. Engineering Analysis – Fall 2009 Dan C. Marinescu Office: HEC 439 B Office hours: Tu-Th 11:00-12:00

  2. Lecture 3 • Last time - Analytical and Numerical Methods for Model Solving • Today: - Overview of Matlab - Laplace Transform - Solving differential equations using the Laplace Transform - Example • Next Time - Arrays in Matlab - Graphics - Number representation and roundoff errors Lecture 2

  3. Matlab • The workspace  The environment (address space) where all variables reside. • After carrying out a calculation, MATLAB assigns the result to the built-in variable called ans; • A “%” character marks the beginning of a comment line. • Three windows: • Command window – used to enter commands and data • Edit window- used to create and edit M-files (programs) such as the factor. For example, we can use the editor to create factor.m • Graphics window(s)- used to display plots and graphics Lecture 2

  4. Command window • Used to enter commands and data. The prompt is “>>” ; Allows the use of Matlab as a calculator when commands are typed in line by line, e.g., >> a = 77 -1 ans = 61 >> b = a * 10 ans =610 Lecture 2

  5. System commands • who/whos list all variables in the workspace • clear  removes all variables from the workspace • computer lists the system MATLAB is running on • version  lists the toolboxes (utilities) available Lecture 2

  6. Variables • Scalar and arrays; numerical data and text. • You do not need to pre-initialize a variable; if it does not exist, MATLAB will create it for you.

  7. Variable names • Variable names up to 31 alphanumeric characters (letters, numbers) and the underscore (_) symbol; must start with a letter. • Reserved names for variables and constants. ans - Most recent answer. eps - Floating point relative accuracy. realmax - Largest positive floating point number. realmin - Smallest positive floating point number. pi - 3.1415926535897.... i - Imaginary unit. j - Imaginary unit. inf - Infinity. nan - Not-a-Number. isnan - True for Not-a-Number. isinf - True for infinite elements. isfinite - True for finite elements. why - Succinct answer. Lecture 2

  8. Variable names (cont’d) • To report the value of variable kiki type its name: >> kiki kiki = 13 • To prevent the system from reporting the value of variable kiki append the semi-solon (;) at the end of a line: >> kiki = 13; Lecture 2

  9. Data display • The format command allows you to display real numbers • short - scaled fixed-point format with 5 digits • long - scaled fixed-point format with 15 digits for double and 7 digits for single • short eng - engineering format with at least 5 digits and a power that is a multiple of 3 (useful for SI prefixes) • The format does not affect the way data is stored internally

  10. Format Examples • >> format short; pians = 3.1416>> format long; pians = 3.14159265358979>> format short eng; pians = 3.1416e+000>> pi*10000ans = 31.4159e+003 • Note - the format remains the same unless another format command is issued.

  11. Script file - set of MATLAB commands • Example: the script factor.m: function fact = factor(n) x=1; for i=1:n x=x*i; end fact=x; %fprintf('Factor %6.3f %6.3f \n' n, fact); end • Scripts can be executed by: • (i) typing their name (without the .m) in the command window; • (ii) selecting the Debug, Run (or Save and Run) command in the editing window; or • (iii) hitting the F5 key while in the editing window. • Option (i) will run the file as it exists on the drive, options (ii) and (iii) save any edits to the file. Example: >> factor(12) ans = 479001600 Lecture 2

  12. Transform Methods • Basic idea: find a convenient representation of the equations describing a physical phenomena. • For example, in signal analysis rather than analyzing a function of time, s(t), study the spectrum of the signal S(f), in other words carry out the analysis in the frequency domain rather than the time domain. • Advantage of Fourier (spectral analysis): • More intuitive physical representation • Instead of correlation (an intensive numerically problem) use multiplication. Lecture 2

  13. Properties of the Laplace Transform • Linearity • Scaling • Frequency shifting • Time shifting • Frequency differentiation • Frequency integration • Differentiation • Integration • Convolution Lecture 2

  14. Lecture 2

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