課程資訊

CALCULUS (GENERAL MATHEMATICS) (A)(1)

99-1

MATH1201

201 101A1

01

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/991cal01

1. Functions and Models
2. Limits and Derivatives
3. Differentiation Rules
4. Applications of Differentiation
5. Integrals
6. Applications of Integration
7. Techniques of Integration
8. Further Applications of Integration
9. Differential Equations
10. Parametric Equations and Polar Coordinates

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

TEXTBOOK: James Stewart, Calculus Early Transcendentals, 6th edition

(僅供參考)

 No. 項目 百分比 說明 1. Midterm Test 40% 2. Final Test 40% 3. Quizzes and homework 20%

 課程進度
 週次 日期 單元主題 第6週 10/18-10/22 [4.1] Maximum and Minimum Values [4.2] The Mean Value Theorem 第9週 11/08-11/12 [5.4] Indefinite Integrals and the Net Change Theorem [5.5] The Substitution Rule 第14週 12/13-12/17 [8.1] Arc Length [8.2] Area of a Surface of Revolution [8.5] Probability (※) 第17週 01/03-01/07 [10.3] Polar Coordinates [10.4] Areas and Lengths in Polar Coordinates 第1-2週 09/13-09/17 [2.1] The Tangent and Velocity Problems. [2.2] The Limit of a Function.(LN 1.10) 第2-1週 09/20-09/24 09/22(三) 中秋節放假一天 第2-2週 09/20-09/24 [2.3] Calculating Limits Using the Limit Laws. [2.4] The Precise Definition of a Limit.[LN.2.4] 第3-1週 09/27-10/01 [2.5] Continuity. [2.6] Limits at Infinity; Horizontal Asymptotes. [2.7] Derivatives and Rates of Change.[LN.2.6] 第3-2週 09/27-10/01 [2.8] The Derivative as a Function. [3.1] Derivatives of Polynomials and Exponential Functions.[LN.2.9] 第4-1週 10/04-10/08 [3.2] The Product and Quotient Rules. [3.3] Derivatives of Trigonometric Functions.[LN.3.3] 第4-2週 10/04-10/08 [3.4] The Chain Rule. [3.5] Implicit Differentiation.[LN. 3.6] 第5-1週 10/11-10/15 [3.6] Derivatives of Logarithm Functions. [3.7] Rates of Change in the Natural and Social Science (※) [3.8] Exponential Growth and Decay. 第5-2週 10/11-10/15 [3.9] Related Rates [3.10] Linear Approximation and Differentials [3.11] Hyperbolic Functions (※) 第7-1週 10/25-10/29 [4.3] How Derivatives Affect the Shape of a Graph. [4.4] Indeterminate Forms and L’Hospital’s Rule. 第7-2週 10/25-10/29 [4.5] Summary of Curve Sketching [4.6] Graphing with Calculus and Calculators [4.7] Optimization Problems 第8-1週 11/01-11/05 [4.8] Newton’s Method (※) [4.9] Antiderivatives [5.1] Areas and Distances 第8-2週 11/01-11/05 [5.2] The Definite Integral [5.3] The Fundamental Theorem of Calculus 第10-1週 11/15-11/19 [6.1] Areas between Curves [6.2] Volumes 第10-2週 11/15-11/19 [6.3] Volumes by Cylindrical Shells [6.4] Work (※) 第11-1週 11/22-11/26 [6.5] Average Value of a Function [7.1] Integration by Parts 第11-2週 11/22-11/26 [7.2] Trigonometric Integrals 第12-1週 11/29-12/03 [7.3] Trigonometric Substitution 第12-2週 11/29-12/03 [7.4] Integration of Rational Functions by Partial Fractions 第13-1週 12/06-12/10 [7.5] Strategy for Integration [7.6] Integration Using Tables and Computer Algebra Systems [7.7] Approximate Integration 第13-2週 12/06-12/10 [7.8] Improper Integrals 第15-1週 12/20-12/24 [9.1] Modeling with Differential Equations [9.2] Direction Fields and Euler’s Method 第15-2週 12/20-12/24 [9.3] Separable Equations [9.4] Models for Population Growth 第16-1週 12/27-12/31 [9.5] Linear Equations [9.6] Predator-Prey Systems (※) 第16-2週 12/27-12/31 [10.1] Curves Defined by Parametric Equations [10.2] Calculus with Parametric Curves