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Checking solutions in the calculator ,16-2
Slope field visualization of solutions ,16-3
The CALC/DIFF menu ,16-3
Solution to linear and non-linear equations ,16-4
Function LDEC ,16-4
Function DESOLVE ,16-7
The variable ODETYPE ,16-8
Laplace Transforms ,16-10
Definitions ,16-10
Laplace transform and inverses in the calculator ,16-11
Laplace transform theorems ,16-12
Dirac’s delta function and Heaviside’s step function ,16-15
Applications of Laplace transform in the solution of linear ODEs ,16-17
Fourier series ,16-26
Function FOURIER ,16-28
Fourier series for a quadratic function ,16-28
Fourier series for a triangular wave ,16-34
Fourier series for a square wave ,16-38
Fourier series applications in differential equations ,16-40
Fourier Transforms ,16-42
Definition of Fourier transforms ,16-45
Properties of the Fourier transform ,16-47
Fast Fourier Transform (FFT) ,16-47
Examples of FFT applications ,16-48
Solution to specific second-order differential equations ,16-51
The Cauchy or Euler equation ,16-51
Legendre’s equation ,16-51
Bessel’s equation ,16-52
Chebyshev or Tchebycheff polynomials ,16-55
Laguerre’s equation ,16-56
Weber’s equation and Hermite polynomials ,16-57
Numerical and graphical solutions to ODEs ,16-57