Calculus (1)

微積分一

授課教師: 李宗儒 Tsung-Ju Lee
學分數: 3
上課時間: 星期一 9:10am - 11:00am, 星期三 9:10am - 10:00am
實習課時間: 星期三 8:10am - 9:00am
上課地點: 經緯廳
課程網站: Moodle

先修課程或先備能力：高中數學

重要公告與注意事項：

  • 評分方式：期中考 35%、期末考 35%、小考 30%
  • 小考預計共 12 次，取 9 次最高分的平均作為小考成績
  • 預定 2023/11/20 舉行期中考、2024/1/3 舉行期末考
  • 每週都會有指定作業，約 8-12 題，無須繳交


預計課程內容與進度：

課程內容
上課日期 章節
預定進度 (＊表示額外補充)
9/4, 9/6 1.1 - 1.3 Introduction; functions, trigonometric functions.
9/11, 9/13 1.4 - 1.5,
2.2, 2.4 		Exponential functions; inverse functions; logarithmic functions; limits of a function; the precise definition of a limit.
9/18, 9/20 2.3, 2.5 Evaluate limits using the limit laws; continuity.
9/25, 9/27 2.6 - 2.8, 3.1 limits at Infinity; horizontal asymptotes; derivatives and rates of change; derivative as a function; derivatives of polynomials and exponential functions.
10/2, 10/4 3.2 - 3.4 The product and quotient rules; derivatives of trigonometric functions; the chain rule.
10/9 (停課), 10/11 3.5 Implicit differentiation.
10/16, 10/18 3.6, 4.1 Derivatives of logarithmic functions; inverse trigonometric functions and their derivatives; maximum and minimum values.
10/23, 10/25 4.2, 4.4 The mean value theorem; indeterminate forms and l'Hospital's rule.
10/30,
11/1 (停課)		 4.3, 4.5 How derivatives affect the shape of a graph; summary of curve sketching.
11/6, 11/8 4.9, 5.1, 5.2 Antiderivatives; areas and distances; the definite integral.
11/13, 11/15 5.3 - 5.4 The fundamental theorem of Calculus; indefinite integrals and the net change theorem.
11/20 (Midterm), 11/22 (停課)
11/27, 11/29 5.5, 7.1 Substitution; integration by parts.
12/4, 12/6 7.2 - 7.4 trigonometric integrals; trigonometric substitution; integration of rational functions by partial fractions.
12/11, 12/13 6.1 - 6.2,
8.1 - 8.2 		Applications of integrations: areas, volumes.
12/18, 12/20 6.3, 7.8, 9.1 Arc length, area of a surface of revolution; improper integrals; ＊Laplace transform.
12/25, 12/27 9.3, 9.5 Modeling with differential equations; separable equations; linear equations; ＊second-order differential equations; ＊solving differential equations by Laplace transform.
1/1 (停課),
1/3 (Final)