Lecture 1: | Fourier Analysis |

Lecture 2: | Least Squares |

Lecture 3: | Normwise Convergence |

Lecture 4: | The Discrete Fourier Transform |

Lecture 6: | The Fast Fourier Transform |

Lecture 7: | Taylor Series |

Lecture 8: | Contour integration |

Lecture 9: | Laurent series |

Lecture 10: | Chebyshev series |

Lecture 11: | Signal smoothing and root finding |

Lecture 12: | Differentiation and integration |

Lecture 13: | Spectral methods |

Lecture 14: | Ultraspherical spectral methods |

Lecture 15: | Functional analysis |

Lecture 16: | Spectrum |

Lecture 17: | Infinite-dimensional linear algebra |

Lecture 18: | Linear partial differential equations |

Lecture 19: | Laplace's equation |

Lecture 20: | Riemann–Hilbert problems |

Lecture 21: | Matrix-valued Riemann–Hilbert problems |