Schedule. Matlab Exam. Documentation. Program Building Blocks. Dynamics Makeup Exam. Matlab Exam. Semester Summary and Wrap up.

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1 Schedule Dynamics Makeup Exam Thursday, May 1, 2:00 p.m., Estabrook problems, covers modules 3 & 4 You may bring 1 sheet of notes Matlab Exam See next slide Semester Summary and Wrap up Wednesday, April 30 Semester Review Thursday, May 1, 10:00-12:00, Room - TBD Final Exam Thursday, May 8, 10:15-12:12, Rooms - TBD Matlab Exam 40 multiple choice (MC) questions given on-line via the web site. Format will be the same as the MC portion of the Matlab exams in EF 101. At least 5 questions will be taken directly from the EF 101 exams. Your EF 101 results are online, Printable: quiz 4, quiz 5. All Matlab commands and techniques that we covered in Lecture, A&S, PS, and HW in both EF 101 and EF 102 are "fair game." You may have 1 sheet of handwritten notes (collected at the of the exam) as well as Matlab and the Matlab Help File system open during the exam. Other open programs, notes (written or on-line), books, etc, are NOT permitted. Program Building Blocks Documentation Data Input Data Formatting / Typing and Manipulations Logic and Relational Operators Flow Control Operators Data Output Documentation Header: Provide date, author, program description, and a listing and description of key variables. In-Line Comments : Describe the purpose/actions of every line of code. Matlab Command: % -the comment operator May also be useful in debugging the code.

2 Data Input Internal, Keyboard, and File. Matlab Commands: internal hardwired data: e.g., time = [ ] internal generated data: colon operator, e.g., time = 1:2:9 linspace, e.g., time = linspace(1,9,5) keyboard input: input, e.g., time = input('input time values: ') read from a file: fopen, e.g., fscanf, e.g., fclose, e.g., mf = fopen('h;\price.txt','rt') data = fscanf(mf,'%g',[3, inf]) fclose(mf) Data Manipulations, etc. variable types: scalars, e.g., x = 3 vectors (lists), e.g., time = [1 3 5] matrices, e.g., aa = [1 5 36] operations on variables: +, -,.*,./,.^n, sqrt, sin, cos and all other trig functions, log, etc. miscellaneous commands length - calculates the length (i.e., number of values) of a vector clear all - clears all memory statistical functions: Data Manipulations Continued mean(a) - calculates the mean (or average value) of the numbers in the vector A median(a) - calculates the median of the numbers in the vector A std(a) - calculates the standard deviation of the numbers in the vector A max(a) - extracts the maximum value of the numbers in the vector A variation - [maxv maxl] = max(a) min(a) - extracts the minimum of the numbers in the vector A variation - [minv minl] = min(a) Given A = [1 2 3] B = [4 5 6] Vector Operations Norm C = norm(a) = Dot Product C = dot(a,b) = 32 Cross Product C = cross(a,b) = [-3 6-3]

3 Matrix Operations * and \ Matrix Multiplication * (8) + 3(7) 4(9) + 3( 6) * = = (8) + 1(7) 2(9) + 1( 6) 9 24 Left divide backslash \ [G] -1 [H] = [G] \ [H] [A]*[U] + [B] = 0 [U] = [A] -1 [-B] = [A] \ [-B] Data Analysis Interpolation linear cubic spline others syntax yi = interp1(x,y,xi,'method') Curve fitting (regression) linear higher order polynomials syntax coef = polyfit(x,y,n) yi = polyval(coef,xi) Trapezoidal Integration A = trapz(y) B = trapz(x,y) Numerical Integration Cumulative Trapezoidal Integration A = cumtrapz(y) B = cumtrapz(x,y) Polynomial Integration A = polyint(p) B = polyint(p,k) Numerical Differentiation Discrete Data Difference Y = diff(x) Y = diff(x,n) Approximate Derivative A = diff(y)./ diff(x) Polynomial Differentiation A = polyder(p)

4 Flow Control for loops repeat a set of commands for a specified number of times while loops repeat a set of commands while a specified condition is true if, else, elseif execute a set of commands if a specified condition is true ( if ) or execute an alternative set of commands if the specified condition is false ( else, elseif ) Relational & Logical Operators Relational operators, used in if, elseif and while loops == equal ~= not equal < less than <= less than or equal > greater than >= greater than or equal Logical operators, may be used with relational operators & AND OR ~ NOT xor EXCLUSIVE OR for loop for Index = StartValue:Increment:EndValue Matlab commands Index must be a legal Matlab variable name StartValue, Increment, and EndValue may be numbers, legal Matlab commands or variable names while loop while <a specified condition is true> Matlab commands Repeat this set of commands until the condition is no longer true Usually used when you do not know how many times you may need to repeat the given Matlab commands.

