The textbook pages given are approximate, since we will not always be following the textbook closely. It is strongly recommended that you read the notes and textbook concurrently with the lectures; the depth of the material is such that you are unlikely to keep up just by attending lectures. It is equally essential that you perform all the homework, especially as many of the homework questions cover material which is essential to the course.

Week | Monday | Wednesday | Thursday | Friday |

1 | Mar 31: pp. 30-32 Metric spaces; examples |
Apr 2: pp. 48-55 Convergent sequences in metric spaces |
Apr 3 No homework due |
Apr 4: pp. 32-36 Basic topology of metric spaces |

2 | Apr 7: pp. 36-40 Compact sets |
Apr 9: pp. 83-89 Continuous functions on metric spaces |
Apr 10 |
Apr 11: pp. 89-93 Continuity and compactness Homework 1 due |

3 | Apr 14: pp. 143-147 Sequences and series of functions |
Apr 16: pp. 147-151 Uniform convergence, and continuity |
Apr 17 |
Apr 18: pp. 151-152 Uniform convergence, and integration Homework 2 due |

4 | Apr 21: pp. 152-154 Uniform convergence, and differentiation |
Apr 23: pp. 159-165 Uniform approximation by polynomials |
Apr 24 |
Apr 25 First Midterm Homework 3 due |

5 | Apr 28: pp. 172-178 Power series |
Apr 30: pp. 172-178 More on power series |
May 1 |
May 2: pp. 179-184 Special functions Homework 4 due |

6 | May 5: pp. 185-192 Fourier series |
May 7: pp. 185-192 More on Fourier series |
May 8 | May 9: pp. 204-211 Review of Linear Algebra Homework 5 due |

7 | May 12: pp. 204-211 Linear transformations |
May 14: pp. 211-215 Functions of several variables; differentiation |
May 15 |
May 16: 215-223 Partial and directional derivatives Homework 6 due |

8 | May 19: pp. 299-302 Measurable sets; sigma algebras |
May 21: 302-304 Outer measure |
May 22 |
May 23 Second Midterm Homework 7 due |

9 | May 26 Memorial day |
May 28: pp. 304-309 Construction of Lebesgue measure |
May 29 |
May 30: pp. 310-314 Simple functions; measurable functions Homework 8 due |

10 | Jun 2: pp. 314-318 The Lebesgue integral |
Jun 4: pp. 322-324 Comparison with the Riemann integral |
Jun 5 |
Jun 6: notes Fubini's theorem Homework 9 due |

Finals Week |
Jun 11, 3pm - 6pm Final (exam code 05) |