Differential and Integral Calculus 1

In this class, students learn the basic concepts and operations of one-variable functions. The first part deals with limits,
derivatives, and extrema, and the second part deals with indefinite and definite integrals for various functions. Students
also learn the basic properties of important functions such as polynomials, exponential functions, logarithmic functions,
trigonometric functions, and inverse trigonometric functions.

Note that these also appear in the fundamentals of statistics and even data science.

Note that these also appear in the fundamentals of statistics and even data science.

The purpose of this class is to understand the meaning of calculus of one-variable functions, and to be able to calculate
them.

- To be able to calculate limit
- To be able to understand the meaning of differentials and related operations, and calculate them.
- To be able to calculate differential, derivative test, and extrema of functions related to statistics.
- To be able to understand the meaning of indefinite and definite integrals, and calculate them.
- To be able to calculate indefinite and definite integrals related to statistics.

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

1. | Limit and continuity of elementary functions such as polynomials | Read through the textbook p.23-p.30 before class. Solve exercises after class. | 190minutes |

2. | Basic properties of differential | Read through the textbook p.33-p.42 before class. Solve exercises after class. | 190minutes |

3. | Trigonometric function | Read through the textbook p.45-p.50 before class. Solve exercises after class. | 190minutes |

4. | Inverse trigonometric function | Read through the textbook p.53-p.62 before class. Solve exercises after class. | 190minutes |

5. | Exponential function, logarithmic function, and their relationship to statistics | Read through the textbook p.65-p.71 before class. Solve exercises after class. | 190minutes |

6. | Derivative test and extremum | Read through the textbook p.84-p.91, p.93-p.99 before class. Solve exercises after class. | 190minutes |

7. | Midterm examination and its explanation | Preparation of midterm examination | 190minutes |

8. | Indefinite integral of elementary functions such as polynomials | Read through the textbook p.113-p.118 before class. Solve exercises after class. | 190minutes |

9. | Indefinite integration by substitution and by parts | Read through the textbook p.121-p.126 before class. Solve exercises after class. | 190minutes |

10. | Indefinite integral of trigonometric functions | Read through the textbook p.128-p.132 before class. Solve exercises after class. | 190minutes |

11. | Indefinite integration of rational and irrational functions | Read through the textbook p.134-p.142 before class. Solve exercises after class. | 190minutes |

12. | Definitive integral and its use (mean) | Read through the textbook p.146-p.152 before class. Solve exercises after class. | 190minutes |

13. | Calculation of definite integral | Read through the textbook p.153-p.161 before class. Solve exercises after class. | 190minutes |

14. | Final examination and their explanations | Preparation of final examination | 190minutes |

Total. | - | - | 2660minutes |

Midterm examination | Final examination | Reports and little examinations | Total. | |
---|---|---|---|---|

1. | 6% | 3% | 9% | |

2. | 29% | 12% | 41% | |

3. | 0% | |||

4. | 35% | 15% | 50% | |

Total. | 35% | 35% | 30% | - |

Midterm examination(35%), Final examination(35%), Reports and little examinations(30%)

- Course that cultivates an ability for utilizing knowledge

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

N/A | 該当しない |

Last modified : Sat Mar 21 13:01:21 JST 2020