This document contains sample MATLAB code to demonstrate various vector, matrix, and function operations. It includes examples of initializing vectors and matrices, performing element-wise operations, matrix multiplication, calculating norms and angles between vectors, generating temperature conversion tables using user inputs, defining a function to find the roots of a quadratic equation, and defining a function to calculate the volume of a spherical tank. Sample code is provided to solve each problem, along with commentary on the results.
This presentation is a part of Computer Oriented Numerical Method . Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques.
This presentation is a part of Computer Oriented Numerical Method . Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques.
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MATLAB sessions: Laboratory 2
MAT 275 Laboratory 2
Matrix Computations and Programming in MATLAB
In this laboratory session we will learn how to
1. Create and manipulate matrices and vectors.
2. Write simple programs in MATLAB
NOTE: For your lab write-up, follow the instructions of LAB1.
Matrices and Linear Algebra
⋆ Matrices can be constructed in MATLAB in different ways. For example the 3 × 3 matrix
A =
8 1 63 5 7
4 9 2
can be entered as
>> A=[8,1,6;3,5,7;4,9,2]
A =
8 1 6
3 5 7
4 9 2
or
>> A=[8,1,6;
3,5,7;
4,9,2]
A =
8 1 6
3 5 7
4 9 2
or defined as the concatenation of 3 rows
>> row1=[8,1,6]; row2=[3,5,7]; row3=[4,9,2]; A=[row1;row2;row3]
A =
8 1 6
3 5 7
4 9 2
or 3 columns
>> col1=[8;3;4]; col2=[1;5;9]; col3=[6;7;2]; A=[col1,col2,col3]
A =
8 1 6
3 5 7
4 9 2
Note the use of , and ;. Concatenated rows/columns must have the same length. Larger matrices can
be created from smaller ones in the same way:
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 2
>> C=[A,A] % Same as C=[A A]
C =
8 1 6 8 1 6
3 5 7 3 5 7
4 9 2 4 9 2
The matrix C has dimension 3 × 6 (“3 by 6”). On the other hand smaller matrices (submatrices) can
be extracted from any given matrix:
>> A(2,3) % coefficient of A in 2nd row, 3rd column
ans =
7
>> A(1,:) % 1st row of A
ans =
8 1 6
>> A(:,3) % 3rd column of A
ans =
6
7
2
>> A([1,3],[2,3]) % keep coefficients in rows 1 & 3 and columns 2 & 3
ans =
1 6
9 2
⋆ Some matrices are already predefined in MATLAB:
>> I=eye(3) % the Identity matrix
I =
1 0 0
0 1 0
0 0 1
>> magic(3)
ans =
8 1 6
3 5 7
4 9 2
(what is magic about this matrix?)
⋆ Matrices can be manipulated very easily in MATLAB (unlike Maple). Here are sample commands
to exercise with:
>> A=magic(3);
>> B=A’ % transpose of A, i.e, rows of B are columns of A
B =
8 3 4
1 5 9
6 7 2
>> A+B % sum of A and B
ans =
16 4 10
4 10 16
10 16 4
>> A*B % standard linear algebra matrix multiplication
ans =
101 71 53
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 2
71 83 71
53 71 101
>> A.*B % coefficient-wise multiplication
ans =
64 3 24
3 25 63
24 63 4
⋆ One MATLAB command is especially relevant when studying the solution of linear systems of dif-
ferentials equations: x=A\b determines the solution x = A−1b of the linear system Ax = b. Here is an
example:
>> A=magic(3);
>> z=[1,2,3]’ % same as z=[1;2;3]
z =
1
2
3
>> b=A*z
b =
28
34
28
>> x = A\b % solve the system Ax = b. Compare with the exact solution, z, defined above.
x =
1
2
3
>> y =inv(A)*b % solve the system using the inverse: less efficient and accurate
ans =
1.0000
2.0000
3.0000
Now let’s check for accuracy by evaluating the difference z − x and z − y. In exact arithmetic they
should both be zero since x, y and z all represent the solution to the system.
