September 13, 2005 Lecture 4 - By P. Lin 1 CPET 190 Lecture 4 Problem Solving with MATLAB lin.

September 13, 2005September 13, 2005 Lecture 4 - By P. LinLecture 4 - By P. Lin 11

CPET 190CPET 190

Lecture 4 Lecture 4

Problem Solving with MATLABProblem Solving with MATLAB

http://www.etcs.ipfw.edu/~linhttp://www.etcs.ipfw.edu/~lin


Lecture 4: MATLAB Array Basics Lecture 4: MATLAB Array Basics

4.1 MATLAB Variables and Arrays4.1 MATLAB Variables and Arrays VariablesVariables Variable InitializationVariable Initialization

• AssignmentAssignment• input()input()

Variable Value DisplayVariable Value Display• disp() functiondisp() function• fprintf() functionfprintf() function

Example 4.1.a Row VectorExample 4.1.a Row Vector Example 4.1.b Column VectorExample 4.1.b Column Vector Example 4.1.c Square Matrix or ArrayExample 4.1.c Square Matrix or Array Example 4.1.d A 2-by-3 Array ExampleExample 4.1.d A 2-by-3 Array Example


Lecture 4: MATLAB Array Basics Lecture 4: MATLAB Array Basics (continue)(continue)

4.2 Problem Solving Examples4.2 Problem Solving ExamplesExample 4-2: Calculating Series ResistanceExample 4-2: Calculating Series ResistanceExample 4-3: Temperature ConversionExample 4-3: Temperature Conversion


4.1 MATLAB Variables and Arrays4.1 MATLAB Variables and Arrays

VariablesVariables• Variable names are case Variable names are case

sensitive and weakly sensitive and weakly typed typed

• Numerical variable type Numerical variable type – “double” type in the – “double” type in the range of 10range of 10-308-308 to 10 to 10308308 with 15 to 16 significant with 15 to 16 significant digitsdigits

• String variables – 16-bit String variables – 16-bit value characters, value characters, enclosed by a pair of enclosed by a pair of single quotes single quotes

>> n = 1e-308>> n = 1e-308n =n = 1.0000e-3081.0000e-308

>> n = 1e-400>> n = 1e-400n =n = 00>> name = ‘MATLAB’>> name = ‘MATLAB’

name =name =

MATLABMATLAB


4.1 MATLAB Variables and Arrays4.1 MATLAB Variables and Arrays

Variable InitializationVariable Initialization• Using assignment Using assignment

statement statement • Using keyboard input Using keyboard input

function – input( )function – input( )

Variable Value DisplayVariable Value Display• disp( )disp( )• fprintf( )fprintf( )

>> x = 10;>> x = 10;>> y = x>> y = xy =y = 1010>> x1 = input('Please enter a >> x1 = input('Please enter a number: ')number: ')Please enter a number: 100Please enter a number: 100x1 = 100x1 = 100>> disp(x1)>> disp(x1) 100100>> fprintf('%f',x1)>> fprintf('%f',x1)100.000000100.000000>> fprintf('%e',x1)>> fprintf('%e',x1)1.000000e+0021.000000e+002


4.1 MATLAB Variables and Arrays 4.1 MATLAB Variables and Arrays (continue)(continue)

ArraysArrays• Definition – an array is a Definition – an array is a

collection data values organized collection data values organized into rows and columns, and into rows and columns, and accessed by its name and accessed by its name and subscriptssubscripts

• Fundamental unit of data in Fundamental unit of data in MATLAB programsMATLAB programs

• Scalars are treated as arrays with Scalars are treated as arrays with one column and one rowone column and one row

A MATALB Example: scalar A MATALB Example: scalar variable nvariable n

>> n = 100;>> n = 100;

Row1

Col 1A Scalar

n

100



ArraysArrays• An array can be single dimension or An array can be single dimension or

multidimensionalmultidimensional• The dimension of the MATLAB array can The dimension of the MATLAB array can

be defined implicitly by assignment be defined implicitly by assignment statement or by size( ) functionstatement or by size( ) function

