NTU Course
Overview

CALCULUS (1)

Offered in 114-1

  • Serial Number

    49735

  • Course Number

    MATH4006

  • Course Identifier

    201 49810

  • Class 10
  • 2 Credits

  • Preallocated

    DEPARTMENT OF ECONOMICS

      Preallocated

    • DEPARTMENT OF ECONOMICS

  • CHAN TSZ ON

  • Intensive Course

    Week 1, 2, 3, 4, 5, 6, 7, 8

  • Mon 3, 4 / Thu 3, 4, 10

  • 共101

  • Type 3

  • 170 Student Quota

    NTU 170

  • No Specialization Program

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

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

  • NTU Enrollment Status

    Enrolled
    0/170
    Other Depts
    0/0
    Remaining
    0
    Registered
    0
  • Course Description
    Calculus 1 (微積分1) Differentiation on functions of a single variable together with its profound applications in various subject areas are introduced in this half-semester course. Especially, this course includes the definitions of limits and continuity, techniques of differentiation, curve sketching, strategies in solving extreme-value problem and more. Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides discussion sessions in which students are able to improve their skills in handling calculations and explore applications of Calculus under the guidance of teaching assistants. 這是一門半學期的課程，主要介紹單變數函數的微分運算，和微分在各領域豐富的應用。內容涵蓋極限與連續的定義，微分技巧，畫函數圖形，和極值問題等。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計算並探索微積分的應用。
  • Course Objective
    Upon completing the course, students are expected to be able to 1. Understand the notion of the limits of a function and compute them. 2. Use limits to describe properties of a function, including continuity and asymptotic behaviors. 3. Define the derivative of a function, understand its geometric meaning, and determine the differentiability of a function. 4. Use chain rule to differentiate composed functions, implicit functions and inverse functions. 5. Employ differentiation to determine the local and global extreme values of functions. 6. Apply Mean Value Theorem to derive properties of a function from its derivatives such as monotonicity and concavity. 7. Apply the L’Hôspital’s rule to compute limits of more sophisticated functions. 學生修習本課程後，應具備以下能力： 1. 理解函數極限 (limit) 的基本概念，並能計算函數的極限值。 2. 能以極限探討函數性質，包括連續性與漸近行為。 3. 能正確定義函數之導數 (derivative)，說明微分之幾何意涵，並判斷函數的可微性。 4. 能計算函數的微分，熟練運用鏈鎖法則 (chain rule) 處理合成函數、隱函數與反函數之微分。 5. 能利用微分求出函數的局部或全域的極值 (local or global extreme values)。 6. 能應用均值定理 (Mean Value Theorem) 推導出函數的性質，包含遞增、遞減、凹凸性。 7. 能運用羅必達法則 (L’Hôpital’s Rule) 計算較複雜函數之極限。
  • Course Requirement
    Before taking this course, students should be skilled in high school mathematics and finish the online Precalculus Self Diagnostic Test https://cool.ntu.edu.tw/courses/50879 which is designed for NTU freshmen. Students are expected to attend and participate actively in lectures as well as discussion sessions. 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」https://cool.ntu.edu.tw/courses/50879。 學生應出席並積極參與課堂與習題課的討論。
  • Expected weekly study hours before and/or after class
  • Office Hour
  • Designated Reading
    待補
  • References
    Textbook: James Stewart, Daniel Clegg, and Saleem Watson, Calculus Early Transcendentals, 9th edition, Metric Version. ISBN: 978-626-7533-06-2 Other useful websites 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%

    Exam

    20%

    Quizzes

    12%

    Worksheets

    8%

    WeBWorK

    10%

    Homework and others

  • Adjustment methods for students
  • Make-up Class Information
  • Course Schedule
    9/01,9/04Week 12.1 The Tangent and Velocity Problems 2.2 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws
    9/08,9/11Week 22.5 Continuity 2.6 Limits at Infinity; Horizontal Asymptotes 2.7 Derivatives and Rates of Change 2.8 The Derivative as a Function [Tutorial: Worksheet (Nash Equilibrium)]
    9/15,9/18Week 33.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions 3.4 The Chain Rule [9/18(Thu) 17:30-18:20 Quiz 1 (2.1 - 2.8)]
    9/22,9/25Week 43.5 Implicit Differentiation 3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions [Tutorial: Worksheet (Derivatives in Economics)]
    10/02Week 53.8 Exponential Growth and Decay (Continuously Compounded Interest) 3.10 Linear Approximations and Differentials 4.1 Maximum and Minimum Values
    10/09Week 64.2 The Mean Value Theorem 4.3 What Derivatives Tell Us about the Shape of a Graph 4.4 Indeterminate Forms and l'Hospital's Rule [10/9(Thu) 17:30-18:20 Quiz 2 (3.1 - 3.6、3.8、3.10)]
    10/13,10/16Week 74.5 Summary of Curve Sketching 4.7 Optimization Problems [Tutorial: Worksheet (Optimizing Costs and Profits)]
    10/20,10/23Week 8
    10/27,10/30Week 9[11/1(Sat) Exam]