>> z - x % error for backslash command
ans =
0
0
0
>> z - y % error for inverse
ans =
1.0e-015 *
-0.4441
0
-0.88 ...
Q1Perform the two basic operations of multiplication and divisio.docxamrit47
Q1
Perform the two basic operations of multiplication and division to a complex number in both rectangular and polar form, to demonstrate the different techniques.
· Dividing complex numbers in rectangular and polar forms.
· Converting complex numbers between polar and rectangular forms and vice versa.
Q2
Calculate the mean, standard deviation and variance for a set of ungrouped data
· Completing a tabular approach to processing ungrouped data.
Q3
Calculate the mean, standard deviation and variance for a set of grouped data
· Completing a tabular approach to processing grouped data having selected an appropriate group size.
Q4
Sketch the graph of a sinusoidal trig function and use it to explain and describe amplitude, period and frequency.
· Calculate various features and coordinates of a waveform and sketch a plot accordingly.
· Explain basic elements of a waveform.
Q5
Use two of the compound angle formulae and verify their results.
· Simplify trigonometric terms and calculate complete values using compound formulae.
Q6
Find the differential coefficient for three different functions to demonstrate the use of function of a function and the product and quotient rules
· Use the chain, product and quotient rule to solve given differentiation tasks.
Q7
Use integral calculus to solve two simple engineering problems involving the definite and indefinite integral.
· Complete 3 tasks; one to practise integration with no definite integrals, the second to use definite integrals, the third to plot a graph and identify the area that relates to the definite integrals with a calculated answer for the area within such.
Q8
Use the laws of logarithms to reduce an engineering law of the type y = axn to a straight line form, then using logarithmic graph paper, plot the graph and obtain the values for the constants a and n.
· See Task.
Q9
Use complex numbers to solve a parallel arrangement of impedances giving the answer in both Cartesian and polar form
· See Task.
Q10
Use differential calculus to find the maximum/minimum for an engineering problem.
· See Task.
Q11
Using a graphical technique determine the single wave resulting from a combination of two waves of the same frequency and then verify the result using trig formulae.
· See Task.
Q12
Use numerical integration and integral calculus to analyse the results of a complex engineering problem
· See Task.
Level of Detail in
Solution
s: Need to show work leading to final answer
Need
Question 1
(a) Find:
(4 + i2)
(1 + i3)
Use the rules for multiplication and division of complex numbers in rectangular form.
(b) Convert the answer in rectangular form to polar form
(c) Repeat Q1a by first converting the complex numbers to polar form and then using the rules for multiplication and division of complex numbers in polar form.
(d) Convert the answer in polar form to rectangular form.
Question 2
The following data within the working area consists of measurements of resistor values from a producti ...
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I am Manuela B. I am a Differential Equations Assignment Expert at mathsassignmenthelp.com. I hold a Master's in Mathematics from, the University of Warwick. I have been helping students with their assignments for the past 13 years. I solve assignments related to Differential Equations.
Visit mathsassignmenthelp.com or email info@mathsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Differential Equations Assignment.
MATLAB sessions: Laboratory 2
MAT 275 Laboratory 2
Matrix Computations and Programming in MATLAB
In this laboratory session we will learn how to
1. Create and manipulate matrices and vectors.
2. Write simple programs in MATLAB
NOTE: For your lab write-up, follow the instructions of LAB1.