• Array Initialization ExamplesArray Initialization Examples 1-D row vector1-D row vector 1-D column vector1-D column vector 2-D array or matrix2-D array or matrix



Example 4.1.a - A 1-Example 4.1.a - A 1-by-4 Array, or Row by-4 Array, or Row Vector ExampleVector Example

>> product = [10 20 30 40];>> product = [10 20 30 40];>> product(1,1)>> product(1,1)ans = 10ans = 10>> m = product(1,2)>> m = product(1,2)m = 20m = 20>> product(1,3) = m>> product(1,3) = mproduct = 10 20 20 40product = 10 20 20 40>> r = 1; c = 4;>> r = 1; c = 4;>> k = product(r,c)>> k = product(r,c)K = 40K = 40

Syntax for accessing individual element:

product(r, c)

Subscripts: r - row, c -column

40302010

Col 1 Col 2 Col 3 Col 4

Row1

product

An array of 1 x 4



Example 4.1.b - A 3-by-1 Example 4.1.b - A 3-by-1 Array, or Column Vector Array, or Column Vector ExampleExample

>> column_vector = [10; 20; 30]>> column_vector = [10; 20; 30]

column_vector =column_vector =

1010

2020

3030

Row1

Row 2

10

20

Row 3 30

Col 1

A Column Vector of 3 x 1

column_vector



Example 4.1.c - A 4 by 4 Example 4.1.c - A 4 by 4 Array ExampleArray Example

>>items = [10 20 30 40; 50 60 >>items = [10 20 30 40; 50 60 70 80; 90 100 110 120; 130 70 80; 90 100 110 120; 130 140 150 160];140 150 160];

>> r = 3; c = 3;>> r = 3; c = 3;

>> items(r, c)>> items(r, c)

ans = 110ans = 110

>> size(items)>> size(items)

ans = 4 4ans = 4 4

Row1

Row 2

40302010

80706050

Row 3

Row 4 160150140130

12011010090

Col 1

Col 2

Col 3

Col 4

An Array of 4 x 4

items



Example 4.1.d - A 2 by 3 Example 4.1.d - A 2 by 3 Array ExampleArray Example

>>>> num = [10 20; 30 40; 50 60] num = [10 20; 30 40; 50 60]

num =num =

10 2010 20

30 4030 40

50 6050 60

Row1

Row 2

2010

4030

Row 3 6050

Col 1

Col 2

An Array (matrix) of 3 x 2

num


4.2 Problem Solving Examples4.2 Problem Solving Examples

Example 4-2: Calculating Series Example 4-2: Calculating Series Resistance.Resistance.

Problem Statement:Problem Statement:• You are asked by your supervisor to design a You are asked by your supervisor to design a

MATLAB program for your colleague. This MATLAB program for your colleague. This program should allow the user to calculate the program should allow the user to calculate the total series resistance of a circuit.total series resistance of a circuit.


4.2 Problem Solving Examples 4.2 Problem Solving Examples (continue)(continue)

Example 4-2: Calculating Series Example 4-2: Calculating Series Resistance.Resistance.

Problem Solving Process and Steps:Problem Solving Process and Steps:• Define the problemDefine the problem• Formulate a mathematical modelFormulate a mathematical model• Develop an algorithmDevelop an algorithm• Write the code for the problemWrite the code for the problem• Test program and verify the solutionTest program and verify the solution• Document the program and solutionDocument the program and solution


4.2 Problem Solving Examples 4.2 Problem Solving Examples (continue)(continue)

Example 4-2: Calculating Series Resistance.Example 4-2: Calculating Series Resistance. Problem Solving Process and Steps:Problem Solving Process and Steps:

1.1. Define the problemDefine the problem

2.2. Formulate a mathematical model - Total R = R1 + R2 Formulate a mathematical model - Total R = R1 + R2 + R3 + … + Rn+ R3 + … + Rn

3.3. Develop an algorithmDevelop an algorithm

Step 3.1: User input R1, R2, R3, … Rn, one at a timeStep 3.1: User input R1, R2, R3, … Rn, one at a time

