If you could solve Section 1.3 for me please

Section 1.1 1. a. Derive the diffusion equation for a chemical pollutant by considering the total amount of the chemical between = = a and s = &. h. If u(x, f) is the solution of the heat equation in a rod (0 0 (I, 0) = /(x) (0, t) = u(L, f) =0, 130, when f (1) = 6sin b. Solve the following initial boundary value problem for the diffusion equation O0 (I, 0) = f() 0=(L,1)=0, 130 when f (x) = 1, 13 1/2 Partial Differential Equations Section 1.3 4. Determine the equilibrium temperature distribution for the thin circular ring described in Figure 24.1 (p. 59). a. by finding the steady state solution directly. Hint: See Section 1.4 of the textbook. h. by computing the limit as f + co of the time-dependent solution. Section 1.4 5. a. Sketch the Fourier series (on the interval -L S es L), and determine the Fourier coefficients of the function f(s) = 1 , 2, 120. b. Sketch the Fourier cosine series and determine the Fourier coefficients of the function f(x) = 0, I