Matrices and Linear Algebra
⋆ Matrices can be constructed in MATLAB in different ways. For example the 3 × 3 matrix
A =
8 1 63 5 7
4 9 2
can be entered as
>> A=[8,1,6;3,5,7;4,9,2]
A =
8 1 6
3 5 7
4 9 2
or
>> A=[8,1,6;
3,5,7;
4,9,2]
A =
8 1 6
3 5 7
4 9 2
or defined as the concatenation of 3 rows
>> row1=[8,1,6]; row2=[3,5,7]; row3=[4,9,2]; A=[row1;row2;row3]
A =
8 1 6
3 5 7
4 9 2
or 3 columns
>> col1=[8;3;4]; col2=[1;5;9]; col3=[6;7;2]; A=[col1,col2,col3]
A =
8 1 6
3 5 7
4 9 2
Note the use of , and ;. Concatenated rows/columns must have the same length. Larger matrices can
be created from smaller ones in the same way:
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 2
>> C=[A,A] % Same as C=[A A]
C =
8 1 6 8 1 6
3 5 7 3 5 7
4 9 2 4 9 2
The matrix C has dimension 3 × 6 (“3 by 6”). On the other hand smaller matrices (submatrices) can
be extracted from any given matrix:
>> A(2,3) % coefficient of A in 2nd row, 3rd column
ans =
7
>> A(1,:) % 1st row of A
ans =
8 1 6
>> A(:,3) % 3rd column of A
ans =
6
7
2
>> A([1,3],[2,3]) % keep coefficients in rows 1 & 3 and columns 2 & 3
ans =
1 6
9 2
⋆ Some matrices are already predefined in MATLAB:
>> I=eye(3) % the Identity matrix
I =
1 0 0
0 1 0
0 0 1
>> magic(3)
ans =
8 1 6
3 5 7
4 9 2
(what is magic about this matrix?)
⋆ Matrices can be manipulated very easily in MATLAB (unlike Maple). Here are sample commands
to exercise with:
>> A=magic(3);
>> B=A’ % transpose of A, i.e, rows of B are columns of A
B =
8 3 4
1 5 9
6 7 2
>> A+B % sum of A and B
ans =
16 4 10
4 10 16
10 16 4
>> A*B % standard linear algebra matrix multiplication
ans =
101 71 53
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 2
71 83 71
53 71 101
>> A.*B % coefficient-wise multiplication
ans =
64 3 24
3 25 63
24 63 4
⋆ One MATLAB command is especially relevant when studying the solution of linear systems of dif-
ferentials equations: x=A\b determines the solution x = A−1b of the linear system Ax = b. Here is an
example:
>> A=magic(3);
>> z=[1,2,3]’ % same as z=[1;2;3]
z =
1
2
3
>> b=A*z
b =
28
34
28
>> x = A\b % solve the system Ax = b. Compare with the exact solution, z, defined above.
x =
1
2
3
>> y =inv(A)*b % solve the system using the inverse: less efficient and accurate
ans =
1.0000
2.0000
3.0000
Now let’s check for accuracy by evaluating the difference z − x and z − y. In exact arithmetic they
should both be zero since x, y and z all represent the solution to the system.
>> z - x % error for backslash command
ans =
0
0
0
>> z - y % error for inverse
ans =
1.0e-015 *
-0.4441
0
-0.88 ...
Q1Perform the two basic operations of multiplication and divisio.docxamrit47
Q1
Perform the two basic operations of multiplication and division to a complex number in both rectangular and polar form, to demonstrate the different techniques.
· Dividing complex numbers in rectangular and polar forms.
· Converting complex numbers between polar and rectangular forms and vice versa.
Q2
Calculate the mean, standard deviation and variance for a set of ungrouped data
· Completing a tabular approach to processing ungrouped data.
Q3
Calculate the mean, standard deviation and variance for a set of grouped data
· Completing a tabular approach to processing grouped data having selected an appropriate group size.
Q4
Sketch the graph of a sinusoidal trig function and use it to explain and describe amplitude, period and frequency.
· Calculate various features and coordinates of a waveform and sketch a plot accordingly.
· Explain basic elements of a waveform.
Q5
Use two of the compound angle formulae and verify their results.
· Simplify trigonometric terms and calculate complete values using compound formulae.
