課程資訊

Calculus (general Mathematics) (b)(1)

111-1

MATH1203

201 101B1

02

3.0

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: Stewart, Calculus: Early Transcendentals 第九版

(僅供參考)

 No. 項目 百分比 說明 1. 期中考 30% 暫定 2. 期末考 30% 暫定 3. max {quiz 1, quiz 2} (暫定) 15% 暫定 4. max {quiz 3, quiz 4} (暫定) 15% 暫定 5. WeBWork 10% 暫定 (每週線上演習，以全學期答對率計算得分)

 課程進度
 週次 日期 單元主題 第1週 ====================================== (由這行說明開始，以下之內容為系統複製前年課程之進度(18週)，其目的在提供同學了解往年課程進行之快慢及其內容。 日後隨著日期與課程進行，將會逐週進行更新，於上方紀錄當週真實進度。 同學請以最新逐週的公布，進行複習，演練習題。） =========2020 Fall ============================ 9/15: 1.5 exponential functions, 2.3 the precise definition of a limit, and the limit laws in 2.2 (a proof on the limit of linear combination of functions was given) 9/17: 2.4 one-sided limits and its relationship with two-sided limit. An introduction of WeBWork given by TAs ========================= First week of 2019 Fall semester: 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 9/22: The squeeze theorem (Theorem 4 on p. 73) with an outline of the proof of Theorem 5, and an application to exercise 49 on p.84. 2.5 Continuity, intermediate value theorem, and examples of various types of discontinuity 9/24: Removable discontinuity and 2.6 limits at infinity and infinite limits; asymptotes of graphs ============================== 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 9/29: 3.1, 3.2, and 3.3 (differentiation rules, derivatives of exponential functions, and higher order derivatives) (3.4 is skipped) ============================== 9/24: 3.1, 3.2 9/26: 3.3 differentiation rules, derivatives of exponential functions, and higher order derivatives 第4週 10/6: Theorem 7 on p. 104 (limit of (sin x)/x as x approaching zero) and related limits, 3.5 derivatives of trig. functions, and 3.6 the chain rule 10/8: 3.7 Implicit differentiation ===================================== 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 10/13: Derivative of logarithmic function, logarithmic differentiation, a limit of e, and examples 10/15: Recitation 演習課 ================================= 10/08: 3.11 linear approximation and differentials 第6週 10/20: 3.11 linearization and differentials, 4.1, and the Rolles's theorem of 4.2 10/22: Quiz 1 ================2019================= 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 -----------------2018--------------- 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 10/27: 4.2 Mean value theorem, 4.3 first derivatives and the monotonic functions, and 4.4 concavity and curve sketching 10/29: 4.5 L'Hopital's rule ==========2019==================== 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 ----------2018------------------------------ 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 11/3: 4.5 L'Hopital's rule 11/5: Recitation 發quiz 1 考卷 與 演習課 =================2019============= 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 11/10: 4.4 Curve sketching revisited and 4.6 applied optimization 11/12: 4.7*, 4.8*, and 5.3 the definite integral (only the definition is introduced) =============2019=================== 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 11/17: 5.4 The fundamental theorem of calculus 11/19: Quiz 2 ===========2019========================= 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 11/24: Midterm exam. 11/26: 5.5 integration by substitution and the first half of 5.6 (up to Theorem 8) ====================2019================== 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 12/1: 5.6 and 8.2 integration by parts 12/3: 8.2 reduction formulas (p. 479) of \sin^n x and \sec^n x, exercise 68, and Wallis product of \pi/2 ==============2019============ 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 12/08: 8.3 integration of \sin^n x \cos^m x.第四堂發期中考考卷 12/10: Recitation 演習 ==============2019=========== 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 12/15: 8.5 Integration of rational functions by partial fractions (only cases 1-3 were studied) 12/17: quiz 3 =======================2019============= 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 12/22: 8.5 (completed) and 8.8 Improper integrals (Type 1 discussed) 12/24: 8.8 Type 2 improper integrals, direct and limit comparison tests =======2019=================== 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 12/29: First order separable and linear differential equations 12/31: Recitation (answer sheets of quiz 3 will be returned) ========2019============================ 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 1/5: 10:20-11:10 review, 11:20-12:10 recitation 1/7: Quiz 4 1/12: Final exam. =============2019=========== 12/31: review. 11:20 - 12:10 recitation 1/2: quiz 4 1/7: final exam. ----------------------------------- 1/3: quiz 4 on separable differential equations, integration by parts, and integrals of rational functions 1/8: Final exam.