課程資訊

Calculus (general Mathematics) (a)(1)

101-1

MATH1201

201 101A1

02

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1011calculus_I_02

http://www.math.ntu.edu.tw/~mathcal/download/991/991A1.pdf

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.

Office Hours

1. Apostol, Calculus, vol. 1 and 2.
2. Courant and John, Introduction to Calculus and Analysis.

Salas, Hille, and Etgen, Calculus, one and several variables, tenth edition.

(僅供參考)

 No. 項目 百分比 說明 1. Homework and Quiz 20% 2. Midterm Exam 40% 3. Final Exam 40%

 課程進度
 週次 日期 單元主題 第1週 9/10,9/12,9/14 Limits, The Pinching Theorem. 第2週 9/17,9/19,9/21 Continuity, Sequences, Bolzano-Weierstrass Theorem, The Completeness of Real Numbers. 第3週 9/24,9/26,9/28 Intermediate-Value Theorem, Bolzano Theorem, Extreme-Value Theorem, Differentiation. 第4週 10/01,10/03,10/05 The Chain Rule, Implicit Differentiation, The Mean-Value Theorem. 第5週 10/08,10/10,10/12 Quiz, Local Extreme Values. 第6週 10/15,10/17,10/19 Concavity and Inflection, Limits at Infinity, Infinite Limits, Asymptotes, Curve Sketching, Absolute Extreme Value. 第7週 10/22,10/24,10/26 Extreme-Value Problem, Differentials. Antiderivatives, Riemann Integral. 第8週 10/29,10/31,11/02 Quiz, Uniform Continuity, Riemann Sum, Mean-Value and Intermediate-Value Theorem for Integrals, The Fundamental Theorem of Calculus. 第9週 11/05,11/07,11/09 Change of Variables, Area Problems, Volumes by Slicing and Solids of Revolution, Centroid, Pappus's Theorem, One-to-One Function, Midterm Exam. 第10週 11/12,11/14,11/16 Inverse Function Theorem, Natural Logarithmic Function and Natural Exponential Function. 第11週 11/19,11/21,11/23 Exponential Growth and Decay, Inverse Trigonometric Functions, Hyperbolic Functions, Inverse Hyperbolic Functions, Techniques of Integration. 第12週 11/26,11/28,11/30 Quiz, First-Order Linear Ordinary Differential Equations(ODEs), Separable First-Order ODEs. 第13週 12/03,12/05,12/07 Second-Order Linear ODEs with Constant Coefficients, Polar Coordinates. 第14週 12/10,12/12,12/14 Quiz, Area in Polar Coordinates, Parameterized Curves. 第15週 12/17,12/19,12/21 Arc Length, Reparameterization, Area of Surface of Revolution. 第16週 12/24,12/26,12/28 Indeterminate Forms, Improper Integrals. 第17週 12/31,1/02,1/04 Monotone Sequences Convergence Theorem, Cauchy Criterion, Proof of Bolzano-Weierstrass Theorem.