Matlab Help - Taylor Series

gap9q3

I am studying and I cannot figure out how to do this practice problem... Can ANYONE help me please! Thanks!


The function 1/(1-x) can be approximated using a specific type of Taylor Series as follows:

1/(1-x)≈Σ(where n=0, and k=∞)=x^0+x^1+x^2+x^3....

Write a program to calculate the series approximation using a "for" loop running from 1 to k. Also, calculate the correct value. Test the code for k=5 & K=10 with x=0.5.

Thanks a lot, I've been working on this for a while, and don't usually get stuck with programming, I just haven't learned the "for" loop too well yet.

shwaip

post the code of any attempt you've made, and we'll help you out.

gap9q3

shwaip wrote:

post the code of any attempt you've made, and we'll help you out.

k=5
x=0.5

k=10
x=0.5

for n = 0:k
x(n) = x(n-1) + x^n
end

shwaip

close.

matlab uses 1-based indexing, so the first element of the array is x(1).

i'd do something like this:

k=5
x=0.5
est=0;
for n=0:k
  est = est + x^n;
end

gap9q3

shwaip wrote:

close.

matlab uses 1-based indexing, so the first element of the array is x(1).

i'd do something like this:

k=5
x=0.5
est=0;
for n=0:k
  est = est + x^n;
end

THANKS!! I think I got it!

My friend and I have one more we can't figure out, if you are willing to help. I'll give you the problem, original code template, and what I have so far.

• An m-file, for_sines.m, with minimal documentation is in the classwork folder – add code to generate and plot the 3 sine waves from Lab 4 using"for" loops. Recall that we plotted sin(2pft) vs. t for f = 6, 8, and 10 Hz and t running from 0 to 2.5 sec in 0.01 sec increments. Lab 4 Assignment is in Lecture 4 in the "classwork" folder. The t array and sine array are initialized in for_sines.m . Other than this initialization, don't use any vector initialization; that is, generate both the final time and frequency vectors and the 3 sine waves using loops. Generate the 3 subplots using a loop. Your code will yield the same graph as before; however, now include frequency is in the title.

Template:
% for_sines.m

% yourname and lab section
    fprintf('\nyourname labsection\n');
% initialize t and sine to zeros
    t=zeros(1,251);
    sine=zeros(3,length(t));
% initialize f to its proper values using a "for" loop
;
% initialize t to its proper values using a "for" loop
;
% calculate the sine and plot using a "for" loop
    figure;

What I have thus far:

% for_sines.m

% yourname and lab section
    fprintf('\n Gretchen Paden, Th 3:00-5:00 \n');
% initialize t and sine to zeros
    t=zeros(1,251);
    sine=zeros(3,length(t));
    sin_t(1,:) = sin(2*pi*f(1).*t)
        t = 0:.01:2.5
        f = 6:2:10
% initialize f to its proper values using a "for" loop
    for f=0:.01:2.5
    disp(f)
    end
% initialize t to its proper values using a "for" loop
    for t = 0:.01:2.5
    disp(f)
    end
% calculate the sine and plot using a "for" loop
    figure;
    for ii
    y(ii,;)=sin(2*pi*f(ii).*t);
    subplot(3,1,ii),plot(x,y(1,:),'k');ylabel('y');xlabel('x');title(Frequency);grid on
    end

Let me know if you can help. Thanks a million!!

shwaip

comments are in code

% for_sines.m

% yourname and lab section
    fprintf('\n Gretchen Paden, Th 3:00-5:00 \n');
% initialize t and sine to zeros
    t=zeros(1,251);
    sine=zeros(3,length(t));

%    sin_t(1,:) = sin(2*pi*f(1).*t)
%        t = 0:.01:2.5
%        f = 6:2:10

%you don't need any of these lines, and you're supposed to initialize t, f using a for loop.
%(your method is actually better, but that's not what's assigned).

% initialize f to its proper values using a "for" loop

    for f=0:.01:2.5
    disp(f)
    end
%all you're doing here is displaying numbers.  you need to store (6,8,10) into an array, f.

% initialize t to its proper values using a "for" loop
    for t = 0:.01:2.5
    disp(f)
    end

%same as above, but now you want to store the values into an array, t.

% calculate the sine and plot using a "for" loop

%you should do this in 2 steps.  first calculate the sin values, and then plot.
%you'll need to loop over f and t.

    figure;
    for ii


      y(ii,;)=sin(2*pi*f(ii).*t);
      subplot(3,1,ii)
      plot(x,y(1,:),'k');
      ylabel('y');
      xlabel('x');
      title('Frequency');
      grid on
    end

gap9q3

THANKS SO MUCH!!! May need more help next week! You are a life saver!!!

gap9q3

Oh, P.S. GO BARACK!!!!

gap9q3

I'm still getting and error...

% for_sines.m

% yourname and lab section
fprintf('\n Gretchen Paden, Th 3:00-5:00 \n');
% initialize t and sine to zeros
t=zeros(1,251);
sine=zeros(3,length(t));

% sin_t(1,:) = sin(2*pi*f(1).*t)
% t = 0:.01:2.5
% f = 6:2:10

% initialize f to its proper values using a "for" loop

for i = 6:2:10
f = i
end

% initialize t to its proper values using a "for" loop
for ii = 0:.01:2.5
t = ii
end

% calculate the sine and plot using a "for" loop

%you should do this in 2 steps. first calculate the sin values, and then plot.
%you'll need to loop over f and t.


figure;
for ii
y(ii,:)=sin(2*pi*f(ii).*t);
subplot(3,1,ii)
plot(x,y(1,:),'k');
ylabel('y');
xlabel('x');
title('Frequency');
grid on
end

shwaip

1) what error.

2) if you post your code inside [php]

paste code here

[/php] it'll look nicer

gap9q3

shwaip wrote:

1) what error.

2) if you post your code inside

% for_sines.m

% yourname and lab section
    fprintf('\n Gretchen Paden, Th 3:00-5:00 \n');
% initialize t and sine to zeros
    t=zeros(1,251);
    sine=zeros(3,length(t));

%    sin_t(1,:) = sin(2*pi*f(1).*t)
%        t = 0:.01:2.5
%        f = 6:2:10

% initialize f to its proper values using a "for" loop

    for i = 6:2:10
    f = i
    end

% initialize t to its proper values using a "for" loop
    for ii = 0:.01:2.5
    t = ii
    end

% calculate the sine and plot using a "for" loop

%you should do this in 2 steps.  first calculate the sin values, and then plot.
%you'll need to loop over f and t.

    figure;
    for n = 1:3
    sine(n,:)=sin(2*pi*f(n).*t);
    end

    for n
    subplot(3,1,n)
    plot(t,sine(1,:));
    ylabel('sin(t)');
    xlabel('t');
    title('Frequency');
    end

it'll look nicer

Error: ??? Index exceeds matrix dimensions.

And the plot is blank

shwaip

it should give you the line that the error is on.

your loops aren't doing what you think they're doing. you might want to try stepping through them (mentally, on paper, or using matlab debug if you know how) and see if they're actually working...