3 Finite Systems of Differential Equations
3.1 Systesms 2x2 first
3.1.1 Eigenvalue equations
3.1.2 Cayley-Hamilton theorem method
3.1.2.1 case one
3.1.2.2 case two
3.2 Systems 4x4
3.2.1 Case one
3.2.2 Case two
3.2.3 Case three
3.2.4 Case four
3.3 Systems nxn
3.3.1 All the eigenvalues are distinct
3.3.2 other cases
4 Infinite Systems of Differential Equations
4.1 Addition formula for the Bessel
functions
4.2 First neighbors interaction
4.3 Second neighbors interaction
4.4 First neighbor interaction with an
extra interaction
4.4.1 Interaction omega-n
4.4.2 Interaction omega-(-1)^n
5 Semi-infinite Systems of Differential Equations
5.1 First a semi-infinite system
5.2 Semi-infinite system with first
neighbors interaction
5.3 Nonlinear system with first neighbors
interaction
6 Partial
Differential Equations
6.1 A simple partial differential equation
6.1.1 A Gaussian function as boundary condition
6.1.2 An arbitrary function as boundary
condition
6.2 Airy system
6.2.1 Airy function as boundary condition
6.3 Harmonic oscillator system
6.4 z-dependent harmonic oscillator
Appendix A
Dirac Notation
Appendix B
Inverse of the Vandermonde and Vandermonde
Confluent Matrices
B.1 The inverse of the Vandermonde matrix
B.2 The inverse of the confluent Vadermonde
matrix
Appendix C
Tridiagonal matrices
C.1 Fibonacci system
Bibliography
Index |