Mathematical Models Real-world situation Formulation interpretation Mathematical Model Mathematical Analysis Mathematical results Figure:The process of mathematical modeling Ordinary Differential Equations
Mathematical Models Real-world situation Formulation Interpretation Mathematical Model Mathematical Analysis Mathematical results Figure: The process of mathematical modeling Ordinary Differential Equations
Terminology Definition(DE) Differential equations:equations containing an unknown func- tion and one or more of its derivatives. 4日10y至，1元3000 Ordinary Differential Equations
Terminology Definition (DE) Differential equations: equations containing an unknown function and one or more of its derivatives. Definition (ODE) Ordinary differential equations: differential equations that involve an unknown function of a single independent variable . Example The population function P(t) dP dt = kP Ordinary Differential Equations
Terminology Definition(DE） Differential equations:equations containing an unknown func- tion and one or more of its derivatives. Definition (ODE) Ordinary differential equations:differential equations that in- volve an unknown function of a single independent variable. 4日10,1元2000 Ordinary Differential Equations
Terminology Definition (DE) Differential equations: equations containing an unknown function and one or more of its derivatives. Definition (ODE) Ordinary differential equations: differential equations that involve an unknown function of a single independent variable . Example The population function P(t) dP dt = kP Ordinary Differential Equations
Terminology Definition (DE) Differential equations:equations containing an unknown func- tion and one or more of its derivatives. Definition (ODE) Ordinary differential equations:differential equations that in- volve an unknown function of a single independent variable. Example The population function P(t) dP =kP dr 4口14①y至，元2000 Ordinary Differential Equations
Terminology Definition (DE) Differential equations: equations containing an unknown function and one or more of its derivatives. Definition (ODE) Ordinary differential equations: differential equations that involve an unknown function of a single independent variable . Example The population function P(t) dP dt = kP Ordinary Differential Equations
Example The temperature u=u(x,t)of a long thin uniform rod satisfies du 2u 01-kx2 where k is the thermal diffusivity of the rod. 4日10y4至，1无2000 Ordinary Differential Equations
Example 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. Ordinary Differential Equations