ChE 121 Engineering Computation S 2013 - Lab 2 (Due:May 27, 2013)

1. Learning Objectives: By completing the Lab, you should be competent in the following:

Using the iskeyword command to list protected MATLAB keywords Modifying the number format in MATLAB Creating predefined matrices and arrays using MATLAB commands Understanding the different matrix operations available Writing MATLAB script files and executing them

2. Instructions: You should perform the Lab on an individual basis. You may, however, seek assistance from TAs when you cant figure things out. To do so just raise your hand and a TA will assist you. Passing the Lab will require that you answer all the questions in the Tasks and Exercise sections .

3. Protected Keywords iskeyword: MATLAB contains several keywords that may not be used as variable names. An example of this is the else keyword, since this is already used by MATLAB in if-statement structures. Usage: iskeyword(string) iskeyword string iskeyword The first two commands will return 1 if the string matches a protected MATLAB keyword, while the third command will display a list of all MATLAB keywords. Task 1: Type: iskeyword(while) Then, use the third iskeyword command to familiarize yourself with other protected keywords. Finally, attempt the following: while = 3

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Note the error message, so you can identify this problem in the future. Notice how while turns blue once you type it, this indicates that it is a keyword that MATLAB recognizes.

4. Number Format MATLAB uses its own code to compute its operations; however, the results can be displayed on the Command Window or in a script file in different formats using MATLABs built-in function format. It is important to remember that the format command is only used to format the output of a calculation. For more information about this command, type: help format in the MATLAB Command Window. Task 2(a): Objective: Evaluate the expression e-2ln(5) and express the result in the formats available in MATLAB. To do this, follow these instructions: >> format short % changing the output format to short >> a=exp(-2) a = 0.1353 >> b = log(5) b = 1.6094 >> a*b ans = 0.2178 >>format long %changing the format to long >> a*b ans = 0.21781373573101 Task 2(b): Type: help format on the MATLAB Command Window and choose 8 formats among the list. Introduce the following matrix into MATLAB and display it in those formats. A = [e-20 ln(10) e2]

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5. Predefined Matrix Types MATLAB has several built-in functions for quickly making commonly used matrix types. Task 3: Try using the following commands: >> ones(3,2) >> zeros(4,4) >> diag([1 2 3]) >> eye(3) >> eye(3,2)

6. Matrix Operations MATLAB is capable of doing element by element mathematical operations as well as standard matrix operations (determinants, inversion, dot products, etc.). There are also built-in MATLAB functions to retrieve specific elements from a matrix as well as to determine the size of a matrix. Task 4: Perform the following commands to familiarize yourself with matrix operations. >> A = [1 2; 3 4]; >> B = [1 3; 2 6]; >> C= [8 9]; Once you have defined matrices A, B and C try the following operations. >>A+B >>A+C >> A.*B >>A*B >>C.^2 >>C^2 >>inv(A) >>A >>det(B)

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>>size(A) >>A(1,2) What is the difference between A*B and A.*B? The first command performs a row-by-column multiplication while the second one performs an element by element multiplication. It is very important to understand the difference between these two operations!

7. Creating scripts in the MATLABs Editor window: We will create a file with the name Lab3_script.m Type in the following MATLAB code inside the editor and save the file. To open the MATLAB editor, go to File New M-file. %Laboratory 2: Script % %Name: David Williams put your name instead %UserID: 202XXXXX put your UserID %Description: This program calculates SIN(X) from 0 to pi % %Clear the screen first clc % Command to clear the MATLAB screen r = 4; x = [0 pi/3 pi/2 2*pi/3 pi] y = sin(x) y Save the file as Lab2_script.m in the directory that you have set in the MATLAB search path. (File Save as) Task 5: Answer the following questions: a) Before running the script file Lab2_script.m, type: >> clear Then, use the command who to find out what variables are stored so far in your workspace. b) Now, in the command window type: >> a = 5; >> b = [2,3,4]; >> c = [1 2 3];

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>> d =Hello There; >> r = 1; Use the appropriate command to find out both the variables stored in your workspace and their size and type. c) What is the value of the variable r stored in your workspace at this moment? d) Run your script Lab2_script.m What did your screen display? e) Answer the following questions:

- What is the value of r? - What is the who function in MATLAB? - Can running a script alter the value of a workspace variable? - What is the function of a semicolon?

f) To get information about the program, you can try typing: >> help Lab2_script Which part of the script file shows up? Where does the help line terminate?

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8. Exercises 1. You create the following array:

t = 0:0.5:8 Using linspace command, what will you do to obtain the same result?

2. Given the following matrices, perform the operations requested below and express it in short format:

A=[2 3 8; 6 8 12; 5 6 12] B=[9 14 -6; 8 24 5; 11 6 5] C=[24, 23, 3; 5 9 8; 6 -3 15]

a) 14A+9B-3C+15*B*(A*2C) b) Inverse of A + Inverse of C + Transpose of (Transpose of B) c) Transpose of C + Inverse of (B*A) d) (Determinant of (Transpose of(Inverse of (Transpose of A))))^2 e) Determinant of A + (Determinant of (Transpose of B))^2 f) A*(Inverse of (B*C)) g) B*((Transpose of B)*B) h) C*((Inverse of C)^(-1))+A*(Transpose of A) i) 3A+2sin(pi/2)B-exp(-9)*C j) Inverse of (A*(Transpose of (B))+Transpose of C 15*(B*C)

Hint: the angles are expressed in radians and perform matrix operations, not element by element operations. 3. Generate a script file to calculate the surface area and volume of a rectangular pyramid with height of 0.5 m that prompts for dimensional user inputs. Test your script file for the following cases: a) Base is a square with side length=8 cm b) Base is rectangular with length= 24 cm, width=5 cm Formulas to be used:

BBB

P WLhPS +

=2 ; 3

hWLV bbP =

Where SP= Pyramid surface area PB = Base perimeter VP=Pyramid Volume

LB= Length of the pyramid base WB= Width of the pyramid base h= Pyramid height

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4. The behavior of a non-ideal gas can be represented by the following Van der Waals equation of state (EOS):

2Va

bVRTP

=

Where, a = 9.2548e6; (cm3.atm/mol2) b = 90.3393; (cm3/mol) R = 82.06; (cm3.atm/mol.K)

Create a script that calculates the pressure from the above EOS using the following data:

Volume (cm3/mole) Temperature (K) 1000 250 1500 300 2000 350 2500 400 3000 450

5. A student records time vs. concentration of component B (in mol/L) obtained in a reactor where a consecutive reaction CBA takes place and the data is shown the following table:

Time(min) Concentration of B (mol/L) 1 0.02

2.5 0.028 4 0.034 6 0.024 9 0.021

Write a single MATLAB script file where you define an array variable TIMCON that holds time and concentration data, and using the array variable TIMCON find the maximum concentration of B obtained in the reactor (assign it to a variable MAXCON) and the corresponding time at which it occurs (assign it to a variable MAXTIME) and further should return the following statement when executed: The maximum concentration is 0.034 mol/L and occurs at 4 minutes. (note: use disp and num2str for the last part of the program)

1. Learning Objectives:2. Instructions:3. Protected Keywords iskeyword:4. Number Format5. Predefined Matrix Types6. Matrix Operations7. Creating scripts in the MATLABs Editor window:8. Exercises