Lecture 1: | Introduction to Julia |

Lecture 2: | Approximating functions |

Lecture 3: | Decay of Fourier coefficients |

Lecture 4: | Convergence of Fourier series |

Lecture 5: | Discrete Fourier coefficients |

Lecture 6: | The discrete Fourier transform |

Lecture 7: | The fast Fourier transform |

Lecture 8: | The discrete Cosine transform |

Lecture 9: | Discrete Chebyshev series |

Lecture 10: | Root finding and Fourier differentiation |

Lecture 11: | Chebyshev differentiation |

Lecture 12: | Solving ODEs with Chebyshev series |

Lecture 13: | Second order ODEs, general orthogonal polynomials |

Lecture 14: | Orthogonal polynomials and Jacobi operators |

Lecture 15: | Variable coefficients and nonlinear ODEs |

Lecture 16: | Homotopy method for nonlinear ODEs |

Lecture 17: | Operator norms and the operator exponential |

Lecture 19: | Operator exponential for unbounded operators |

Lecture 20: | Operator exponential with boundary conditions |

Lecture 22: | The SVD and low rank approximation of functions |

Lecture 23: | Solving PDEs in squares |

Lecture 24: | Time evolution PDEs in squares |