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週次 |
日期 |
單元主題 |
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第1週 |
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(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 |
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第2週 |
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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 |
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第3週 |
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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 |
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第4週 |
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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 |
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第5週 |
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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 |
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第6週 |
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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
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第7週 |
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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 |
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第8週 |
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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 |
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第9週 |
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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
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第10週 |
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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 |
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第11週 |
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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 |
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第12週 |
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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 |
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第13週 |
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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 |
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第14週 |
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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 |
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第15週 |
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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 |
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第16週 |
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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)
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第17週 |
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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. |