Q6
Find the differential coefficient for three different functions to demonstrate the use of function of a function and the product and quotient rules
· Use the chain, product and quotient rule to solve given differentiation tasks.
Q7
Use integral calculus to solve two simple engineering problems involving the definite and indefinite integral.
· Complete 3 tasks; one to practise integration with no definite integrals, the second to use definite integrals, the third to plot a graph and identify the area that relates to the definite integrals with a calculated answer for the area within such.
Q8
Use the laws of logarithms to reduce an engineering law of the type y = axn to a straight line form, then using logarithmic graph paper, plot the graph and obtain the values for the constants a and n.
· See Task.
Q9
Use complex numbers to solve a parallel arrangement of impedances giving the answer in both Cartesian and polar form
· See Task.
Q10
Use differential calculus to find the maximum/minimum for an engineering problem.
· See Task.
Q11
Using a graphical technique determine the single wave resulting from a combination of two waves of the same frequency and then verify the result using trig formulae.
· See Task.
Q12
Use numerical integration and integral calculus to analyse the results of a complex engineering problem
· See Task.
Level of Detail in
Solution
s: Need to show work leading to final answer
Need
Question 1
(a) Find:
(4 + i2)
(1 + i3)
Use the rules for multiplication and division of complex numbers in rectangular form.
(b) Convert the answer in rectangular form to polar form
(c) Repeat Q1a by first converting the complex numbers to polar form and then using the rules for multiplication and division of complex numbers in polar form.
(d) Convert the answer in polar form to rectangular form.
Question 2
The following data within the working area consists of measurements of resistor values from a producti ...
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SAMPLE QUESTIONExercise 1 Consider the functionf (x,C).docxanhlodge
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
More instructions for the lab write-up:
1) You are not obligated to use the 'diary' function. It was presented only for you convenience. You
should be copying and pasting your code, plots, and results into some sort of "Word" type editor that
will allow you to import graphs and such. Make sure you always include the commands to generate
what is been asked and include the outputs (from command window and plots), unless the pr.
Lab 5 template Lab 5 - Your Name - MAT 275 Lab The M.docxsmile790243
Lab 5 template
%% Lab 5 - Your Name - MAT 275 Lab
% The Mass-Spring System
%% EX 1 10 pts
%A) 1 pts | short comment
%
%B) 2 pts | short comment
%
%C) 1 pts | short comment
%
%D) 1 pts
%E) 2 pts | List the first 3-4 t values either in decimal format or as
%fractions involving pi
%F) 3 pts | comments. | (1 pts for including two distinct graphs, each with y(t) and v(t) plotted)
%% EX 2 10 pts
%A) 5 pts
% add commands to LAB05ex1 to compute and plot E(t). Then use ylim([~,~]) to change the yaxis limits.
% You don't need to include this code but at least one plot of E(t) and a comment must be
% included!
%B) 2 pts | write out main steps here
% first differentiate E(t) with respect to t using the chain rule. Then
% make substitutions using the expression for omega0 and using the
% differential equation
%C) 3 pts | show plot and comment
%% EX 3 10 pts
%A) 3 pts | modify the system of equations in LAB05ex1a
% write the t value and either a) show correponding graph or b) explain given matlab
% commands
%B) 2 pts | write t value and max |V| value; include figure
%note: velocity magnitude is like absolute value!
%C) 3 pts | include 3 figures here + comments.
