## 2020-2021– Semester II

## Calendar

Week | Topics |

1 | Vector Algebra |

2 | Lines and Planes |

3 | Curves and paths in 2 and 3 dimensions |

4 | Arclength and Curvature |

5 | Functions of Several Variables |

Exam I | Wednesday, February 24. 5:30-7:30 PM |

6 | The Derivative |

7 | The Derivative as a Linear Map |

8 | Curve Integrals |

9 | Optimization |

10 | Higher Derivatives |

Exam II | Monday, April 5 5:30-7:30 PM |

11 | Double and Triple Integrals |

12 | The Change of Variable Formula |

13 | Green’s Theorem. |

Exam III | Monday, April 26 |

14 | Parametrized Surfaces. |

15 | Stoke’s Type Theorems |

Exam IV | Date determined by Registrar |

#### Miscellaneous Notes

- Vectors
- R^n as a Euclidean Space
- Lines in R^n
- Planes in R^n
- The Vector Product
- Determinants and Orientation in R^2
- Matrix Multiplication -Brief Review
- Reformulation of the usual Derivative
- The Derivative of a Scalar Function
- The Derivative of a Vector Valued Function
- The Chain Rule for Curves
- The Chain Rule for Vector Valued Functions
- Unit Speed Reparametrization
- Twisting and Turning
- Line Integrals of Scalar Functions
- Line Integrals of Vector Fields
- Vector Fields and Potential Functions
- Optimization – Summary
- Optimization with Constraints
- Double Integrals
- Change of Variables Theorem
- Formulae for Integration
- Physical Applications of Stokes’ Theorem