Recent content by splelvis

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    How to Relate r(t)=x^2(t)+y^2(t) to r'=r-r^3 in Differential Equations?

    Homework Statement i had solve the C1 question, But in c2, i am not sure what is the relationship between r(t)=x^2(t)+y^2(t) and the r'=r-r^3. not get the meaning of that question, how to use the r(t)=x^2(t)+y^2(t) to get the r'=r-r^3? can anyone explain to me? thanks!
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    Integrating Ln(√(4-y^2)+2) from -2 to 2

    is that should be log(2cos(x)+2)2cos(x)dx? anyway that is good , thank you
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    Integrating Ln(√(4-y^2)+2) from -2 to 2

    from -2 to 2, integral Ln(√(4-y^2)+2)dy, how to integral that?
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    Double Integrals: Evaluate I for Domain D

    to evaluate the integral: I=dxdy/(x^2+y^2)^(1/2) over domain D: given by 1<=x^2+y^2<=4. what should i take the limits to integral? dx and dy
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    Numerical approximation of the solution

    u''(x)=f(x), boundary conditions u(a)=0,u(b)=0. (u(x+h)-2u(x)+u(x-h))/h^2=f(x); maltab code: clear all a=0; b=1; n=10; h=(b-a)/(n+1); x_with_boundary=linspace(a,b,n+2)'; x=x_with_boundary(2:n+1); A=h^(-2).*(diag(ones(1,n-1),-1)+diag(-2.*ones(1,n),0)+diag(ones(1,n-1),1))...
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    MATLAB Matlab second derivative approximation

    i have find my error, f9should be f9(x(i),y(j))
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    MATLAB Matlab second derivative approximation

    clear all; nx=50; ny=30; hx=pi/nx; x=linspace(0,pi,nx+1); y=linspace(0,pi,ny+1); x_plus_h=x+hx.*ones(1,nx+1); x_minus_h=x-hx.*ones(1,nx+1); for i=1:nx+1 for j=1:ny+1 f_xx(j,i)=(f9(x_plus_h(i),y(j))-2*f9+f9(x_minus_h(i),y(j)))./(hx.^2); end; end; [xx,yy]=meshgrid(x,y)...