# 播放清單 (請按影片的右上角選取)
source: nctuocw Last updated on 2015年3月24日
本課程是由交通大學應用數學系提供。
授課教師：應用數學系 莊重教授
課程資訊：http://ocw.nctu.edu.tw/course_detail....
授權條款：Creative Commons BY-NC-SA 3.0
更多課程歡迎瀏覽交大開放式課程網站：http://ocw.nctu.edu.tw/
本課程除了微分積分之方法與計算之外，學習重點在於基本數學觀念的理解。例如中間值定理、平均值定理、極值定理等。這些定理不僅本身有其基本應用的價值，背後也有它們數學的涵義與想法。瞭解這些想法，一方面可以推廣這些定理，另一方面當我們面臨更複雜的問題時，解決問題初步的試探可以以這些基本數學想法做為基礎或做為類比。這是數學做為一種科學思考的價值。
Lec01 莊重老師真心告白 4:03
Lec02 課程介紹 9:19
Lec03 1.5~1.6 50:29
Lec04 2.2~2.3 1:10:13
Lec05 2.4 The Precise Definition of a Limit 13:55
Lec06 2.5 Continuity 37:17
Lec07 2.6 Limits at Infinity; Horizontal Asymptotes 18:12
Lec08 2.7 Derivatives and Rates of Change 27:02
Lec09 2.8 The Derivative as a Function 24:03
Lec10 3.1 Derivatives of Polynomials and Exponential Functions 27:30
Lec11 3.2 The Product and Quotient Rules 16:00
Lec12 3.3 Derivatives of Trigonometric Functions 25:38
Lec13 3.4 The Chain Rule 57:58
Lec14 3.5 Implicit Differentiation 41:30
Lec15 3.6 Derivatives of Logarithmic Functions 19:43
Lec16 3.9 Related Rates 29:03
Lec17 3.10 Linear Approximations and Differentials 30:55
Lec18 4.1 Maximum and Minimum Values 19:19
Lec19 4.2 The Mean Value Theorem 20:57
Lec20 4.3~4.5 38:11
Lec21 4.4 Indeterminate Forms and L’Hospital’s Rule 33:07
Lec22 4.7 Optimization Problems 50:23
Lec23 4.9 Antiderivatives 9:42
Lec24 5.1 Areas and Distances 28:12
Lec25 5.2 The Definite Integral 34:26
Lec26 5.3 The Fundamental Theorem of Calculus 47:37
Lec27 5.4 Indefinite Integrals and the Net Change Theorem 25:37
Lec28 5.5 The Substitution Rule 48:47
Lec29 6.1 Areas between Curves 16:39
Lec30 6.2~6.3 45:26
Lec31 6.5 Average Value of a Function 11:34
Lec32 7.1 Integration by Parts 27:26
Lec33 7.2 Trigonometric Integrals 23:43
Lec34 7.3 Trigonometric Substitution 29:11
Lec35 7.4 Integration of Rational Functions by Partial Fractions 31:05
Lec36 7.7 Approximate Integration 31:06
Lec37 7.8 Improper Integrals 39:32
Lec38 8.1 Arc Length 36:50
Lec39 8.2 Area of a Surface of Revolution 33:39
Lec40 8.5 Probability 41:17
Lec41 10.1 Curves Defined by Parametric Equations 7:22
Lec42 10.2 Calculus with Parametric Curves 14:00