5 if statement if <a specified condition is true> Execute Matlab commands Simplest form of the statement. if - else statement if <a specified condition is true> Execute some Matlab commands else <the specified condition is false> Execute some other Matlab commands if - elseif - else statement if <a specified condition is true> Execute some Matlab commands elseif <another specified condition is true> means original specified condition is false Execute some other Matlab commands else means both specified conditions are false Execute some other Matlab commands Data Output Screen, Printer, or File. Formatted Text and Plots. Matlab Commands - Formatted Text: fprintf - prints formatted output to the command window or file. \n - line feed, i.e., move to the next line \t - tab, i.e., move to the next tab stop %<flag><width>.<precision><conversion specifier> - format control e.g., mf = fopen('output.txt','wt') fprintf(mf,'\n\n time = %5.2f sec \n', time) fclose(mf)

6 Data Output Continued plots: figure(n) - activates figure number n clf reset - clears active figure plot(x,y) - plots the data points stored in x and y plot3(x,y,z) - plots the data points stored in x, y and z axis([xmin xmax ymin ymax]) - sets axis limits axis([xmin xmax ymin ymax zmin zmax]) title('text') - puts a title on the plot xlabel('text') - puts a label on the x axis ylabel('text') - puts a label on the y axis zlabel('text') - puts a label on the z axis plots continued: Data Output Continued leg('text','text', ) - puts a leg on the plot. text(xval,yval,['text']) - puts a text note on the plot starting at the coordinates specified by xval and yval. num2str(variable name,precision) -converts the number stored in the given variable name to text and the number of digits printed is controlled by the precision. hold on - retain old data when plotting new data. subplot - creates several plots on the same page. Inline Function Definition Syntax: FunctionName = inline(expr) Constructs an inline function object named FunctionName from the MATLAB expression contained in the string EXPR. The input argument is automatically determined by searching EXPR for an isolated lower case alphabetic character, other than i or j. If you have more than one input variable, you must to specify them as additional parameters. Useful for one-liners. Examples: cosd = inline('cos(a.*pi./180)') z1 = inline('3.*x 2.*y','x','y') Matlab Script and Function Overview Matlab Script List of Matlab commands in a m.file. Uses the workspace for variable storage. This is what we have used so far. Matlab Function Also stored in a m.file. Starts with the command function. Allows input and output parameters. Has its own variable space - does NOT use the workspace for variable storage/ Can contain sub-functions (i.e, functions inside functions). Can "call" other functions.

7 Function Notes Usually used to perform a single task. Functions are usually very short. Complex tasks (and functions) are built from two or more simple functions. Used to modularize and standardize code. Break the program into a series of individual (possibly complex) tasks. Break each task into a series of simple functions Used to generalize operations. Avoid cut & paste of similar sections of code. How would you? Plot a sin curve from 0 to 360 o Generate a 5x1 column vector full of ones Generate a 5x3 matrix full of random numbers Find the slope of a best-fit line through x = [ ] and y = [ ] Plot the line y=3x+5 from x=0 to x=12 Determine the number of rows in a 2D matrix How would you? Prompt user for a number of apples Determine approximate area under a curve defined by a set of data points X and Y. Determine slope at a particular point on a curve defined by a polynomial with coefficients C Generate a list of 10 points evenly spaced between 0 and pi, inclusive Given a 3D force vector [10,12, 2] and a direction vector [3,4,1], find the magnitude of the force in the given direction function main x = [ 1 2 ; 3 4] y = [ 3 3 ] a = 1; printme(x(2,1)); printme(4); return What Happens? function printme(a) fprintf( A=%3.1f\n,a); return