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課程名稱 |
微積分2
CALCULUS (2) |
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開課學期 |
113-1 |
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授課對象 |
生命科學院院學士學位 |
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授課教師 |
蔡國榮 |
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課號 |
MATH4007 |
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課程識別碼 |
201E49820 |
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班次 |
16 |
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學分 |
2.0 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
第9,10,11,12,13,14,15,16 週
星期二1(8:10~9:00)星期四8,9,10(15:30~18:20) |
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上課地點 |
普102普102 |
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備註 |
初選不開放。本課程以英語授課。密集課程。英文授課.初選不開放.密集課程.統一教學.實習課另外安排. 參閱分班編組課程
限本系所學生(含輔系、雙修生)
總人數上限：150人 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
This course will be lectured in English.
In this course, we will continue our journey in Calculus and turn our attention to the theory of integration (à la Riemann). We shall begin with the definition and techniques of integration, derive the Fundamental Theorem of Calculus that provides an important link between integration & differentiation, compute areas and volumes of some 2D/3D objects, discuss applications to analytic (plane) geometry and solve certain first order differential equations.
Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study.
This course also provides TA classes in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants.
Provisional schedule :
Week 9 Integrations : Definitions and FTC
5.1 The Area and Distance Problems
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
Week 10 Techniques of Integrations (I)
5.5 The Substitution Rule
7.2 Trigonometric Integrals
7.3 Trigonometric Substitutions
11/7, Thu, Quiz 1 (Coverage : 5.1-5.4)
Week 11 Techniques of Integrations (II)
7.1 Integrations by Parts
7.4 Integration of Rational Functions by Partial Fractions
7.8 Improper Integrals
11/14, Thu, Worksheet 1 : Medical Imaging
Week 12 Applications of Integrations
6.1 Areas Between Curves
6.5 Average Value of a Function
8.5 Probability
11/21, Thu, Exam 1 (Coverage : Week 9-11)
Week 13 Introduction to Differential Equations
9.1 Modeling with Differential Equations
9.3 Separable Equations
9.4 Models for Population Growths
9.5 Linear Equations
Week 14 Introduction to Taylor series (I)
11.8 Power series (No convergence issues)
11.9 Representation of Functions as Power Series
12/5, Thu, Quiz 2 (Coverage : Week 12-13)
Week 15 Introduction to Taylor series (II)
11.10 Taylor and Maclaurin Series
12/12, Thu, Worksheet 2 : Introduction to Bifurcation
Week 16 Exam Week
12/19, Thu, Exam 2 (Coverage : Week 12-15) |
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課程目標 |
Students will be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. Calculus 1, 2, 3, 4 provide the basis for the study of various advanced courses like Engineering Mathematics, Mathematical Analysis and Differential Equations.
To be specific, upon completing the course, students are expected to be able to
1. Define the integrals of a continuous function over a closed and bounded interval
2. Derive and apply properties of definite integrals
3. Derive and apply the Fundamental Theorem of Calculus to compute definite integrals
4. Use techniques such as substitutions and integration by parts to compute an antiderivative of a function
5. Define an improper integral and apply it in computing probability
6. Set up and solve separable and first order differential equations |
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課程要求 |
The prerequisites are high school mathematics and Calculus 1. |
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預期每週課後學習時數 |
Besides the 4-hour lectures per week, students should expect to spend around 2-3 hours weekly in digesting the lecture materials as well as completing exercises offered by the lecturer or the teaching assistant(s). |
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Office Hours |
每週五 15:30~17:20
每週二 15:30~17:20
每週一 14:00~15:00 備註： Mon 2:00pm-3:00pm (Hosted by TA Leo)
Tue, Fri 3:30pm-5:20pm (Appointment at other times is possible) |
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指定閱讀 |
Stewart, Clegg, Watson, CALCULUS: EARLY TRANSCENDENTALS, Metric, 9th Edition
The course will be supplemented by the lecture notes of the instructor. |
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參考書目 |
NTUOCW on Calculus 2 :
https://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/111S103 |
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評量方式
(僅供參考) |
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針對學生困難提供學生調整方式 |
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上課形式 |
以錄影輔助 |
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作業繳交方式 |
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考試形式 |
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其他 |
由師生雙方議定 |
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週次 |
日期 |
單元主題 |
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Week 9 |
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Integrations : Definitions and FTC
5.1 The Area and Distance Problems
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem |
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Week 10 |
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Techniques of Integrations (I)
5.5 The Substitution Rule
7.2 Trigonometric Integrals
7.3 Trigonometric Substitutions
11/7, Thu, Quiz 1 (Coverage : 5.1-5.4) |
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Week 11 |
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Techniques of Integrations (II)
7.1 Integrations by Parts
7.4 Integration of Rational Functions by Partial Fractions
7.8 Improper Integrals
11/14, Thu, Worksheet 1 : Medical Imaging |
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Week 12 |
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Applications of Integrations
6.1 Areas Between Curves
6.5 Average Value of a Function
8.5 Probability
11/21, Thu, Exam 1 (Coverage : Week 9-11) |
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Week 13 |
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Introduction to Differential Equations
9.1 Modeling with Differential Equations
9.3 Separable Equations
9.4 Models for Population Growths
9.5 Linear Equations |
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Week 14 |
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Introduction to Taylor series (I)
11.8 Power series (No convergence issues)
11.9 Representation of Functions as Power Series
12/5, Thu, Quiz 2 (Coverage : Week 12-13) |
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Week 15 |
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Introduction to Taylor series (II)
11.10 Taylor and Maclaurin Series
12/12, Thu, Worksheet 2 : Introduction to Bifurcation |
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Week 16 |
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Exam Week
12/19, Thu, Exam 2 (Coverage : Week 12-15) |
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