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課程名稱 |
微積分甲上
Calculus (general Mathematics) (a)(1) |
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開課學期 |
102-1 |
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授課對象 |
科技管理組 |
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授課教師 |
朱樺 |
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課號 |
MATH1201 |
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課程識別碼 |
201 101A1 |
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班次 |
13 |
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學分 |
4 |
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全/半年 |
全年 |
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必/選修 |
必修 |
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上課時間 |
星期一5,6(12:20~14:10)星期五1,2(8:10~10:00) |
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上課地點 |
新103新103 |
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備註 |
大二以上限20人.
限本系所學生(含輔系、雙修生)
總人數上限：100人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1021caqlculusB |
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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 |
課程大綱
1. Limits and continuity,
2. Differentiation,
3. Application of Differentiation,
4. Integration,
5. Application of integrals,
6. Transcendental functions,
7. Techniques of Integration,
8. Infinte Series
9. Function of Several Variables
10. Multiple Integration
11. Vector Analysis
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課程目標 |
學生能從此課程中學習到微積分的理論與應用 |
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課程要求 |
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預期每週課後學習時數 |
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Office Hours |
每週三 12:20~13:20
每週五 12:20~13:20 備註： 助教Office hour:若要來找助教，請先用email聯絡預約時間。 |
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參考書目 |
課本
Calculus: Early Transcendentals 7th edition,
作者： James Stewart |
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指定閱讀 |
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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. |
期末考 |
30% |
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2. |
期中考 |
25% |
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3. |
小考二 |
15% |
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4. |
小考一 |
15% |
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5. |
習題 |
15% |
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週次 |
日期 |
單元主題 |
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第1週 |
09/09,09/13 |
[1.5] Exponential Functions
[1.6] Inverse Functions and Logarithms
[2.1] The Tangent and Velocity Problems
[2.2] The Limit of a Function
[2.3] Calculating Limits Using the Limit Laws |
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第2週 |
09/16,09/20 |
[2.4] The Precise Definition of a Limit
[2.5] Continuity;
09/20(五)中秋節調整放假 |
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第3週 |
09/23,09/27 |
[2.6] Limits at Infinity; Horizontal Asymptotes
[2.7] Derivatives and Rates of Change
[2.8] The Derivative as a Function
[3.1] Derivatives of Polynomials and Exponential Functions |
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第4週 |
09/30,10/04 |
[3.2] The Product and Quotient Rules
[3.3] Derivatives of Trigonometric Functions
[3.4] The Chain Rule
[3.5] Implicit Differentiation
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第5週 |
10/7,10/11 |
[3.6] Derivatives of Logarithmic Functions
[3.7] Rates of Change in the Natural and Social Sciences（※）
[3.8] Exponential Growth and Decay
[3.9] Related Rates
[3.10] Linear Approximations and Differentials
[3.11] Hyperbolic Functions（※） |
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第6週 |
10/14,10/18 |
10/14(一)小考一(暫定);
[4.1] Maximum and Minimum Values
[4.2] The Mean Value Theorem |
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第7週 |
10/21,10/25 |
[4.3] How Derivatives Affect the Shape of a Graph
[4.4] Indeterminate Forms and L’Hospital’s Rule
[4.5] Summary of Curve Sketching
[4.6] Graphing with Calculus and Calculators（※）
[4.7] Optimization Problems |
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第8週 |
10/28,11/01 |
[4.8] Newton’s Method（※）
[4.9] Antiderivatives
[5.1] Areas and Distances
[5.2] The Definite Integral
[5.3] The Fundamental Theorem of Calculus |
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第9週 |
11/04,11/08 |
[5.4] Indefinite Integrals and the Net Change Theorem
[5.5] The Substitution Rule |
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第10週 |
11/11,11/15 |
[6.1] Areas Between Curves
[6.2] Volumes
[6.3] Volumes by Cylindrical Shells
[6.4] Work（※）;
11/15(五) 本校校慶 停課一天 |
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第11週 |
11/18,11/22 |
[6.5] Average Value of a Function
[7.1] Integration by Parts
[7.2] Trigonometric Integrals
[7.3] Trigonometric Substitution
[7.4] Integration of Rational Functions by Partial Fractions |
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第12週 |
11/25,11/29 |
[7.5] Strategy for Integration
[7.6] Integration Using Tables and Computer Algebra Systems
[7.7] Approximate Integration
[7.8] Improper Integrals
[8.1] Arc Length |
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第13週 |
12/02,12/26 |
[8.2] Area of a Surface of Revolution
[8.3] Applications to Physics and Engineering
[8.4] Applications to Economics and Biology（※）
[8.5] Probability（※） |
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第14週 |
12/09,12/13 |
12/09(一)小考二(暫定);
[9.1] Modeling with Differential Equations
[9.2] Direction Fields and Euler’s Method
[9.3] Separable Equations
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第15週 |
12/16,12/20 |
[9.4] Models for Population Growth
[9.5] Linear Equations
[9.6] Predator-Prey Systems （※） |
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第16週 |
12/23,12/27 |
[10.1] Curves Defined by Parametric Equations
[10.2] Calculus with Parametric Curves
[10.3] Polar Coordinates |
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第17週 |
2013/12/30,2014/01/03 |
[10.4] Areas and Lengths in Polar Coordinates
[10.6] Conic Sections in Polar Coordinates |
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