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6.3 Stability analysis0:04:46

6.3 Stability analysis using product solutions

6.3 Fourier-Von Neumann0:05:53

6.3 Fourier-Von Neumann stability analysis

6.3 Finite Difference0:09:59

6.3 Finite Difference Method example

6.3 Finite difference0:07:15

6.3 Finite difference methods for the heat equation

6.2 Difference approximations0:08:17

6.2 Difference approximations for second derivatives

6.2 Difference Approximations0:06:06

6.2 Difference Approximations for derivatives

8.4 Eigenfunction Expansion0:10:42

8.4 Eigenfunction Expansion for nonhomgeneous boundary conditions

8.3 Eigenfunction Expansions0:09:00

8.3 Eigenfunction Expansions for homgeneous boundary conditions

Reference distributions0:06:58

Reference distributions

8.2 Time-independent nonhomogeneous0:09:37

8.2 Time-independent nonhomogeneous parts

7.7 Bessel eigenvalue0:07:37

7.7 Bessel eigenvalue problem

7.7 Introduction to0:08:05

7.7 Introduction to Bessel Functions

7.7 Introduction to0:08:40

7.7 Introduction to the Vibrating Circular Membrane Problem

Self-adjointness of the0:02:48

Self-adjointness of the Laplacian

Orthogonal Helmholtz eigenfunctions0:03:18

Orthogonal Helmholtz eigenfunctions

7.5 Self-adjointness of0:03:15

7.5 Self-adjointness of the Laplacian

7.5 Multi-dimensional Lagrange0:05:02

7.5 Multi-dimensional Lagrange identity and Green's formula

7.4 Properties of0:05:07

7.4 Properties of the Helmholtz equation

7.3 Solving the0:09:47

7.3 Solving the vibrating membrane equation

7.3 Double Fourier0:05:46

7.3 Double Fourier series

7.3 Higher dimensional0:06:54

7.3 Higher dimensional eigenvalue problems

7.2 Higher dimensional0:03:42

7.2 Higher dimensional product solutions

7.2 Higher-dimensional PDEs0:03:38

7.2 Higher-dimensional PDEs

5.6 Eigenvalue estimates0:09:55

5.6 Eigenvalue estimates