% use title('text') to attach a title to the figure
%D) 2 pts | What needs to happen (in terms of the characteristic equation)
%in order for there to be no oscillations? Impose a condition on the
%characteristic equation to find the critical c value. Write out main steps
%% EX4 10 pts
% A) 5 pts | include 1 figure and comment
%B) 2 pts
% again find dE/dt using the chain rule and make substitutions based on the
% differential equation. You should reach an expression for dE/dt which is
% in terms of y'
%C) 3 pts | include one figure and comment
Exercise (1):
function LAB05ex1
m = 1; % mass [kg]
k = 9; % spring constant [N/m]
omega0=sqrt(k/m);
y0=0.4; v0=0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on;
%------------------------------------------------------
function dYdt= f(t,Y,omega0)
y = Y(1); v= Y(2);
dYdt = [v; -omega0^2*y];
Exercise (1a):
function LAB05ex1a
m = 1; % mass [kg]
k = 9; % spring constant [N/m]
c = 1; % friction coefficient [Ns/m]
omega0 = sqrt(k/m); p = c/(2*m);
y0 = 0.4; v0 = 0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0,p); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on
%------------------------------------------------------
function dYdt= f(t,Y,omega0,p)
y = Y(1); v= Y(2);
dYdt = [v; ?? ]; % fill-in dv/dt
More instructions for the l ...
M210 Songyue.pages
__MACOSX/._M210 Songyue.pages
M210-S16-class-5.pdf
M 210 More drawing in LATEX February 23, 2016
Arcs
An arc of radius r from point (p,q) with initial angle ϕ (phi) and final angle ψ (psi) is drawn in
TikZ by the code
LATEX\draw (p,q) arc (phi:psi:r);
Note that TikZ does not require the center (a,b), which is often easier to determine that the arc’s
initial point. Polar coordinates (relative to the arc’s center) can be used to express the initial point
in terms of the arc’s center.
(a,b)
(p,q)
ϕ
ψ
r
p = a + r cosϕ
q = b + r sinϕ
In tikzpicture environment enter
\draw ({a+r*cos(phi)},{b+r*sin(phi)}) arc (phi:psi:r);
for the specific values of a, b, r, ϕ (phi) and ψ (psi).
LATEX
According to the TikZ’s manual, by default arcs are drawn in positive (counter-clockwise) direction,
assuming initial angle ϕ to be smaller than ψ. However, I have been able to draw arcs in negative
(clockwise) direction by choosing an initial angle larger than final angle.
Precise Label Positioning
The relative positions above, below, left, right, above left, above right, below left, and
below right, provide positioning relative to the node (indicated by the dot) as illustrated in the
following figures.
below
above
left right
above left
below left
above right
below right
While it is possible to adjust the separation between label and node, it is not that easy to adjust
the angle (the above provide label placement only for angles in multiples of 45◦). The following will
work to place the label (that is its center) at the the indicated position: precise distance s at relative
angle θ from the position of the node.
node
lab
el
s
node coordinates (nx,ny)
label coordinates (lx, ly)
θ
To place label at the above mentioned position use the code (where θ is theta degrees):
M 210 — February 23, 2016 page 44
LATEX\draw ({nx + s*cos(theta)}, {ny + s*sin(theta)}) node {label};
To rotate the label as in the above illustration, use code:
LATEX\draw ({nx + s*cos(theta)}, {ny + s*sin(theta)}) node {\rotatebox{theta}{label}};
Special Triangles
In trigonometry the triangles with degrees 45-45-90 and 30-60-90 provide exact values for the trigono-
metric functions. It is quite easy to obtain the exact values of angles of 15 and 75 degrees from those
of 30 degrees by half- and double-angle formulas and other trigonometric identities, however, these
values can also be obtained from the following figure containing an equilateral triangle in a square
with sides equal to 2.
1
The Regular Pentagon. Use trigonometric functions to draw a regular pentagon with its lower
side along the line segment from (−1,0) to (1,0). Start by drawing this line segment.
LATEX\begin{center}
\begin{tikzpicture}[scale=2]
\draw[line width=1.2pt] (-1,0) -- (1,0);
\end{tikzpicture}
\end{center}
Extend the line segment on both sides by adding the following code.
LATEX\draw[line width=1.2pt] (1,0) -- ({1+2*cos(72)},{2*sin(72)});
\draw[line width=1.2pt] ...
