This is a course on linear space and vector calculus. You will learn the notion of linear spaces, kernel and image of a linear
map and vector calculus with differential forms.

The object of this course is to understand the notion of linear spaces and linear maps and to be able to use differential
forms in vector calculus.

- To be able to understand the notion of linear spaces and linear maps.
- To be able to calculate the diagonalization of simple symmetric matrices.
- To be able to use differential forms in vector calculus.

Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
---|---|---|---|

1. | Linear space and subspace | Review of linear algebra | 150minutes |

2. | Linear maps | Review of linear space and subspace | 200minutes |

3. | Inner product space, assignment 1 | Review of linear maps | 200minutes |

4. | Kernel and image of a linear map | Review of inner product space | 200minutes |

5. | Gram-Schmidt orthogonalization | Review of kernel and image of a linear map | 200minutes |

6. | Diagonalization of symmetric matrices | Review of Gram-Schmidt orthogonalization | 200minutes |

7. | Review and assignment 2 | Review of all topics | 200minutes |

8. | Vector operators | Review of vector analysis | 200minutes |

9. | Differential forms | Review of vector operators | 200minutes |

10. | Exterior derivative | Review of differential forms | 200minutes |

11. | Surface integrals | Review of exterior derivative | 200minutes |

12. | Stokes' theorem | Review of surface integrals | 200minutes |

13. | Gauss' theorem | Review of Stokes' theorem | 200minutes |

14. | Review and assignment 3 | Review of all topics | 200minutes |

Total. | - | - | 2750minutes |

Assignment 1 | Assignment 2 | Assignment 3 | Total. | |
---|---|---|---|---|

1. | 10% | 20% | 0% | 30% |

2. | 10% | 20% | 0% | 30% |

3. | 0% | 0% | 40% | 40% |

4. | 0% | 0% | ||

5. | 0% | 0% | ||

Total. | 20% | 40% | 40% | - |

ways of feedback | specific contents about "Other" |
---|---|

Feedback in the class |

Knowledge of Vector Calculus (without differential forms) and fundamental linear algebra are needed.

- Non-social and professional independence development course

Work experience | Work experience and relevance to the course content if applicable |
---|---|

N/A |

Last modified : Sat Sep 09 06:08:45 JST 2023