Step 3.2: Compute subtotal resistanceStep 3.2: Compute subtotal resistance

Step 3.3: Repeat until the end of resistance enteringStep 3.3: Repeat until the end of resistance entering

Step 3.4: Print total resistanceStep 3.4: Print total resistance

4. Write the code for the problem4. Write the code for the problem


Example 4-2: Calculating Series Example 4-2: Calculating Series Resistance – Solution 1Resistance – Solution 1

MATLAB Solution 1MATLAB Solution 1• Understand who users Understand who users

areare• How to input resistance How to input resistance

values?values?• The mathematical The mathematical

model or equationmodel or equation

Total R = R1 + R2 + R3 + Total R = R1 + R2 + R3 + … + Rn… + Rn

• How to display or print How to display or print total resistance value?total resistance value?

>> r1 = 10; r2 = 20;>> r1 = 10; r2 = 20;

>> r3 = 40;>> r3 = 40;

>> r_total = r1 + r2 + r3>> r_total = r1 + r2 + r3

r_total =r_total =

7070



% Program: n_resistor.m% Program: n_resistor.m% Author: M. Lin% Author: M. Lin% Date: August 20, 2004% Date: August 20, 2004% Description:% Description:% This program does the follwoings:% This program does the follwoings:% 1. Prompts the user to enter the% 1. Prompts the user to enter the% number of resistors in series% number of resistors in series% 2. Prompts the user to enter individual% 2. Prompts the user to enter individual% resistor value, and compute the% resistor value, and compute the% subtotal % subtotal % value.% value.% 3. Updates the loop counter until all % 3. Updates the loop counter until all % resistance are entered% resistance are entered% 4. Compute and print the total % 4. Compute and print the total

resistanceresistance% Variables used:% Variables used:% r_total -- Total Resistance% r_total -- Total Resistance% r -- Input Resistance% r -- Input Resistance% n -- Number of resistors% n -- Number of resistors

r_total = 0;r_total = 0;n = input('Number of Resistors: n = input('Number of Resistors: ‘ )‘ )while n > 0while n > 0 r = input('Enter a resistance: ‘ )r = input('Enter a resistance: ‘ ) r_total = r_total + r;r_total = r_total + r; n = n-1;n = n-1;endendfprintf('Total Resistance = %f', fprintf('Total Resistance = %f', r_total)r_total)


Example 4-2: Calculating Series Example 4-2: Calculating Series Resistance – Solution 2 Resistance – Solution 2 (continue)(continue)


Example 4-2: Run n_resistor.m at Example 4-2: Run n_resistor.m at the Command Windowthe Command Window

Current Directory

n_resistor.m3 hit Enter key

10 hit Enter key

30 hit Enter key

20 hit Enter key

Total Resistance


4.2 Problem Solving Examples4.2 Problem Solving Examples

Example 4-3: Problem Statement: Design a Example 4-3: Problem Statement: Design a MATLAB program that reads an input temperature MATLAB program that reads an input temperature in degree Fahrenheit, converts it to an in degree Fahrenheit, converts it to an temperature in degree Kelvin and degree Celsius.temperature in degree Kelvin and degree Celsius.

Analysis of the ProblemAnalysis of the Problem• ReferencesReferences• National Institute of Standards, National Institute of Standards,

http://physics.nist.gov/cuu/Units/index.htmlhttp://physics.nist.gov/cuu/Units/index.html• Conversion of Temperatures, Conversion of Temperatures,

http://www.chemie.fu-berlin.de/chemistry/general/units_enhttp://www.chemie.fu-berlin.de/chemistry/general/units_en.html#temp.html#temp

• http://www.bipm.org/en/si/http://www.bipm.org/en/si/


Example 4.3 Temperature Conversion - Example 4.3 Temperature Conversion - Analysis of the Problem Analysis of the Problem (cont.)(cont.)

