Transform the following equations into the integral form similar to (5.1). For each equation, identify, if present, the rate of change term, volumetric source term, convective flux term, and diffusive flux term.

a) Linear convection equation \(u_{t}+c u_{x}=0\), where \(c>0\) is a constant.

b) One-dimensional heat equation \(u_{t}=a^{2} u_{x x}+f(x)\).

c) Three-dimensional heat equation \(u_{t}=abla^{2} u+g(\boldsymbol{x})\). (Hint: Use the identity \(abla^{2} u=\operatorname{div}(abla u)\) and the divergence theorem.)

d) Three-dimensional Poisson equation \(abla^{2} u=g(\boldsymbol{x})\).

e) One-dimensional Burgers equation \(u_{t}+u u_{x}=\mu u_{x x}\), where \(\mu>0\) is a constant.