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5. A N-by-N diagonal matrix is one of the form d 1 d2 , ...

5. A N-by-N diagonal matrix is one of the form d 1 d2 , d N where d1, d2, , d N are some numbers. The inverse of D is simply 1/d1 1/d2 D-1 , 1/ dN provided no d1, d2, , d n is zero. Diagonal matrices can be constructed quite easily using the diag function in MATLAB . For example the...

1. (20 points)Suppose z=[10 40 50 80 30 70 60 90]. What does...

1. (20 points)Suppose z=[10 40 50 80 30 70 60 90]. What does this vector look like after each of these commands? (i) z(z>=50) (i) (({:2:7)=zeros(1,4) (iii)z(7:-2:1)=fliplr(z(1:2:7) = (iv) z([3 4 8 1])=[] = 2. (20 points) Use the linspace function to create vectors identical to the follo...

former Serv's f (+) = 90 + W a. 1 of cos(ntx) d + , L = K ...

former Serv's f (+) = 90 + W a. 1 of cos(ntx) d + , L = K 2 n=1 of n = 4 W - 2 \ + (- - ) t Cos(nx) K 2 A n=1 ( ti) ( n-1 (- - I , n = (us(nk) . & 2 F(+) - = 2/K K + E - (-1)"- \ n=1 X I Cus(nx) . (nt1)(n-1) fl+ ) 8 2 - (-1) n - \ 2 t W (n+1)(n-1...

1. Computer Problem 1. IVP, x’= f(t,x) = 3x,x(0) = 1. ...

1. Computer Problem 1. IVP, x’= f(t,x) = 3x,x(0) = 1. f) Now track errors t vs eh(t) curves for each of the h from d. g) Now show error in a different way. Plot logh vs logeh(5) (i.e. the error at just the terminal time t = 5). What do you expect to see and what do you actually see – ...

Consider the function 4.x² - 7, - 2 x V 1, f(x) = 3,...

Consider the function 4.x² - 7, - 2 x V 1, f(x) = 3, 1 < . V 2. (c) Plot a 10-term Fourier series approximation of f on [ - 2,2]. This cannot be handwritten - options for producing plots include (but are not limited to) MAPLE, MATLAB, Excel, Wolfram.Alpha. (d) Optional Extra Cred...

If Y (t) is the solution of the following Initial Value Prob...

If Y (t) is the solution of the following Initial Value Problem (IVP): y/=6e"ly-20)72 y(0) = -1, our final goal is to obtain the value Y(1) by solving numerically the IVP. a) Check that the function Y (t) = 2t - e-6t is the solution of this IVP. It is not necessary to deduce it, but on...

Problem Set 6 Total number of points: 100. 1. (35 points...

Problem Set 6 Total number of points: 100. 1. (35 points) A hemispherical tank of radius R is initially filled with water. There is a hole of radius ro at the bottom of the tank through which the water drains under the influence of gravity (Fig. 1). Thus the velocity U of water exiting the bot...

Problem Set 5 1. (15 points) Consider the following system ...

Problem Set 5 1. (15 points) Consider the following system of equations f1(x1,x2 = COS (2x1) - cos(2x2) - 0.4 (1) f2(x1,x2 - 2(x2 - x1) + sin(2x2) - sin(2x1)-1.2 - (2) Solve the above system using Newton-Raphson method, a starting point of (0,1), and by setting your own tolerance. 2. (25 poi...

Problem Set 4 1. (15 points) Explain why the Midpoint Rule ...

Problem Set 4 1. (15 points) Explain why the Midpoint Rule can integrate a straight line exactly and the Simpson's Rule can integrate a cubic exactly. 2. (25 points) Consider the integral over one panel of width h: I f(x) dx. Utilize the error analysis of the midpoint formula presented in clas...

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