MATLAB DOCUMENTATION ON SOME OF THE MODULES
A.Generate videos in which a skeleton of a person doing the following Gestures.
1.Tilting his head to right and left
2.Tilting his hand to right and left
3.Walking
in matlab.
B. Write a MATLAB program that converts a decimal number to Roman number and vice versa.
C.Using EZ plot & anonymous functions plot the following:
· Y=Sqrt(X)
· Y= X^2
· Y=e^(-XY)
D.Take your picture and
· Show R, G, B channels along with RGB Image in same figure using sub figure.
· Convert into HSV( Hue, saturation and value) and show the H,S,V channels along with HSV image
E.Record your name pronounced by yourself. Try to display the signal(name) in a plot vs Time, using matlab.
F.Write a script to open a new figure and plot five circles, all centered at the origin and with increasing radii. Set the line width for each circle to something thick (at least 2 points), and use the colors from a 5-color jet colormap (jet).
G. NEWTON RAPHSON AND SECANT METHOD
H.Write any one of the program to do following things using file concept.
1.Create or Open a file
2. Read data from the file and write data to another file
3. Append some text to already existed file
4. Close the file
I.Write a function to perform following set operations
1.Union of A and B
2. Intersection of A and B
3. Complement of A and B
(Assume A= {1, 2, 3, 4, 5, 6}, B= {2, 4, 6})
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WhatsApp at +1(315)557-6473.
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Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
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Travaux Pratique Matlab + Corrige_Smee Kaem Chann
1. 1/3Smee
Matlab (TP1) 25%pt
1. Vectors and Matrices Initialize the following variables:
A=[
5 … 5
⋮ ⋱ ⋮
5 … 5
]
9×9
(use ones,zeros) ,B= (A 9x9 matrix of all 0 but with the values [1 2 3 4 5 4 3 2 1] on
diagonal, use zeros, diag) C= (A 3x4 matrix, use NaN) ,D=
2. Define the vector V = [0 1 2 ... 39 40]. What is the size of this vector? Define the vector W containing the first five and the last
five elements of V then define the vector Z = [0 2 4 ... 38 40] from V.
3. Define the matrix What are its dimensions m x n? Extract from this matrix
and .. Make a matrix Q obtained by taking the matrix M intersected between all the 3rd
rows
and one column out of 2. Calculate the matrix products NP = N x P, NtQ = N 'x Q and NQ = N x Q, then comment the results.
4. Define the variable 𝑥 = [
𝜋
6
,
𝜋
4
,
𝜋
3
] and calculate y1=sin(x) and y2=cos(x) Then calculate tan(x) using only the previous y1 and y2.
5. The following vectors are considered:
𝑢 = (
1
2
3
) , 𝑣 = (
−5
2
1
) 𝑎𝑛𝑑 𝑤 = (
−1
−3
7
)
a. Calculate t=u+3v-5w
b. Calculate ‖𝑢‖, ‖𝑣‖, ‖𝑤‖ and the cosine of the angle α formed by the vectors u and v, and α in degrees.
6. Application:This problem requires you to generate temperature conversion tables. Use the following equations, which describe
the relationships between tempera-tures in degrees Fahrenheit(TF) , degrees Celsius(TC), kelvins( TK ) , and degrees Rankine
(TR ) , respectively: 𝑇𝐹 = 𝑇𝑅 − 459.67 𝑜
𝑅, 𝑇𝐹 =
9
5
𝑇𝐶 + 32 𝑜
𝐹, 𝑇𝑅 =
9
5
𝑇𝑘 You will need to rearrange these expressions to solve
some of the problems.
(a) Generate a table of conversions from Fahrenheit to Kelvin for values from 0°F to 200°F. Allow the user to enter the
increments in degrees F between lines. Use disp and fprintf to create a table with a title, column headings, and appropriate
spacing.
