課程資訊

Calculus (general Mathematics) (a)(1)

101-1

MATH1201

201 101A1

03

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1011_Calculus_A03

One variable calculus

Study the process of approximation and its limitation (errors), learn the tools and techniques for analyzing
regular mappings with applications, and deepen the understanding of elementary functions.

High School Mathematics

Office Hours

Salas, Hille and Etgen, Calculus: One and Several variables, Tenth Edition,
Wiley.

(僅供參考)

 No. 項目 百分比 說明 1. 期中考 40% 11/10 (六) 13:30~16:00 考試範圍 2.1~5.9 (英文命題) 2. 期末考 40% 1/5 (六) 13:30~16:00 考試範圍 6.1~11.7 (英文命題) 3. 小考及作業 20% 約兩週一次小考 ***** 作業不必繳但在週一演習課上台做

 課程進度
 週次 日期 單元主題 第0週 每週一第9節實習 每週三56節上課 每週五56節上課 實習教室: 新生303 (學號後三碼除以3餘0), 403 (餘1), 404 (餘2) **************** 上課教室: 新生103 ********** Office hours: 張鎮華 週三78節 天數館521室 ***** 許祐鴻 週一56節 天數館544室 ********* 蘇哲聖 週五78節 天數館456室 ******** 吳宜欣 週四56節 教研館326室 第1週 9/10,9/12,9/14 [2.1] The Limit Process (An Intuitive Introduction). [2.2] Definition of Limit. [2.3] Some Limit Theorems. [2.4] Continuity. 第2週 9/17,9/19,9/21 [2.5] The Pinching Theorem; Trigonometric Limits. [2.6] Two Basic Theorems. [3.1] The Derivative. [3.2] Some Differentiation Formulas 第3週 9/24,9/26,9/28 [3.3] The d/dx Notation; Derivatives of Higher Order. [3.4] The Derivative as a Rate of Change. [3.5] The Chain Rule. [3.6] Differentiating the Trigonometric Functions. [3.7] Implicit Differentiation; Rational Powers 第4週 10/01,10/03,10/05 [4.1] The Mean-Value Theorem. [4.2] Increasing and Decreasing Functions. [4.3] Local Extreme Values. [4.4] Endpoint Extreme Values; Absolute Extreme Values. 第5週 10/08,10/10,10/12 10/10 holiday [4.5] Some Max-Min Problems. [4.6] Concavity and Points of Inflection 第6週 10/15,10/17,10/19 [4.7] Vertical and Horizontal Asymptotes; Vertical Tangents and Cusps. [4.8] Some Curve Sketching. *[4.9] Velocity and Acceleration; Speed. [4.10] Related Rates of Change Per Unit Time. [4.11] Differentials. *[4.12] Newton-Raphson Approximations. 第7週 10/22,10/24,10/26 [5.1] An Area Problem; A Speed-Distance Problem. [5.2] The Definite Integral of a Continuous Function. [5.3] The Function f(x) = INT t from a to x f(t) dt [5.4] The Fundamental Theorem of Integral Calculus. 第8週 10/29,10/31,11/02 [5.5] Some Area Problems. [5.6] Indefinite Integrals. [5.7] Working Back from the Chain Rule; the u-Subtitution. [5.8] Additional Properties of the Definite Integral. [5.9] Mean-Value Theorems for Integrals; Average Value of a Function. 第9週 11/05,11/07,11/09 [6.1] More on Area. [6.2] Volume by Parallel Cross-Sections; Discs and Washers. 11/09 Buffer time ********** 11/10(六) 13:30~16:00 期中考考試範圍 2.1~5.9 (英文命題). 第10週 11/12,11/14,11/16 [6.3] Volume by the Shell Method. [6.4] The Centroid of a Region; Pappus’s Theorem on Volumes. 7. The Transcendental Functions [7.1] One-to-One Functions; Inverse Functions. [7.2] The Logarithm Function, Part I. 第11週 11/19,11/21,11/23 [7.3] The Logarithm Function, Part II. [7.4] The Exponential Function. [7.5] Arbitrary Powers; Other Bases. [7.6] Exponential Growth and Decay. 第12週 11/26,11/28,11/30 [7.7] The Inverse Trigonometric Functions. [7.8] The Hyperbolic Sine and Cosine. 8. Techniques of Integration [8.1] Integral Tables and Review. [8.2] Integration by Parts. 第13週 12/03,12/05,12/07 [8.3] Powers and Products of Trigonometric Functions. [8.4] Integrals Featuring root(aa-xx), root(aa+xx), root(xx-aa). [8.5] Rational Functions; Partial Functions. [8.6] Some Rationalizing Substitutions. *[8.7] Numerical Integration. 第14週 12/10,12/12,12/14 [9.1] First-Order Linear Equations. [9.2] Integral Curves; Separable Equations. [9.3] The Equation y''+ ay'+ by = 0. 10. The Conic Sections; Polar Coordinates; Parametric Equations [10.2] Polar Coordinates. [10.3] Graphing in Polar Coordinates. 第15週 12/17,12/19,12/21 [10.4] Area in Polar Coordinates. [10.5] Curves Given Parametrically. [10.6] Tangents to Curves Given Parametrically. [10.7] Arc Length and Speed. [10.8] The Area of a Surface of Revolution; Pappus’s Theorem on Surface Area. 第16週 12/24,12/26,12/28 [11.1] The Least Upper Bound Axiom. [11.2] Sequences of Real Numbers. [11.3] The Limit of a Sequence. [11.4] Some Important Limits. [11.5] The Indeterminate Forms (0/0). 第17週 12/31,1/02,1/04 [11.6] The Indeterminate Form (∞/∞); Other Indeterminate Forms. [11.7] Improper Integrals. 1/04 Buffer time ********** 1/5(六) 13:30~16:00 期末考考試範圍 6.1~11.7 (英文命題).