課程資訊

Calculus (general Mathematics) (a)(1)

103-1

MATH1201

201 101A1

05

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1031MATH1201_05

1. Limits and Continuity
2. Differentiation
3. Applications of Derivatives
4. Integration
5. Applications of Definite Integrals.
6. Integrals and Transcendental Functions
7. Techniques of Integration
8. Infinite Series.

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.

High School Mathematics
Office Hours

Thomas, Weir and Hass, Thomas' Calculus, Early Transcendentals. 12th ed.

(僅供參考)

 No. 項目 百分比 說明 1. Midterm Examination 40% 2. Final Examination 40% 3. Quiz 20%

 課程進度
 週次 日期 單元主題 第1週 9/15,9/16,9/18 Sequences. Limit and Limit Laws. Limit of a Function. 第2週 9/22,9/23,9/25 One-Sided Limits. Continuity. Limits Involving Infinity. 第3週 9/29,9/30,10/02 Derivatives. Differential Rules. Derivatives of Trigonometric Functions. Chain Rule. Implicit Differentiation. 第4週 10/06,10/07,10/09 Derivatives of Inverse Functions. Inverse Trigonometric Functions. Related Rates. Linearization. Extreme Values of Functions. 第5週 10/13,10/14,10/16 Quiz 1. Mean Value Theorem. Monotonic Functions and the First Derivative Test. Concavity. Asymptotes of Graphs. Curve Sketching. 第6週 10/20,10/21,10/23 Inderterminate Forms and L'Hopital's Rule. Taylor Expansion with Remainder. Applied Optimation. 第7週 10/27,10/28,10/30 Definite Integral. 第8週 11/03,11/04,11/06 Quiz 2. Riemann Sums. Fundamental Theorem of Calculus. Indefinite Integrals. Natural Logarithm. 第9週 11/10,11/11,11/13 Logarithm and Exponential. Midterm Examination. 第10週 11/17,11/18,11/20 More on Indeterminate Forms. Integration by Substitution. Integration by Parts. Integration of Rational Functions. 第11週 11/24,11/25,11/27 Integration by Rationalization. 第12週 12/01,12/02,12/04 Quiz 3. Numerical Integration. More on Polynomial Approximation. 第13週 12/08,12/09,12/11 Volumes. Arc Length. Areas of Surfaces of Revolution. Moments and Center of Mass. Centroid. 第14週 12/15,12/16,12/18 Parametrization of Plane Curves. Calculus with Parametric Curves. Polar Coordinates. 第15週 12/22,12/23,12/25 Quiz 4. Graphing in polar Coordinates. Areas and Arc Length in Polar Coordinates. Conic Sections. Conics in Polar Coordinates. 第16週 12/29,12/30 Classification of Curves Defined by Quadratic Forms. 第17週 1/05,1/06,1/08 Quiz 5. More on Conic Sections and Polar Curves.