課程資訊

Calculus (general Mathematics) (a)(1)

100-1

MATH1201

201 101A1

06

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1001phlee

1.Limits and Continuity 2.Differentiation 3.Applications of Derivatives 4.Integration 5.Transcendental Functions 6.Techniques of Integration 7. Applications of Integration 8. Parametric Curves and Polar Curves.

A relatively rigorous introduction of differentiation and integration of functions of a single variable and some applications to geometry and physics.

Office Hours

E. Landau：Foundation of Analysis.
T. Apostol : Calculus, Vol.1.

R.A.Adams: Calculus, a Complete Course, 7th ed.

(僅供參考)

 No. 項目 百分比 說明 1. Mid-Term 40% 2. Final Examination 40% 3. Quizzes 20%

 課程進度
 週次 日期 單元主題 第1週 9/13,9/16 Sequences and Convergence. Limits of Functions. 第2週 9/19,9/20,9/23 One-Sided Limits. Limt at Infinity and Infinite Limits. Continuity. Complete Axiom. The Max-Min Theorem. The Intermiate-Value Theorem. The Derivative. 第3週 9/26,9/27,9/30 Differential Rules. The Chain Rule. Derivatives of Trigonometric Functions. Higher-Order derivatives. Implicit Differentiation. The Mean-Value Theorem. 第4週 10/03,10/04,10/07 Quiz 1. Increasing and Decreasing Functions. Extreme Values. Concativity and Inflections. 第5週 10/10,10/11,10/14 Asymptotes. Sketching the Graph of a Function. Extreme-Value Problems. Related Rates. Using Differentials and Derivatives. Linear Approximations. 第6週 10/17,10/18,10/21 The Definite Integral. 第7週 10/24,10/25,10/28 Quiz 2. Exercises. 第8週 10/31,11/01,11/04 Properties of the Definite Integrals. The Fundamental Theorem of Calculus. 第9週 11/07,11/08,11/11 Midterm Examination. Areas of Plane Regions. 第10週 11/14,11/15,11/18 Inverse Functions. The Natural Logarithm and Exponential. Exponential and Logarithmic Functions. The Inverse Trigonometric Functions. 第11週 11/21,11/22,11/25 Cauchy's Mean-Value Theorem. Taylor Polynomials. Indeterminate Forms. 第12週 11/28,11/29,12/02 The Method of Substitution. Integration by Parts. Reduction Formulas. 第13週 12/05,12/06,12/09 Integration of Rational Functions. Integrals Transformable to Thoses of Rational Functions. The Trapezoid and Midpoint Rules. 第14週 12/12,12/13,12/16 Simpson's Rule. Volume by Slicing--Solids of Revolution. More on Volumes by Slicing. 第15週 12/19,12/20,12/23 Arc Length and Surface Area. Mass, Moments and Center of Mass. 第16週 12/26,12/27,12/30 Centroids. Parametric Curves. Smooth Parametric Curves and Their Slopes. 第17週 1/02,1/03,1/06 Arc Lengths and Areas of Parametric Curves. Polar Coordinates and Polar Curves. Slopes, Arc Lengths and Areas for Polar Curves.