6

1

1.1 1.2 1.3 1.4

1.4.1 1.4.2

1.5 1.5 : Fourier

2 2.1 2.2 2.3

2.3.1 2.3.2 2.3.3 2.3.4 ()2.3.5 2.3.6 2.3.7 , , 2.3.8

2.3 : 2.4 ( )

2.4.1 2.4.2 2.4.3

2.5 Laplace : 2.5.1 Laplace

7

2.5.2 Laplace 2.5.3 ( )2.5.4 Laplace

3 Fourier3.1 E 3.2 3.3 Fourier

3.3.1 Fourier3.3.2 Fourier3.3.3 A f(x) 3.3.4 3.3.5 Fourier

3.4 Fourier 3.5 Fourier 3.6 Fourier

4 : 4.1 4.2 4.3 4.4 4.5 4.6

4.6.1 Snell4.6.2 () 4.6.3

5 Sturm-Liouville5.1 5.2

5.2.1 5.2.2

5.3 Sturm-Liouille 5.3.1 5.3.2 Sturm-Liouville5.3.3

5.4 5.5 Sturm-Liouville 5-5: 5.6 Rayleigh 5.7 : 5.8 5.9 ( )5.10

6

8

6.1 6.2. aylor6.3.

6.3.1 6.3.2 M 6.3.3 6.3.4 Fourier-von Neumann6.3.5

6.3.6 6.3.7 - 6.3.8 6.3.9

6.4 6.5 6.6. laplace6.7

6.7.1 - ( )6.7.2

7 7.1 7.2

7.2.1 : 7.2.2 : 7.2.3

7.3 7.3: 7.4 L2 + = 07.5 Green, 7.5: Gram - Schmidt7.6 Rayleigh Laplace

7.6.1 Rayleigh7.6.2 Laplace

7.7 Bessel 7.7.1 7.7.2 7.7.3 ( )7.7.4 Bessel 7.7.5 Bessel7.7.6 Bessel 7.7.7 Bessel7.7.8 7.7.9

7.8 Bessel 7.8.1 Bessel7.8.2 7.8.3 Bessel

9

7.8.4 Bessel 7.9 Laplace

7.9.1 7.9.2 7.9.3 7.9.4 7.9.5 Bessel

7.10 Legendre 7.10.1 7.10.2 7.10.3 Legendre Legendre7.10.4 7.10.5 , ,

7.10.6 Laplace

8 8.1 8.2 8.3

( )8.4 Green ( )8.5 8.6 oisson

9 Green 9.1 9.2 9.3 Green

9.3.1 9.3.2 9.3.3 Green9.3.4 Dirac Green9.3.5 9.3.6 9.3: Green Dirac

9.4 Fredholm Green9.4.1 9.4.2 Fredholm9.4.3 Green

9.5 Green E oisson9.5.1 9.5.2 Dirac Green9.5.3 Green

10

Fredholm9.5.4 Green ( )9.5.5 Green

9.5.6 Green 9.5.7 Green Green

9.5.8 Green - (y > 0)

Green 9.5.9 Green :

9.6 9.6.1 9.6.2 9.6.3

10 . Fourier10.1 10.2 H 10.3 Fourier

10.3.1 Fourier10.3.2 Fourier10.3.3 Fourier Gauss

10.3 : Fourier Gauss10.4 Fourier

10.4.1 10.4.2 Fourier . 10.4.3 10.4.4 Fourier

10.5 Fourier : H -

10.5.1 10.5.2 - 10.5.3 Fourier10.5.4 10.5.5 - 10.5.6 Fourier

10.6 10.6.1 10.6.2 Laplace - 10.6.3 Laplace -10.6.5

( Fourier)10.6.6 Fourier

10.7

11

11 Green 11.1 11.2 Green

11.2.1 11.2.2 Green 11.2.4 Green11.2.5 Green 11.2.6 Green11.2.7 Green d Alembert11.2.8 Green (Huygens)11.2.9 Green 11.2.10

11.3 Green 11.3.1 11.3.2 - 11.3.3 Green 11.3.4 Green11.3.5 11.3.6 Green11.3.7 Green11.3.8 Green 11.3.9 Green (- )11.3.10 Green ( )

12 12.1 12.2

12.2.1 12.2.2

12.3 12.3.1 12.3.2 ( )12.3.3 d Alembert

12.4 - 12.5 12.6

12.6.1 12.6.2 12.6.3 (Q = 0)12.6.4 12.6.5

12.7 - 12.7.1 12.7.2

12

12.7.3 - 13 Laplace

13.1 13.2 Laplace

13.2.1 13.2.2 Laplace13.2.3 13.2.4

13.3 Green

13.4 13.5 13.6 Green 13.7

13.8

( )14 : , ,

14.1 14.2

14.2.1 14.2.2

14.3 14.3.1 f14.3.2 Green 14.3.3 Green 14.3.4

14.4 14.5

14.5.1 14.5.2

14.6 ( )14.6.1

14.6.2

14.7 ( )14.7.1 Schrdinger14.7.2 Korteweg-de Vries14.7.3 : Korteweg-de Vries14.7.4 14.7.5 Schrdinger

14.8 14.8.1 14.8.2

13

14.8.3 14.8.4 14.8.5 Ginzburg-Landau14.8.6 Ginzburg-Landau 14.8.7 14.8.8 - Turing

14.9 : 14.9.1 : 14.9.2 : 14.9.3 14.9.4 14.9.5 ( )

14.10 :

14.10.1 14.10.2