(b) Generate a table of conversions from Celsius to Rankine. Allow the user to enter the starting temperature and the increment
between lines. Print 25 lines in the table. Use disp and fprintf to create a table with a title, column headings, and appropriate
spacing.
(c) Generate a table of conversions from Celsius to Fahrenheit. Allow the user to enter the starting temperature, the increment
between lines, and the number of lines for the table. Use disp and fprintf to create a table with a title, column headings, and
appropriate spacing.
7. Defined function Write in Matlab to find roots of quadratic equation 𝑦 = 𝑎𝑥2
+ 𝑏𝑥 + 𝑐 by contained the roots 𝑥 = [𝑥1 𝑥2].
Now, apply your program for the following cases:
a. a=1,b=7,c=12 b. a=1,b=-4,c=4 c. a=1,b=2,c=3
8. Using a function to calculate the volume of liquid (V) in a spherical tank,
given the depth of the liquid (h) and the radius (R).
V=SphereTank(R,h)
Now, apply your program for the following cases:
a. R=2,h=1 b. R=h=5 𝑉 =
𝜋ℎ2(3𝑅−ℎ)
3
2. 2/3Smee
Solution
1.
A=5*ones(9) or A=5.+zeros(5,5)
B. a=[1:5,4:-1:1]
b=diag(a)
c=zeros(9,9)
D=b+c
or D=diag([1:5,4:-1:1])+zeros(9,9)
C=NaN(3,4)
D=([1:10;11:20;21:30;31:40;41:50;51:60;61:70;71:80;81:90;91:100])'
2.
V=[0:40]
size(V)
W=[V(:,1:5) V(:,37:41)]
Z=V(:,[1:2:40])
3.
M=[1:10;11:20;21:30]
size(M)
N=M(:,1:2)
P=M([1 3],[3 7])
Q=M(:,[1:2:10])
NP=N*P
NtQ=N'*Q
NQ=
%Error because both its size is not available for multiple matric
4.
x=[pi/6 pi/4 pi/3]
y1=sin(x)
y2=cos(x)
y=y1./y2
5.
u=[1;2;3]
v=[-5;2;1]
w=[-1;-3;7]
t=u+3*v-5*w
U=norm(u)
V=norm(v)
W=norm(w)
z=dot(u,v);
a=z/[U*V]
b=acosd(a)
6.
a.
incr=input('put the value of the incressing temperature')
F=0:incr:200;
K=(5.*(F+459.67)./9);
table=[F;K];
disp('Conversions from Fahrenheit to kelvin')
disp('In_F conversion to Kelvin')
fprintf('%3.4f %3.4frn',table);
b.
S=input('put the value of the starting temperature')
C=linspace(S,200,25);
R=(C+273.15).*1.8;
table=[C;R];
disp('Conversions from C to Rekin')
3. 3/3Smee
disp('In_C conversion to Rekin')
fprintf('%3.4f %3.4frn',table);
c.
S=input('put the value of the starting temperature')
incr=input('put the value of the incressing temperature')
C=linspace(S,200,incr);
F=1.8.*C+32
table=[C;F];
disp('Conversions from C to F')
disp('In_C conversion to F')
fprintf('%3.4f %3.4frn',table);
7. Defined Function
function x = quadratic(a,b,c)
delta = 4*a*c;
denom = 2*a;
rootdisc = sqrt(b.^2 - delta); % Square root of the discriminant
x1 = (-b + rootdisc)./denom;
x2 = (-b - rootdisc)./denom;
x = [x1 x2];
end
Comment Window
quadratic(1,7,12)
quadratic(1,-4,4)
quadratic(1,2,3)
8.
function volume=SphereTank(radius,depth)
volume= pi*depth.^2*(3.*radius-depth)/3;
end
Comment Window
SphereTank(2,1)
SphereTank(5,5)
______________________________________________________________________________________________________________________
8/13/2017
5:32PM
Corrected by
Mr.Smee Kaem Chann
Tel : +885965235960