Example (Heat equation) The temperature u=u(x,t)of a long thin uniform rod satisfies du 2u where k is the thermal diffusivity of the rod. Definition (PDE) Partial differential equations:differential equations that involve an unknown function of more than one independent variables, together with partial derivatives of the function. 4口14①y至，元2000 Peipei Shang School of Mathematical Sciences shang@tongji.edu.Ordinary Differential EquationsExample (Heat equation) The temperature u = u(x,t) of a long thin uniform rod satisfies ∂u ∂ t = k ∂ 2u ∂ x 2 , where k is the thermal diffusivity of the rod. Definition (PDE) Partial differential equations: differential equations that involve an unknown function of more than one independent variables, together with partial derivatives of the function. Peipei Shang School of Mathematical Sciences shang@tongji.edu.cn Ordinary Differential Equations