課程資訊

Calculus (general Mathematics) (b)(1)

108-1

MATH1203

201 101B1

06

3.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1081MATH1203_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. 期中考 35% 暫定 2. 期末考 35% 暫定 3. max {quiz 1, quiz 2} 15% 4. max {quiz 3, quiz 4} 15%

 課程進度
 週次 日期 單元主題 第1週 9/10, 9/12 2.3 The precise definition of a limit 2.2 Limit of a function and limit laws (a proof on the limit of linear combination of functions was given) 2.4 One sided limit and its relation with two-sided limit 第2週 9/17, 9/19 9/17: 2.5 Continuity, examples of various types of discontinuity, and 2.6 limits involving infinity. 9/19: Asymptotes of graphs, properties of continuity, and intermediate value theorem 第3週 9/24, 9/26 9/24: 3.1, 3.2 9/26: 3.3 differentiation rules, derivatives of exponential functions, and higher order derivatives 第4週 10/1, 10/3 10/1: 3.5 derivatives of trig. functions, 3.6 the chain rule, and 3.7 implicit differentiation (3.4 is skipped) 10/3: 3.8 exponential and logarithmic functions 第5週 10/8, 10/10* 10/08: 3.11 linear approximation and differentials 第6週 10/15, 10/17 10/15: 4.1 absolute/relative max. and min. values, extreme value theorem, and 4.2 mean value theorem 2019/10/17 (Thur.) Quiz 1 on chapters 2 and 3 -------------------------------- 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 10/22, 10/24 10/22: 4.3 and 4.4 concavity and curve sketching 10/24: 4.4 examples of curve sketching, 後半小時發小考1考卷 ---------------------------------------- 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 10/29, 10/31 10/29: 4.5 indeterminate forms 10/31: 4.6 applied optimization ----------------------------------- 2018/10/30: more examples of curve sketching and indeterminate forms (4.4 and 4.5) 2018/11/01: quiz 2 第9週 11/05, 11/07 11/05: 4.8 antiderivatives, 5.2 and 5.3 definition and properties of Riemann sums and definite integrals. 11/07: Quiz 2 ------- 2018 ------------------------ 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 11/12, 11/14 11/12: 5.4 The fundamental theorem of calculus, and 5.5 integration by substitution 11/14: 發 quiz 2 考卷與演習課 ----------2018------------------------- 11/13: Definition and properties of Riemann integrals. 11/15: 校慶 第11週 11/19, 11/21 11/19: Midterm exam. 11/21: 5.6 area between curves -------------------------- 11/20: Midterm exam. 11/22: 5.4 The fundamental theorem of calculus 第12週 11/26, 11/28 11/26 and 11/28: 6.1 and 6.2 volumes by disk and shell methods -------------------------- 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 12/03, 12/05 12/03: 6.3 arc length, inverse sine, and 7.1 formal definitions of logarithm and exponential functions (11:40-12:10 發，並檢討 期中考) 12/05: 7.2 separable differential equations, and 8.2 integration by parts ------------------------------ 12/4: 6.1 and 6.2 volumes by disk and shell methods 12/6: 6.3 arc length 第14週 12/10, 12/12 12/10: 8.1 and 8.2 12/12: Quiz 3 (up to 6.3) ------------------------------- 12/11: separable differential equations, integration by parts 12/13: Quiz 3 第15週 12/17, 12/19 12/17: 8.5 integration of rational functions and partial fractions 12/19: 8.3 (sine and cosine) ------------------------------------ 12/18: 8.2, 8.3 (sine and cosine), and 8.5 12/20: 8.5 第16週 12/24, 12/26 12/24: Improper integrals, comparison and limit comparison theorems 12/26: 18:00 - 18:20 發 quiz 3 考卷 ----------------------------------------- 12/25: Improper integrals 12/27: Improper integrals (direct and limit comparison theorems) 第17週 12/31, 1/2 12/31: review. 11:20 - 12:10 recitation 1/2: quiz 4 1/7: final exam. ----------------------------------- (由這行說明開始，包含本週與以下之內容為系統複製去年課程之進度，其目的在提供同學了解往年課程進行之內容與快慢。日後，隨著日期與課程進行，將會逐週進行更新。同學請以最新逐週公布的『課程大綱』為準，進行複習並演練習題。） 1/3: quiz 4 on separable differential equations, integration by parts, and integrals of rational functions 1/8: Final exam.