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欢迎光临丁云龙老师教学网页+ V& E! _" _+ s0 b
http://csm01.csu.edu.tw/0166/2007Ting/index.htm5 c' l5 B9 J A) ~5 Z. G3 K, W
1. 此教学课程模拟麻省理工开放式课程, 加入影音讲解, 内容针对初学入门者, 偏重运算, 尤其适合技职体系的同学9 L0 m6 [5 W5 C8 h* _4 P+ Y3 j
2. 这是一个开放式影音课程, 可配合学校教学, 达到预习及复习的效果* S! m3 Z' x" L4 Y6 J- U" I* U
3. 此教学课程以四技大一微积分为主, 高中数学 及国高中衔接课程为辅
% e. h! Z! O- d! A4. 限于人力、时间等因素，此教学网页暂不设置讨论区$ O# z& p* r$ E! I9 ~- k
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CHAPTER 1 LIMITS OF FUNCTIONS: ?) v+ K$ s0 c" B- m; q
Section 1-1 Limits5 F1 ], u2 P6 h8 m- a
Section 1-2 One-Sided Limit
# A; w# i* z/ oSection 1-3 Continuity$ r; |5 B. s! g+ x$ C/ m
Section 1-4 A Limit at Infinity and Infinite Limit; O2 \0 d7 z: ?- a* L. M
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CHAPTER 2 DERIVATIVE; e. W5 v* x( @* A3 K* H
Section 2-1 Definition of Derivative
& Y4 \0 P" O& p( f$ FSection 2-2 The Rule of Differentiation1 }2 \$ v0 B% b5 P" G6 [
Section 2-3 Chain Rule and Implicit Differentiation8 [6 u& Y5 J( x, C( A2 V3 J
Section 2-4 Derivatives of Exponential and Logarithmic F
1 p$ Q# a* x4 g* s- x( B) K5 c1 _; RSection 2-5 Numerical Approximate –Differentials( C1 S" w6 `, H; d
Section 2-6 Derivatives of Trigonometric Functions
! U3 {; {( r. [# V( Q4 jSection 2-7 Derivatives of Inverse Trigonometric F" c6 N& X, p' Y. z
: S; h/ V a4 ?% B: i( YCHAPTER 3 APPLICATIONS OF DERIVATIVES
& m8 ?% j5 \- K8 `. U5 U" mSection 3-1 The Mean Value Theorem and its Applications
K g) z! f* x* Y& r* S# n! \Section 3-2 Increasing and Decreasing Functions! l) d9 @" O; y4 L m+ h
Section 3-3 Maximum and Minimum Values% K) `5 b" A$ c) s
Section 3-4 The Max -Min Problems
& i7 P9 g0 W# M/ \6 y3 ISection 3-5 Concavity and Points of Inflection 4 A& J/ D+ t9 C% w( t9 C ]" _7 R, G' W
Section 3-6 Asymptotes/ M' D4 I& N {$ P9 _0 c8 [
Section 3-7 Sketching curve
. h' E$ S* j6 S7 M, K, {- kSection 3-8 L' Hopital's Rule
) B% e5 w$ U, V' {3 _! }% e, kSection 3-9 Taylor Series4 m" J% d3 m c) N: R
Section 3-10 Applications In Marginal Analysis0 J% ~& u! q4 w% ~6 m; Z! }) e
Section 3-11 Elasticity
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CHAPTER 4 THE INDEFINITE INTEGRALS
( k+ G$ j1 S6 O' d! OSection 4-1 Antiderivative and The Indefinite Integrals. o4 e% i* d! A& Y; U( g+ d$ K: a
Section 4-2 Integration by Changing Variables4 }9 o* a5 k! c0 ~3 F
Section 4-3 Integration by Parts
3 \6 A6 w! J. b$ zSection 4-4 The Trigonometric Integrals
; J( Y4 S$ |- cSection 4-5 The Integration by Partial Fractions# s; ^1 V0 ]+ J4 n) E; m! d
Section 4-6 Trigonometric and Half-Angle Substitution2 a6 V5 m( c" Z3 p" Z5 y! I* o
9 e$ j% O1 b' [' DCHAPTER 5 THE DEFINITE INTEGRALS! [( ^0 I! I" U% J
Section 5-1 Areas and the Definition of Definite Integral
* c( G9 O$ c* s7 W& L/ Q6 bSection 5-2 The Fundamental Theorem of Calculus6 K) f7 K1 Q% l- e0 r" A- @$ b
Section 5-3 The Approximate Integration
0 a: S" E m$ i8 Z5 y2 xSection 5-4 The Improper Integrals
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# x+ L: Z8 F- {- w. Q& J: x8 [CHAPTER 6 APPLICATIONS OF INTEGRATION6 m. P+ a8 Q1 w6 [
Section 6-1 Areas between Curves) A% e$ l! v$ J$ ~0 h, S* F
Section 6-2 Areas in Polar Coordinates
2 s9 w. _: R$ H4 C$ d$ b+ w7 Z4 tSection 6-3 Arc Length, p% W% A: D- p$ F
Section 6-4 Volumes and The Volumes of Revolution8 C0 C h9 I/ O2 ^
Section 6-5 Area of a Surface of Revolution 4 m) _6 O( n4 ]$ ]) S; |3 E
Section 6-6 Centroid of A Plane Region6 q6 A9 Z8 P. L& v3 z/ C
Section 6-7 Work and The Problems of The Engineering
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: \' X# K) b7 KCHAPTER 7 PARTIAL DERIVATIVES
! z) e- ]. Z. R# K. V* s/ LSection 7-1 Limits and Continuity% N+ B: H) O9 A' Z' r) U
Section 7-2 Partial Derivatives( j) j/ l, C) C( U
Section 7-3 The Differentials and Chain Rules. ^. n, i5 j, E
Section 7-4 Extrema of Functions of Two Variables
/ P0 M; {9 I1 ]0 y: I# B! _Section 7-5 Directional Derivatives, Gradient and Tangent Plane, ?3 m/ M8 g5 G, J4 s
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CHAPTER 8 MULTIPLE INTEGRALS) ]$ G8 M$ \& i, ]
Section 8-1 Integrals over a Rectangle, t$ W( U4 u% c t. x: p
Section 8-2 Integrals over a Region
) k7 l6 [1 \ [; V5 Z, `Section 8-3 Three-Dimensional Iterated Integrals% G3 Q% c3 S' L) {, \. H& L
Section 8-4 Multiple Integration in Polar, Cylindrical and Spherical Coordinates1 z' W) X: a" O! x/ Q% a) U
Section 8-5 Applications of Multiple Integrals6 H! e" n3 F& F3 [/ _
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发表于 2008-11-30 02:38:09
very good!
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