1. There are some built in constants in MATLAB; i, j, pi, eps, inf, NaN. Whether a name is a built in constant or not can be checked by the statement ''which -all <name>''.
2. Type the following vector in the command window:
a) 𝐴= 123 b) 𝐵= 01−2−3 c) 𝐶= −120410−2106
i) Use MATLAB to find the value in the second row and the third column of matrix C.
ii) Use MATLAB to find the second row of matrix C.
iii) Use MATLAB to find the third column of matrix C.
iv) Use MATLAB to delete the second column of matrix C.
3. You can also perform Element-wise assignment of the Matrix elements.
a) >> A(1,1)=1; b) >> A_r1=[1 2]; c) >> e_col1=[1;3.7;8];
>> A(2,1)=3.7; >> A_r2=[3.7 -0.002]; >> e_col2=[2;2e-3;1.3e5];
>> A(1,2)=2; >> A_r3=[8 13000]; >> e_col3=[5;1.3e7;7];
>> A(3,2)=1.3e5; >> A=[A_r1; A_r2; A_r3] ; >> E=[e_col1 e_col2 e_col3];
4. Construct two matrices on your own; A and B and use the following operators:
a) A+B b) A-B c)A * B d) A.*B e) A. /B f)A. ^B
Also, Try some useful functions for Linear Algebra in MATLAB;
a) rank b) det c)inv d) eig e) ones f) eye g) diag h) transpose(use A')
Note: You can type ''help matfun'' (Matrix functions-numerical linear Algebra) in the command window for more information, or type ''elmat'' (Elementary matrices and matrix manipulation).
6. You can try some functions for creating arrays in MATLAB;
7. Plotting; Here are some useful functions for creating plots.
Example:
>> x=0:pi:2*pi; >> x=0:pi/100:2*pi;
>> y=sin(x); >> plot(x,sin(x))
>> y1=sin(x-.25); >> hold on
>> y3=sin(x-.5); >> plot(x, cos(x))
>> plot(x,y,x,y1,x,y3) >> hold off
Q. Given the autonomous system, 𝑥 =𝑎𝑥
where, 𝑎=−1𝑇, where T is the time constant. The solution for the differential equation is,
𝑥 𝑡 =𝑒𝑎𝑡𝑥𝑜 . Set T=5 and the initial condition x(0)=1.
a) create a script in MATLAB(.m file) where you plot the solution x(t) in the time interval 0 ≤t ≤25.
b) Add grid, and proper title and axis labels to the plot.
c) check out the help for the following 2D functions in MATLAB; semilogx, bar, hist, pie,scatter.
8. Create a vector with random numbers between 0 and 100. Find the following statistics; mean, median, standard deviation(std(x)) , minimum(min(x)), maximum(max(x)) and the variance(var(x)).
9. Given two complex numbers: 𝑐=4+𝑗3 𝑑=1−𝑗
a) Find the real and imaginary part of c and d in MATLAB. Also, find c+d and c-d, c*d and c/d.
b)Check specific functions abs, angle, imag, real, conj and complex.
c) Find r and θ. Find also the complex conjugate.
10. MATLAB offers lots of functions on polynomials, such as conv, roots, deconv, polyval, polyint, polyfit,etc . Look up these functions in the Help system in MATLAB.
Q. Define the following polynomial in MATLAB: 𝑝 𝑥 =−2.1𝑥4+2𝑥3+5𝑥+11
a) Find the roots of the polynomial.
b) Find p(x=2).
11. Given the following polynomials: 𝑝1 𝑥 =1+𝑥−𝑥2 𝑝2 𝑥 =2+𝑥3
a) Find the polynomial 𝑝 𝑥 =𝑝1 𝑥 .𝑝2 𝑥
b) Find the roots of the polynomial (p(x)=0) and find p(x=2).
c) Find the differentiation of 𝑝2(𝑥)
12. Find the sixth order polynomial that best fits the following function. 𝑦=sin(𝑥)
Also, plot both the function and the sixth order polynomial to compare the results.
13. Create the following expression in MATLAB. 𝑓 𝑥 =log 𝑎𝑥2+𝑏𝑥+𝑐 −sin(𝑎𝑥2+𝑏𝑥+𝑐)4𝜋𝑥2+cos 𝑥−2 (𝑎𝑥2+𝑏𝑥+𝑐)
Given, a=1, b=3,c=5, Find f(9) , [ Tip! You can split the expressions into different parts. This makes the expression simpler to read and understand, and you minimize the risk of making an error while typing the expression in MATLAB.]
14. Find the solution for the given equation. 𝑥1+2𝑥2=5
3𝑥1+4𝑥2=6 7𝑥1+8𝑥2=9
You need to set the equations on the following form,
a) 𝐴𝑥=𝑏 and calculate x=inv(A)*b.
b) Try using x=A\ b.
15. You can use the functions ''tic'' and ''toc'' to find the execution time. Try this simple program that calculates 𝑦=cos 𝑡 𝑓𝑜𝑟 𝑡=1 𝑡𝑜 100000
clear
tic
t_max=100000;
y=zeros(t_max,1);
for t=1:t_max
y(t,1)=cos(t);
end
toc
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