課程資訊

Calculus (general Mathematics) (a)(1)

101-1

MATH1201

201 101A1

06

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

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 9/11,9/13 Sequences and Convergence. Limits of Functions. One-Sided Limits. Limits at Infinity. Infinite Limits. 第2週 9/18,9/20 Continuity. Complete Axiom. The Max-Min Theorem. The Intermiate-Value Theorem. The Derivative. Differential Rules. 第3週 9/25,9/27 The Chain Rule. Derivatives of Trigonometric Functions. Higher-Order derivatives. Implicit Differentiation. 第4週 10/02,10/04 The Mean Value Theorem. Increasing and Decreasing Functions. Extreme Values. Concativity and Inflections. Quiz 1. 第5週 10/09,10/11 Asymptotes. Sketching the Graph of a Function. Related Rates. Extreme-Value Problems. Using Differentials and Derivatives. Linear Approximations. Definite Integrals. 第6週 10/16,10/18 Properties of the Definite Integral. 第7週 10/23,10/25 Fundamental Theorem of Calculus. Integrability of Continuous Functions. Riemann Sums. Inverse Functions. Quiz 2. 第8週 10/30,11/01 The Natural Logarithm and Exponential. Exponential and Logarithmic Functions. The Inverse Trigonometric Functions. The Method of Substitution. 第9週 11/06,11/08 Integration by Parts. Reduction Formulas. Midterm Examination. 第10週 11/13 Integration of Rational Functions. 第11週 11/20,11/22 Rationalization. The Trapezoid and Midpoint Rules. Simpson Rule. Quiz 3. 第12週 11/27,11/29 Areas of Plane Regions. Volumes by Slicing. Solid of Revolution. Arc Length and Surface Area. Mass. 第13週 12/04,12/06 Moments and Center of Mass. Centroid. Cauchy's Mean Value Theorem. Taylor Polynomials. Quiz 4. 第14週 12/11,12/13 Indeterminate Forms. Conics. Smooth Parametric Curves and Their Slopes. Arc Lengths of Parametric Curves. 第15週 12/18,12/20 Areas Bounded by Parametric Curves. Curves Defined by Implicit Functions. 第16週 12/25,12/27 Curves Defined by Quadratic Forms. Polar Coordinates and Polar Curves. Quiz 5. 第17週 1/03 Slopes, Areas and Arc Length for Polar Curves.