北京大学 数学物理方法 课件01

Outline 1 5 fi n n 2007cS C S Wu1 n Outline 1 5 5 U 5 5 2 u D g d Lambert 1 C S Wu1 n Outline 1 5 5 U 5 5 2 u D g d Lambert 1 C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s 1 5 5 U 5 5 2 u D g d Lambert 1 C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s 5 L a 5 L 2u t2 a2 2u fL 2 t2 a2 2 9D u t 2u fL t 2 Poisson 2u fL 2 55 L 1u1 2u2 1L u1 2L u2 C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s 5 L a 5 L 2u t2 a2 2u fL 2 t2 a2 2 9D u t 2u fL t 2 Poisson 2u fL 2 55 L 1u1 2u2 1L u1 2L u2 C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s 5 r 5 L u f u L 5 f fi g k g g XJf 0 g C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s 5 r 5 L u f u L 5 f fi g k g g XJf 0 g C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s 5 r 5 L u f u L 5 f fi g k g g XJf 0 g C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s 5 r 5 L u f u L 5 f fi g k g g XJf 0 g C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s 5 aq r C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s 5 aq r C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s o 0 XJ u L u f K u L u f U 5 eu1 u2 g L u 0 L u1 0L u2 0 K 5 c1u1 c2u2 g L c1u1 c2u2 0 c1 c2 C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s o 0 XJ u L u f K u L u f U 5 eu1 u2 g L u 0 L u1 0L u2 0 K 5 c1u1 c2u2 g L c1u1 c2u2 0 c1 c2 C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s U 5 eu1 u2 g L u f L u1 fL u2 f K u1 u2 A g L u1 u2 0 g A A g E g g g A A g C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s U 5 eu1 u2 g L u f L u1 fL u2 f K u1 u2 A g L u1 u2 0 g A A g E g g g A A g C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s U 5 eu1 u2 g L u f L u1 fL u2 f K u1 u2 A g L u1 u2 0 g A A g E g g g A A g C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s U 5 n eu1 u2 O v g L u1 f1L u2 f2 K 5 c1u1 c2u2 v g L c1u1 c2u2 c1f1 c2f2 C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s 1 5 5 U 5 5 2 u D g d Lambert 1 C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s k k X 2u x y x2 0 u x y c1 y xc2 y c1 y c2 y qX 2u x y x y 0 u x y c1 x c2 y c1 x c2 y C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s k k X 2u x y x2 0 u x y c1 y xc2 y c1 y c2 y qX 2u x y x y 0 u x y c1 x c2 y c1 x c2 y C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s k k X 2u x y x2 0 u x y c1 y xc2 y c1 y c2 y qX 2u x y x y 0 u x y c1 x c2 y c1 x c2 y C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s k k X 2u x y x2 0 u x y c1 y xc2 y c1 y c2 y qX 2u x y x y 0 u x y c1 x c2 y c1 x c2 y C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s Laplace 2u x2 2u y2 0 C x iy x iy u x u x u x u u u y u y u y i u u C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s Laplace 2u x2 2u y2 0 C x iy x iy u x u x u x u u u y u y u y i u u C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s Laplace 2u x2 2u y2 0 C x iy x iy u x u x u x u u u y u y u y i u u C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s Laplace 2u x2 2u y2 0 C x iy x iy u x u x u x u u u y u y u y i u u C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s Laplace 2u x2 2u y2 0 C x iy x iy u x u x u x u u u y u y u y i u u C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s Laplace 2u x2 2u y2 0 C x iy x iy u x u x u x u u u y u y u y i u u C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s Laplace 2u x2 2u y2 0 2u x2 2u 2 2 2u 2u 2 2u y2 2u 2 2 2u 2u 2 C 2u 0 2u x2 2u y2 0 u x y f x iy g x iy C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s Laplace 2u x2 2u y2 0 2u x2 2u 2 2 2u 2u 2 2u y2 2u 2 2 2u 2u 2 C 2u 0 2u x2 2u y2 0 u x y f x iy g x iy C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s Laplace 2u x2 2u y2 0 2u x2 2u 2 2 2u 2u 2 2u y2 2u 2 2 2u 2u 2 C 2u 0 2u x2 2u y2 0 u x y f x iy g x iy C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s Laplace 2u x2 2u y2 0 2u x2 2u 2 2 2u 2u 2 2u y2 2u 2 2 2u 2u 2 C 2u 0 2u x2 2u y2 0 u x y f x iy g x iy C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s U d u 5 fl K C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s fl K o k A d 5 A U X U X C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s fl K o k A d 5 A U X U X C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s 5 fl K z 5 fl K C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s 5 fl K z 5 fl K u p fl K C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s 5 fl K z 5 fl K u p fl K C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s Laplace K Poisson C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s Laplace K Poisson C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String Superpositionability of Solutions General Solution of PDE s Laplace K Poisson C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution 1 5 5 U 5 5 2 u D g d Lambert 1 C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 C x at x at u x u x u x u u u t u t u t a u u C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 C x at x at u x u x u x u u u t u t u t a u u C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 C x at x at u x u x u x u u u t u t u t a u u C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 C x at x at u x u x u x u u u t u t u t a u u C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 C x at x at u x u x u x u u u t u t u t a u u C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 C x at x at u x u x u x u u u t u t u t a u u C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 2u x2 2u 2 2 2u 2u 2 2u t2 a2 2u 2 t 2 2u 2u 2 C 2u 0 2u t2 a2 2u x2 0 u x t f x at g x at C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 2u x2 2u 2 2 2u 2u 2 2u t2 a2 2u 2 t 2 2u 2u 2 C 2u 0 2u t2 a2 2u x2 0 u x t f x at g x at C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 2u x2 2u 2 2 2u 2u 2 2u t2 a2 2u 2 t 2 2u 2u 2 C 2u 0 2u t2 a2 2u x2 0 u x t f x at g x at C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 2u x2 2u 2 2 2u 2u 2 2u t2 a2 2u 2 t 2 2u 2u 2 C 2u 0 2u t2 a2 2u x2 0 u x t f x at g x at C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 u x t f x at g x at d L d f x at L x mD t 0 f x a mD C g x at K L x D t 0 g x a D C C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 u x t f x at g x at d L d f x at L x mD t 0 f x a mD C g x at K L x D t 0 g x a D C C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 u x t f x at g x at d L d f x at L x mD t 0 f x a mD C g x at K L x D t 0 g x a D C C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 u x t f x at g x at f x at g x at D p Z6 5 g k U 5 C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution g 2u t2 a2 2u x2 0 u x t f x at g x at f x at g x at D p Z6 5 g k U 5 C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution 1 5 5 U 5 5 2 u D g d Lambert 1 C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution fl K 2u t2 a2 2u x2 0 x 0 u x t t 0 x x u t t 0 x x u x t f x at g x at f x g x x a f 0 x g0 x x C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution fl K 2u t2 a2 2u x2 0 x 0 u x t t 0 x x u t t 0 x x u x t f x at g x at f x g x x a f 0 x g0 x x C S Wu1 n Main Properties of Linear PDE s Wave Propagation in Infi nite String General Solution of d Lambert Solution fl K 2u t2 a2 2u x2 0 x 0 u x t t 0 x x u t t 0 x x 1 f x g x x f x g