Mathematics Homework Solutions

Convolution of Function f*f

I need to verify that how f*f becomes xf(x) in given f.

Heat Equation

Heat Equation. See attached file for full problem description.

A simple steady-state problem of heat equation

A simple steady-state problem of heat equation. See attached file for full problem description.

Simple Heat Equation

Simple Heat Equation. See attached file for full problem description.

Separation of Variables

Separation of Variables. See attached file for full problem description.

Sine Wave

I need a solution with Matlab command. See attached file for full problem description.

Partial Differential Equations

Partial Differential Equations. I'm having trouble in determining a linear operator. See attached file for full problem description.

PDE in heat equation

Please see the attachment file. I don't know how to start for the part1 problem. I need your advice. For the second one, I used fourier transfor so that I got dU/dt = K(iw)^2 U U(0,t) = 0 U(w,0) = F(w) ,so the equation become ODE in capital U( with respect to time).

Polar Coordinates

Polar Coordinates. See attached file for full problem description.

Heat Equation

Heat Equation. See attached file for full problem description.

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