NTU Course
NewsHelpOverview

CALCULUS (4)

Offered in 112-2

  • Serial Number

    69104

  • Course Number

    MATH4009

  • Course Identifier

    201 49840

  • Class 05
  • 2 Credits

  • Compulsory

    DEPARTMENT OF CHEMISTRY / DEPARTMENT OF ATMOSPHERIC SCIENCES / DEPARTMENT OF MECHANICAL ENGINEERING / DEPARTMENT OF CHEMICAL ENGINEERING / DEPARTMENT OF BIOMEDICAL ENGINEERING

      Compulsory

    • DEPARTMENT OF CHEMISTRY

    • DEPARTMENT OF ATMOSPHERIC SCIENCES

    • DEPARTMENT OF MECHANICAL ENGINEERING

    • DEPARTMENT OF CHEMICAL ENGINEERING

    • DEPARTMENT OF BIOMEDICAL ENGINEERING

  • CHENYANYU

  • Intensive Course

    Week 9, 10, 11, 12, 13, 14, 15, 16

  • Wed 8, 9, 10 / Fri 1, 2

  • Putong Lecture Building Rm.101 (普101)

  • Type 3

  • 152 Student Quota

    NTU 150 + non-NTU 2

  • No Specialization Program

  • Chinese
  • NTU COOL
  • Core Capabilities and Curriculum Planning
  • Notes
    The course is conducted in Chinese but uses English textbook。Intensive courses。
  • Limits on Course Adding / Dropping

    • Restriction: within this department (including students taking minor and dual degree program)

  • NTU Enrollment Status

    Loading...
  • Course Description
    這是一門半學期的課程，分為「向量微積分」與「泰勒展式」兩大主題。 「向量微積分」討論的主體是定義域、值域皆屬於 R^n的向量場。我們將定義如何在曲線或曲面上積分向量場，並介紹作用在向量場上的兩種微分運算，「散度」與「旋度」。課程將解釋Green定理、Stokes定理、散度定理如何結合向量場的微分與積分運算，而被理解為高維度的「微積分基本定理」。應用上，我們將推導電磁學中的 Gauss 定律，計算封閉曲面的電通量。 「泰勒展式」這主題推廣「極限」的概念，探討如何以多項式逼近複雜的函數。為了達到這個目的，我們將介紹無窮級數與冪級數的收斂性，利用泰勒定理估計餘項，進而推導出常見函數的泰勒展式。最後我們將示範多項式逼近的實際應用。 課堂上將講解定義並推導重要定理，以培養學生邏輯推理與分析能力；同時會示範微積分在各領域的應用，幫助學生將微積分與其他專業科目結合。本課程還設有習題課，學生將在助教的帶領下熟練微積分的計算並完成學習單上的小型研究題目。
  • Course Objective
    修完本課程學生能熟悉微積分工具，並應用在各學科。「微積分1, 2, 3, 4」將奠定學生修讀工程數學、分析、微分方程等進階課程的基礎。
  • Course Requirement
    學生應熟練高中數學，並完成為台大新生預備的線上「微積分學前自我檢測」。 學生應出席並積極參與課堂與習題課的討論。
  • Expected weekly study hours after class
  • Office Hour
    Wed13:30 - 15:00
  • Designated Reading
  • References
    Textbook: James Stewart, Daniel Clegg, and Saleem Watson, Calculus Early Transcendentals, 9th edition. 其他相關資訊 微積分統一教學網站: http://www.math.ntu.edu.tw/~calc/Default.html 台大微積分考古題: http://www.math.ntu.edu.tw/~calc/cl_n_34455.html 數學知識網站: http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal 免費線上數學繪圖軟體Desmos Calculator: https://www.desmos.com/calculator 免費知識型計算引擎: https://www.wolframalpha.com
  • Grading
    50%

    Final

    6/1(Sat) 09:00~11:30 Test in English

    20%

    Quizes

    5/8 (Wed) 17:30-18:20 Quiz 1 (Range：16.1-16.5)(改卷助教：林和靖) 5/22 (Wed) 17:30-18:20 Quiz 2 (Range：16.7-16.9& 11.2-11.3& 11.5-11.6)(改卷助教：鄭傑升)

    10%

    homework

    題目請見課程內容，請自己完成，如有抄襲，以零分計算。每次2分，取最高5次。負責助教如下： HW1&4：蕭銜甫 HW2&5：陳炫 HW3：鄭傑升 HW6：林和靖

    10%

    webwork

    請依webwork的期限完成，成績的部分將直接由系統計算 http://webwork.math.ntu.edu.tw/webwork2/112_Calculus4_05_09/

    10%

    worksheet

    分數計算部分，完成度80%以上拿3分，50%-79%拿2分，49%以下1分。 5/3前將worksheet 1上傳至作業區，準時交最高3%，遲交1% 5/10前將worksheet 2上傳至作業區，準時交最高3%，遲交1% 5/24前將worksheet 3上傳至作業區，準時交最高3%，遲交1% 三次都準時交者，可額外得到1%，學習單請自己完成，如有抄襲，以零分計算

  • Adjustment methods for students
    Adjustment MethodDescription
    Assignment submission methods

    Extension of the deadline for submitting assignments

    Mutual agreement to present in other ways between students and instructors

    Others

    Negotiated by both teachers and students

  • Course Schedule
    4/17, 4/19Week 916.1 Vector Fields 16.2 Line Integrals 16.3 The Fundamental Theorem for Line Integrals (WS) 16.4 Green's Theorem
    4/24, 4/26Week 1016.5 Curl and Divergence 16.6 Parametric Surfaces and Their Areas (WS) Worksheet (Conservative Vector Fields)
    5/1, 5/3Week 1116.7 Surface Integrals 16.8 Stokes' Theorem 16.9 The Divergence Theorem 11.1 Sequences(*)
    5/8, 5/10Week 1211.2 Series 11.3 The Integral Test and Estimates of Sums (WS) 11.4 The Comparison Tests (*) Worksheet (Parametric Surfaces)
    5/15, 5/17Week 1311.5 Alternating Series and Absolute Convergence (WS) 11.6 The Ratio and Root Tests 11.7 Strategy for Testing Series (*) Worksheet (Tests for Convergence of Series)
    5/22, 5/24Week 1411.8 Power Series 11.9 Representations of Functions as Power Series 11.10 Taylor and Maclaurin Series 11.11 Applications of Taylor Polynomials (WS)
    5/29, 5/31Week 15緩衝時間 期考 6/1(六) 09:00~11:30 考試以英文命題