数学物理方法Chapt 3.1 3.2.pptxVIP

Chapt 3: Differential Equations Separation of Variables;(P329 MMP) 几个重要概念术语 (terms)： 1. 自变量、因变量 2. ODE PDE 3. Linear operator (线性算符) 4. 齐次、线性 5. Linearly independent solutions 线性无关解 6. Order, degree (阶、次）;1. Differential Equations：自变量、因变量;2. ODE PDE;ODE PDE;3. Linear Operator (线性算符); ;4. 齐次、线性 (Homogeneous, Linear);补充;Chapt 3: Differential Equations;5. Solutions to ODE：linearly independent;Solutions to ODE：linear combination (superposition principle);?;6. Order, Degree (阶、次) ;Summary ;Chapt 3: Differential Equations;Chapt 3: Differential Equations;3.2 First-order ODEs;3.2 First-order Equations;1. Separable Equations;Example : PARACHUTIST 跳伞;?; ; ;it is always important to check the solution, we verify that our solution satisfies the original differential equation:;Chapt 3: Differential Equations;下周一交作业 3.1, 3.2, 3.3（10月28日）;Chapt 3: Differential Equations;More on the Parachute Problem “Parachute Problem.ppt” （公共邮箱）; 2. Exact differentials;We note that separability and exactness are independent attributes. All separable ODEs are automatically exact, but not all exact ODEs are separable.;证明;Example 2: A nonSeparable Exact ODE;More discussions;Chapt 3: Differential Equations;3. Equations Homogeneous in x and y;A generalization of Homogeneous in x and y is to modify the definition of homogeneity by assigning different weights to x and y (note that corresponding weights must then also be assigned to dx and dy). ;Chapt 3: Differential Equations;General Solution Particular Solution ;4. Linear First-order ODEs;Chapt 3: Differential Equations;Discussions （1）;Discussions （2）;Example : RL circuit;Solve the following linear first-order ODE for y(x)