The degree FahrenheitThe degree Fahrenheit (°F)(°F) - - non-metric non-metric temperature scaletemperature scale

Freezing temperature of water - 32Freezing temperature of water - 32°°FF Boiling temperature of water - 212°FBoiling temperature of water - 212°F

• Formula for C to F ConversionFormula for C to F Conversion Degree Degree F = C (9/5) + 32F = C (9/5) + 32


Example 4-3 Temperature Conversion Example 4-3 Temperature Conversion – Analysis of the Problem – Analysis of the Problem (cont.)(cont.)

The degree Celsius (°C)The degree Celsius (°C) scale - dividing the scale - dividing the range of temperature between the freezing range of temperature between the freezing and boiling temperatures of pure water at and boiling temperatures of pure water at standard atmospheric conditions (sea level standard atmospheric conditions (sea level pressure) into 100 equal parts. pressure) into 100 equal parts.

FormulasFormulasDegree C = kelvin - 273.15Degree C = kelvin - 273.15

Degree C = (F – 32)/1.8Degree C = (F – 32)/1.8


Example 4-3 Temperature Conversion Example 4-3 Temperature Conversion – Analysis of the Problem – Analysis of the Problem (cont.)(cont.)

The The kelvin (K) kelvin (K) temperature scale is an extension temperature scale is an extension of the degree Celsius scale down to of the degree Celsius scale down to absolute zeroabsolute zero, , a hypothetical temperature characterized by a a hypothetical temperature characterized by a complete absence of heat energy. complete absence of heat energy.

Temperatures on this scale are called Temperatures on this scale are called kelvinkelvin, NOT , NOT degrees kelvin, kelvin is not capitalized, and the degrees kelvin, kelvin is not capitalized, and the symbol (capital K) stands alone with no degree symbol (capital K) stands alone with no degree symbol. symbol.

FormulasFormulaskelvin = C + 273.15kelvin = C + 273.15 degree F = C (9/5) + 32degree F = C (9/5) + 32


Example 4-3 Temperature Example 4-3 Temperature Conversion – Program DesignConversion – Program Design

We use the following values for validating the We use the following values for validating the computes answers:computes answers:The boiling point temperature of water The boiling point temperature of water • 212°F 212°F 100°C 100°C 373.15 K373.15 K

The sublimation point of dry iceThe sublimation point of dry ice• -110°F-110°F -77.89°C-77.89°C 195.26 K195.26 K

Formulas for computationFormulas for computationTTCC in degree C = (T in degree C = (TFF – 32.0)* (9/5) – 32.0)* (9/5) kelvin = Tkelvin = TCC + 273.15 + 273.15

User input will be from keyboard using input( ) User input will be from keyboard using input( ) functionfunction

Display output using fprintf() functionDisplay output using fprintf() function


Example 4-3 Temperature Conversion Example 4-3 Temperature Conversion – Coding MATLAB Program– Coding MATLAB Program


Example 4-3 Temperature Example 4-3 Temperature Conversion – Testing the ProgramConversion – Testing the Program

>>temp_convert>>temp_convert

Please enter the temperature in F: 212Please enter the temperature in F: 212

Temperature in F 212.00Temperature in F 212.00

Temperature in C 100.00Temperature in C 100.00

Temperature in kelvin 373.15Temperature in kelvin 373.15

>> temp_convert>> temp_convert

Please enter the temperature in F: -110Please enter the temperature in F: -110

Temperature in F -110.00Temperature in F -110.00

Temperature in C -78.89Temperature in C -78.89

Temperature in kelvin 194.26Temperature in kelvin 194.26


SummarySummary

MATLAB Variables and ArraysMATLAB Variables and Arrays

• VariableVariable

• Variable InitializationVariable Initialization

• Arrays and examplesArrays and examples Problem Solving ExamplesProblem Solving Examples

• Calculating series resistanceCalculating series resistance

• Temperature conversionTemperature conversion


Question?Question?

AnswersAnswers

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September 13, 2005 Lecture 4 - By P. Lin 1 CPET 190 Lecture 4 Problem Solving with MATLAB lin.

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