**Math 513 Matlab Scripts**

fourier_series.m | (Gibbs Phenomena) |

Problem_5_1_2.m | (Plot Fourier transform amplitude and phase) |

Problem_5_3_6.m | (Plot effect of modulation) |

Problem_5_5_2.m | (Symbolic integration for Convolution) |

Wave equation | (Wave propagation) |

Wave equation | D'Lambert solution. |

Heat equation |
u(0,t) = u(L,t) = 0, u(x,0) = x (pi -x)
(Dirichlet
problem) |

Heat equation |
u
(Insulated end)_{x}(0,t) = u(L,t) = 0, u(x,0) = x, |

Heat equation | u(0,t) = 0, u(L,t) = const,
u(x,0) = 0,
(Constant end) |

Heat equation |
u
(Neumann
Problem)_{x}(0,t) = u_{x}(L,t) = 0, u(x,0) = x, |

Heat Equation | Solution of Heat equation with
u(0,t) = 0, u(L,t)
= const, u(x,0) = 0,
using Laplace Transform. Error
function solution |

Heat Equation | Solution of Heat equation on infinite interval with
u(x,0) =
constant, using Fourier transform. |

Laplace Equation | u(x,z0) = gz0 + gcx, u_{x}(0,y)
= u_{x}(L, y) = 0, u_{y}(x,0) = 0. |