日本語 English
| 開講年度/ Academic YearAcademic Year |
20232023 |
| 科目設置学部/ CollegeCollege |
理学部/College of ScienceCollege of Science |
| 科目コード等/ Course CodeCourse Code |
自動登録/automatic registrationautomatic registration |
| テーマ・サブタイトル等/ Theme・SubtitleTheme・Subtitle |
|
| 授業形態/ Class FormatClass Format |
対面（全回対面）/Face to face (all classes are face-to-face)Face to face (all classes are face-to-face) |
| 校地/ CampusCampus |
池袋/IkebukuroIkebukuro |
| 学期/ SemesterSemester |
春学期/Spring SemesterSpring Semester |
| 曜日時限・教室/ DayPeriod・RoomDayPeriod・Room |
木2･4342/Thu.2･4342 Thu.2･4342 |
| 単位/ CreditCredit |
22 |
| 科目ナンバリング/ Course NumberCourse Number |
MAT2300 |
| 使用言語/ LanguageLanguage |
日本語/JapaneseJapanese |
| 備考/ NotesNotes |
|
| テキスト用コード/ Text CodeText Code |
CA017 |
Students will deepen their understanding of differentiation of multivariable functions by applying it to various examples.
The objective is to attain mastery of the differentiation of multivariable functions. In particular, to acquire computational and applicational skills.
This class builds upon the concepts learned in “Introduction to Differential and Integral Calculus” and “Differential and Integral Calculus 1” and teaches the concept of multivariable differentiation. Students learn how the various concepts that appear in the differentiation of single variable functions extend to cases with multiple variables. As application, students learn to solve extreme value problems. They also learn about the implicit function theorem and the inverse mapping theorem, which are important for applied calculus.
※Please refer to Japanese Page for details including evaluations, textbooks and others.
いろいろな実例への応用を通して、多変数関数の微分に対する理解を深める。
多変数関数の微分法に習熟することを目標とする。特に、計算力と応用力を身につける。
Students will deepen their understanding of differentiation of multivariable functions by applying it to various examples.
The objective is to attain mastery of the differentiation of multivariable functions. In particular, to acquire computational and applicational skills.
この授業では「微分と積分入門」、「微分と積分１」の講義内容を踏まえ、多変数の微分の概念を基礎から学ぶ。1変数関数の微分にに現れる諸概念が多変数の場合にどのように拡張されていくかを学ぶ。応用として、極値問題の解法を習得する。また、応用上重要な陰関数定理と逆写像定理についても学ぶ。
This class builds upon the concepts learned in “Introduction to Differential and Integral Calculus” and “Differential and Integral Calculus 1” and teaches the concept of multivariable differentiation. Students learn how the various concepts that appear in the differentiation of single variable functions extend to cases with multiple variables. As application, students learn to solve extreme value problems. They also learn about the implicit function theorem and the inverse mapping theorem, which are important for applied calculus.
| 1 | 多変数の関数、開集合・閉集合 |
| 2 | 多変数関数の極限と連続性 |
| 3 | 偏微分 |
| 4 | １次近似と全微分 |
| 5 | 合成関数の微分 |
| 6 | テイラー近似 |
| 7 | 臨界値と極値 |
| 8 | 最大・最小問題 |
| 9 | 陰関数定理（１） |
| 10 | 陰関数定理（２） |
| 11 | 条件付き極値問題（１） |
| 12 | 条件付き極値問題（２） |
| 13 | 逆写像定理（１） |
| 14 | 逆写像定理（２） |
1変数の微分の基礎事項（連続関数、微分の定義と性質、合成関数の微分、テイラー近似など）と「線形代数学1」の授業内容を復習しておくこと。
| 種類 (Kind) | 割合 (%) | 基準 (Criteria) |
|---|---|---|
| 筆記試験 (Written Exam) | 45 | |
| 平常点 (In-class Points) | 55 |
小テスト(25%) 授業内課題(30%) |
| 備考 (Notes) | ||
| 「微分と積分2」の講義と演習は一体のものとして評価する。 | ||
| No | 著者名 (Author/Editor) | 書籍名 (Title) | 出版社 (Publisher) | 出版年 (Date) | ISBN/ISSN |
|---|---|---|---|---|---|
| 1 | 難波誠 | 『微分積分学』 | 裳華房 | 1996 | 4785314087 |
| その他 (Others) | |||||
|---|---|---|---|---|---|
| 授業中に適宜紹介する。 |