# Course Log

Here you will find information about the material that was already covered or will be covered in the next few lectures.

Covered | |
---|---|

4/30 | Review for Final Project |

4/28 | Review for Final Project |

4/23 | Midterm Exam 2 (in class) |

4/21 | Review for Midterm Exam 2 |

4/16 | §45 Jacobian Theorem, Change of Variables |

4/14 | §45 Transformations by Linear and Nonlinear Mappings |

4/9 | §44 The Integral as Iterated Integral, §45 Transformations of Sets with Content |

4/7 | §44 Characterization of Content Function, Further Properties of Integral |

4/2 | §43 Existence of Integral, §44 Content and Integral, Sets with Content |

3/31 | §43 Properties of Integral, Darboux’s upper and lower integrals, Riemann’s Criterion for Integrability |

3/26 | §43 Content zero, Definition of Integral |

3/24 | §42 Extremum Problems with Constraints, Exercises, Inequality Constraints |

3/17–19 | Spring Break |

3/12 | §42 Extremum Problems with Constraints, Lagrange’s Theorem |

3/10 | Review for Midterm Exam 1 |

3/5 | §42 Local Extrema, Second Derivative Test |

3/3 | §41 Implicit Functions (finish) |

2/26 | §41 Surjective Mapping Theorem (finish), Open Mapping Theorem, Inversion Theorem, Implicit Functions (start) |

2/24 | §41 C^{1} functions, Approximation Lemma, Injective Mapping Theorem, Surjective Mapping Theorem |

2/19 | No class (to be made up) |

2/17 | No class (to be made up) |

2/12 | §40 Mixed derivatives, higher derivatives, Taylor’s theorem |

2/10 | §40 Chain Rule, Mean Value Theorem, Mixed derivatives (start) |

2/5 | §39 Examples, Existence of the derivative, §40 Algebraic operations and derivative |

2/3 | §23 Uniform continuity, §21 Linear functions, §39 Partial derivatives, differentiability |

1/29 | §22 Relative topology, Global Continuity Theorem, preservation of connectedness, compactness, continuity of inverse function |

1/27 | §17 Sequences of functions, pointwise and uniform convergence, §20 Continuity at a point (different definitions) |

1/22 | §14 Convergence of sequences, §§15-16 Subsequences, Bolzano-Weierstrass (revisited), Cauchy sequences |

1/20 | §11 Cantor Intersection Thm, Corollaries, §12 Connected sets |

1/15 | §10 Cluster points, Bolzano-Weierstrass, Nested Cells, §11 Compactness, Heine-Borel |

1/13 | §8 Cartesian spaces, inner products, norms, §9 Open and closed sets, interior, boundary, exterior points |