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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 |
醫學工程學系 |
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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 |
07 |
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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
星期三8,9,10(15:30~18:20)星期五1,2(8:10~10:00) |
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上課地點 |
新102新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.三10為實習課.
限本系所學生(含輔系、雙修生) 或 限僑生、國際學生
總人數上限：160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 of Riemann
Week 10 Technique of Integration (I) : Substitution
Week 11 Technique of Integration (II) : Integration by Parts
Week 12 Integrals of Rational Functions and Applications
Week 13 Improper Integrals and Probability
Week 14 Introduction to Differential Equations
Week 15 Exam week
Week 16
Introduction to Laplace Transform (Non-examinable) |
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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
7. Use integrals to compute geometric invariants of a curve or a solid |
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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 |
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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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No. |
項目 |
百分比 |
說明 |
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1. |
Exam |
50% |
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2. |
Quizzes |
20% |
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3. |
Assessment |
30% |
Homework, WeBWorK, Worksheets and others |
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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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