課程資訊

CALCULUS (GENERAL MATHEMATICS) (A)(1)

97-1

MATH1201

201 101A1

01

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/971cal01

1. Functions and Models
2. Limits and Derivatives
3. Differentiation Rule
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

After completing this course, students should be well versed in the mathematical language needed for applying the concepts of calculus to numerous applications in science and engineering. They should also be well prepared for courses in differential equations, linear algebra, or advanced calculus.

Office Hours

James Stewart, CALCULUS, Early Transcendentals, 6th edition

(僅供參考)

 No. 項目 百分比 說明 1. 期中考 40% 2. 期末考 40% 3. 作業 20% 小考+作業+演習課表現

 課程進度
 週次 日期 單元主題 第1週 9/17,9/19 [1.5] Exponential Functions [1.6] Inverse Functions and Logarithms [2.1] The Tangent and Velocity Problems [2.2] The Limit of a Function 第2週 9/24,9/26 [2.3] Calculating Limits Using the Limit Laws [2.4] The Precise Definition of a Limit [2.5] Continuity [2.6] Limits at Infinity; HorizontalAsymptotes 第3週 10/01,10/03 [2.7] Derivatives and Rates of Change [2.8] The Derivative as a Function [3.1] Derivatives of Polynomials and Exponential Functions [3.2] The Product and Quotient Rules [3.3] Derivatives of Trigonometric Functions 第4週 10/08,10/10 [3.4] The Chain Rule [3.5] Implicit Differentiation [3.6] Derivatives of Logarithmic Functions 第5週 10/15,10/17 [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 10/22,10/24 [4.1] Maximum and Minimum Values [4.2] The Mean Value Theorem [4.3] How Derivatives Affect the Shape of a Graph [4.4] Indeterminate Forms and L’Hospital’s Rule 第7週 10/29,10/31 [4.5] Summary of Curve Sketching [4.6] Graphing with Calculus and Calculators [4.7] Optimization Problems [4.8] Newton’s Method [4.9] Antiderivatives 第8週 11/05,11/07 [5.1] Areas and Distances [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9週 11/12,11/14 緩衝時間, Midterm Exam 第10週 11/19,11/21 [6.1] Areas between Curves [6.2] Volumes [6.3] Volumes by Cylindrical Shells [6.4] Work 第11週 11/26,11/28 [6.5] Average Value of a Function [7.1] Integration by Parts [7.2] Trigonometric Integrals [7.3] Trigonometric Substitution 第12週 12/03,12/05 [7.4] Integration of Rational Functions by Partial Fractions [7.5] Strategy for Integration [7.6] Integration Using Tables and Computer Algebra Systems [7.7] Approximate Integration 第13週 12/10,12/12 [7.8] Improper Integrals [8.1] Arc Length [8.2] Area of a Surface of Revolution [8.3] Applications to Physics and Engineering 第14週 12/17,12/19 [8.4] Applications to Economics and Biology [8.5] Probability [9.1] Modeling with Differential Equations [9.2] Direction Fields and Euler’s Method 第15週 12/24,12/26 [9.3] Separable Equations [9.4] Models for Population Growth [9.5] Linear Equations [9.6] Predator-Prey Systems 第16週 12/31,1/02 [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 第17週 1/07,1/09 緩衝時間 第18週 1/14,1/16 Final Exam