課程資訊

Calculus (general Mathematics) (a)(1)

102-1

MATH1201

201 101A1

03

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1021calculusA

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

Calculus: Early Transcendentals 7th edition， 作者： James Stewart

(僅供參考)

 No. 項目 百分比 說明 1. 期中考 40% 2. 期末考 40% 3. 平時成績 20% 包含小考、作業、演習課表現等

 課程進度
 週次 日期 單元主題 第1週 9/09,9/11,9/13 [1.5] Exponential Functions
[1.6] Inverse Functions and Logarithms
[2.1] The Tangent and Velocity Problems
[2.2] The Limit of a Function
[2.3] Calculating Limits Using the Limit Laws 第2週 9/16,9/18,9/20 [2.4] The Precise Definition of a Limit
[2.5] Continuity 第3週 9/23,9/25,9/27 [2.6] Limits at Infinity; Horizontal Asymptotes
[2.7] Derivatives and Rates of Change
[2.8] The Derivative as a Function
[3.1] Derivatives of Polynomials and Exponential Functions 第4週 9/30,10/02,10/04 [3.2] The Product and Quotient Rules
[3.3] Derivatives of Trigonometric Functions
[3.4] The Chain Rule
[3.5] Implicit Differentiation
Quiz 1 第5週 10/07,10/09,10/11 [3.6] Derivatives of Logarithmic Functions
[3.7] Rates of Change in the Natural and Social Sciences（※）
[3.8] Exponential Growth and Decay
[3.9] Related Rates
[3.10] Linear Approximations and Differentials
[3.11] Hyperbolic Functions 第6週 10/14,10/16,10/18 [4.1] Maximum and Minimum Values
[4.2] The Mean Value Theorem
Quiz 2 第7週 10/21,10/23,10/25 [4.3] How Derivatives Affect the Shape of a Graph
[4.4] Indeterminate Forms and L’Hospital’s Rule
[4.5] Summary of Curve Sketching
[4.6] Graphing with Calculus and Calculators（※）
[4.7] Optimization Problems 第8週 10/28,10/30,11/01 [4.8] Newton’s Method（※）
[4.9] Antiderivatives
[5.1] Areas and Distances
Quiz 3
Midterm Exam on Nov. 2 第9週 11/04,11/06,11/08 [5.2] The Definite Integral
[5.3] The Fundamental Theorem of Calculus
[5.4] Indefinite Integrals and the Net Change Theorem
[5.5] The Substitution Rule 第10週 11/11,11/13,11/15 [6.1] Areas Between Curves
[6.2] Volumes
[6.3] Volumes by Cylindrical Shells
[6.4] Work（※） 第11週 11/18,11/20,11/22 [6.5] Average Value of a Function（※）
[7.1] Integration by Parts
[7.2] Trigonometric Integrals
[7.3] Trigonometric Substitution
[7.4] Integration of Rational Functions by Partial Fractions 第12週 11/25,11/27,11/29 [7.5] Strategy for Integration
[7.7] Approximate Integration
[7.8] Improper Integrals
[8.1] Arc Length
Quiz 4 第13週 12/02,12/04,12/06 [8.2] Area of a Surface of Revolution
[8.3] Applications to Physics and Engineering
[8.4] Applications to Economics and Biology（※）
[8.5] Probability（※） 第14週 12/09,12/11,12/13 [9.1] Modeling with Differential Equations
[9.2] Direction Fields and Euler’s Method（※）
[9.3] Separable Equations
[9.4] Models for Population Growth
Quiz 5 第15週 12/16,12/18,12/20 [9.5] Linear Equations 第16週 12/23,12/25,12/27 [10.1] Curves Defined by Parametric Equations
[10.2] Calculus with Parametric Curves
[10.3] Polar Coordinates
[10.4] Areas and Lengths in Polar Coordinates
[10.6] Conic Sections in Polar Coordinates
Quiz 6 第17週 12/30,1/01,1/03 Final Exam on Jan. 5