In this lecture we learn vector analysis. A vector analysis is required to put it in the hydrodynamics, the elastic dynamics,
the electric magnetic science and the heat conduction theory and develop basic theory as the mathematical means and it has
developed. A vector analysis is extension of linear algebra and the differential calculus integration science and is the phenomenon-like
contents. I deal with a differential and integral calculus way of vector-valued function in two dimensions or a three-dimensional
vector field at this session. It's Stowe camphor tree theorem that the differential calculus and the basic formula which shows
that integration is reverse calculation "The definite integration from a in f (x) to b was equal to F (b )- F (a). But, F'
(x)= f (x)." were considered in a vector field in the function of 1 variable. This theorem is expansion to 1 of multi variable
function of the basic formula of the differential and integral calculus way.

We learn algebra of vector, the derivative and integration of vector value functions, curves, surface, scalar field and vector
field.

- We can find inner product and cross product and calculate the derivative and the integration of vector functions.
- We can find the length, tangent vector and principal unit normal vector of space curves.
- We can find the gradient of scalar field, the divergence and curl of vector field and the line integral for vector field.
- We can explore some example of the divergence theorem and the Stokes theorem.

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

1. | Vector, inner product | text pp.1-5 | 30minutes |

2. | Cross product | text pp.6-11 | 30minutes |

3. | Derivative and integration of vector function | text pp.14-20 | 30minutes |

4. | Scalar field, gradient | text pp.20-27 | 30minutes |

5. | divergent, curl | text pp.28-35 | 30minutes |

6. | space curve | text pp.36-39 | 30minutes |

7. | scaler's line integrals, vector's line integrals | text pp.40-43 | 30minutes |

8. | surface, scalar's surface integrals, vector's surface integrals | text pp.43-47 | 30minutes |

9. | divergence | text pp.50-52 | 30minutes |

10. | divergence theorem | text pp.52-56 | 30minutes |

11. | crul | text pp.57-59 | 30minutes |

12. | Stokes theorem | text pp.59-61 | 30minutes |

13. | Applications of integral theorems | text pp.62-71 | 30minutes |

14. | exam | lesson 1〜13 | 30minutes |

Total. | - | - | 420minutes |

exercise | exam | Total. | |
---|---|---|---|

1. | 5% | 10% | 15% |

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

3. | 10% | 20% | 30% |

4. | 5% | 20% | 25% |

Total. | 30% | 70% | - |

- Course that cultivates an ability for utilizing knowledge

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

N/A | N/A |

Last modified : Fri Mar 18 23:01:04 JST 2022