課程資訊

Calculus (general Mathematics) (b)(1)

107-1

MATH1203

201 101B1

06

3.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1071MATH1203_06

Differential and integral calculus of one variable functions with applications.

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.

High School Mathematics

Office Hours

Textbook: Thomas' calculus, early transcendentals. 13th edition in SI units.
Revised by M. D. Weir and J. Hass. Pearson 2016. 東華書局/新月圖書 代理

(僅供參考)

 No. 項目 百分比 說明 1. 課堂小考 20% 暫定 2. 期末考 40% 暫定 3. 期中考 40% 暫定

 課程進度
 週次 日期 單元主題 第1週 9/11, 9/13 2.3 The precise definition of a limit 2.2 Limit of a function and limit laws 2.4 One sided limits 第2週 9/18, 9/20 9/18: 2.5 Continuity (including various types of discontinuity and intermediate value theorem) 9/20: 2.6 Limits involving infinity; asymptotes of graphs 第3週 9/25, 9/27 9/25: 3.1, 3.2 9/27: 3.3 differentiation rules 第4週 10/2, 10/4 10/2: 3.5 derivatives of trig. functions, and 3.6 the chain rule (3.4 is skipped) 10/4: 3.7 implicit differentiation 第5週 10/9, 10/11 10/09: 3.8 exponential and logarithmic functions 10/11: quiz 1 第6週 10/16, 10/18 10/16: 3.9 a brief introduction of inverse trigonometric functions (including their derivatives), and 3.11 linearization and differentials 10/18: absolute/relative max. and min. values, and extreme value theorem。後半小時發小考1考卷 第7週 10/23, 10/25 10/23: theoretical parts of 4.1 - 4.3, and L'Hopital's rule in 4.5 10/25: 4.4 concavity and curve sketching 第8週 10/30, 11/01 10/30: more examples of curve sketching and indeterminate forms (4.4 and 4.5) 11/01: quiz 2 第9週 11/6, 11/8 11/6: 4.6 applied optimization 11/8: 4.8 antiderivatives and 5.2 partition of an interval, and so on. 4.7 and 5.1 are skipped 第10週 11/13, 11/15 11/13: Definition and properties of Riemann integrals. 11/15: 校慶 第11週 11/20, 11/22 11/20: Midterm exam. 11/22: 5.4 The fundamental theorem of calculus 第12週 11/27, 11/29 11/27: 5.5 integration by substitution 11/29: 5.6 and 6.1 area between curves and volumes using cross-sections 第13週 12/4, 12/6 12/4: 6.1 and 6.2 volumes by disk and shell methods 12/6: 6.3 arc length 第14週 12/11, 12/13 12/11: separable differential equations, integration by parts 12/13: Quiz 3 第15週 12/18, 12/20 12/18: 8.2, 8.3 (sine and cosine), and 8.5 12/20: 8.5 第16週 12/25, 12/27 12/25: Improper integrals 12/27: Improper integrals (direct and limit comparison theorems) 第17週 1/1, 1/3 1/3: quiz 4 on separable differential equations, integration by parts, and integrals of rational functions 1/8: Final exam.