| 一、課程基本資料 Course Information | ||||||||||||||||||||||||||||||||||||||||
| 科目名稱 Course Title： (中文)高等微積分（二）Ａ組 (英文)ADVANCED CALCULUS(2) |
開課學期 Semester：110學年度第2學期 開課班級 Class：數學二 |
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| 授課教師 Instructor：張秀瑜 CHANG, SHIOW-YU | ||||||||||||||||||||||||||||||||||||||||
| 科目代碼 Course Code：BMA21901 | 單全學期 Semester/Year：單 | 分組組別 Section：Ａ組 | ||||||||||||||||||||||||||||||||||||||
| 人數限制 Class Size： | 必選修別 Required/Elective：必 | 學分數 Credit(s)：4 | ||||||||||||||||||||||||||||||||||||||
| 星期節次 Day/Session： 二12 四34 | 前次異動時間 Time Last Edited：111年05月24日11時29分 | |||||||||||||||||||||||||||||||||||||||
| 數學系基本能力指標 Basic Ability Index | ||||||||||||||||||||||||||||||||||||||||
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| 二、指定教科書及參考資料 Textbooks and Reference (請修課同學遵守智慧財產權，不得非法影印) |
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| ●指定教科書 Required Texts William R. Wade : Introduction to Analysis (4th Edition) ●參考書資料暨網路資源 Reference Books and Online Resources 1.Advanced Calculus, Gerald B. Folland. 歐亞書局 2.Principles of Real Analysis, Third Edition, C.D. Aliprantis and Owen Burkinshaw 新月書局 3.Walter Rudin: Principles of Mathematical Analysis. | ||||||||||||||||||||||||||||||||||||||||
| 三、教學目標 Objectives | ||||||||||||||||||||||||||||||||||||||||
| 高等微積分是微積分的延續。 由微積分的極限定義與極值定裡開始, 學習分析學的基礎邏輯, 驗證微積分理論的推導.從而了解分析學之中心概念的一致性與連續性。藉以培養分析學基本的推導能力，以 及數學應用的基礎。 |
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| Advanced calculus is at a deeper level that is found in the standard calculus books. We study an entirely theoretical nature that covers such as the topology of Euclidean space, the theory of the Riemann integral, and proofs of some theorems that has been taken on faith before. Thus we can unify the concepts of foundations of analysis. Hence we not only get the structure and presentation of mathematical proofs in analysis but also establish the elementary step of mathematical applications. | ||||||||||||||||||||||||||||||||||||||||
| 四、課程內容 Course Description | ||||||||||||||||||||||||||||||||||||||||
| ●整體敘述 Overall Description 1.Integration in R: Mean Value Theorem for Integrals; The Fundamental Theorem of Calculus; Change of Variables; Improper Riemann Integration Integration in Higher Dimension: Riemann Integration on Rectangles; Measurable Sets and Integration on Measurable Sets; Fubini's theorem; Change of Variables 2.Topologies of Euclidean Spaces: the usual topology and the relative topology; Connectivity; Continuous functions; Interior, Closure, and Boundary 3. Convergence in Euclidean Spaces: Limits of Sequence; Hine-Borel Theorem; Limits of Functions; Compact Sets 4. Differentiability in Euclidean Spaces: Partial Derivatives and Partial Integrals ; Linear Transformations; the Definition of Differentiability; Derivatives, Differentials, and Tangent planes; the Chain Rule; the Mean Value Theorem and Taylor's Formula; the Inverse Function Theorem |
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| ●分週敘述 Weekly Schedule | ||||||||||||||||||||||||||||||||||||||||
| 五、考評及成績核算方式 Grading | ||||||||||||||||||||||||
| 本科目 ☑同意/☐不同意 期末退修 | ||||||||||||||||||||||||
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| 六、授課教師課業輔導時間和聯絡方式 Office Hours And Contact Info | ||||||||||||||||||||||||
| ●課業輔導時間 Office Hour 星期二 : 10:10~12:00 星期四 : 8:00~10.00 |
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●聯絡方式 Contact Info
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| 七、教學助理聯絡方式 TA’s Contact Info | |||||||||
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| 八、建議先修課程 Suggested Prerequisite Course | |||||||||
| 九、課程其他要求 Other Requirements | |||||||||
| 十、學校教材上網、數位學習平台及教師個人網址 University’s Web Portal And Teacher's Website | |||||||||
| 學校教材上網網址 University’s Teaching Material Portal： 東吳大學Moodle數位平台：http://isee.scu.edu.tw |
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| 學校數位學習平台 University’s Digital Learning Platform： ☐東吳大學Moodle數位平台：http://isee.scu.edu.tw ☐東吳大學Tronclass行動數位平台：https://tronclass.scu.edu.tw | |||||||||
| 教師個人網址 Teacher's Website： | |||||||||
| 其他 Others： | |||||||||
| 十一、計畫表公布後異動說明 Changes Made After Posting Syllabus | |||||||||