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欢迎光临丁云龙老师教学网页
/ z7 v+ H9 l* P2 j5 Fhttp://csm01.csu.edu.tw/0166/2007Ting/index.htm6 Y a: Y# B6 ~7 g3 G7 j
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' x: o: r& p; T5 R; F. R
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; C8 p' a" n5 {; v1 e3. 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
' Y- f# i' E9 h9 t: C& }4. 限于人力、时间等因素,此教学网页暂不设置讨论区6 g$ m, e' K2 R1 }% m
( N* Q) F* x4 pCHAPTER 1 LIMITS OF FUNCTIONS
3 l4 E, A: v& r- ]& \Section 1-1 Limits( `4 S7 W( L7 k" |- ?" Z7 L
Section 1-2 One-Sided Limit7 r; Q' u1 l' q
Section 1-3 Continuity8 j, N R: c- u4 X
Section 1-4 A Limit at Infinity and Infinite Limit
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2 ^7 m9 f$ o' _+ H. Q: E$ DCHAPTER 2 DERIVATIVE
/ _' N1 p8 Z Y4 g9 ^8 V5 GSection 2-1 Definition of Derivative' v7 T: n9 A0 l/ R% B0 p }
Section 2-2 The Rule of Differentiation
; h1 m/ U8 J$ U lSection 2-3 Chain Rule and Implicit Differentiation/ {/ B( `$ n1 f% P1 Q
Section 2-4 Derivatives of Exponential and Logarithmic F 0 X! J, ^7 g& y; e
Section 2-5 Numerical Approximate –Differentials
% w8 _3 x; S. g& [" Z+ z) k! R& u' oSection 2-6 Derivatives of Trigonometric Functions
$ }1 s. \# W( z7 TSection 2-7 Derivatives of Inverse Trigonometric F0 \2 F; C! R1 U) D
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CHAPTER 3 APPLICATIONS OF DERIVATIVES
- D8 o5 |9 q/ V$ D5 H6 nSection 3-1 The Mean Value Theorem and its Applications
0 v- k4 B2 r8 q/ [: u# `: U) t3 oSection 3-2 Increasing and Decreasing Functions" E. e; F T) X1 u/ p9 G0 b* I
Section 3-3 Maximum and Minimum Values9 G7 y3 R5 s4 b |: \6 \( [
Section 3-4 The Max -Min Problems% j. \- R* T. n& q3 q/ V! G; S
Section 3-5 Concavity and Points of Inflection
+ ^ }" `) _) Y. P. K. K1 E }' m2 ~6 G/ dSection 3-6 Asymptotes
* i: Y5 X$ U2 d! B' i& QSection 3-7 Sketching curve, e. V! ?* t% R( N
Section 3-8 L' Hopital's Rule
4 v8 C; a A) ~* N" V1 ]Section 3-9 Taylor Series* E" W; @4 J6 W& q1 Q# ~$ y
Section 3-10 Applications In Marginal Analysis
* @+ h. Z' Y- S- v# P( ZSection 3-11 Elasticity. W9 g3 o; U3 O% e H# e
7 ]" }8 L5 _5 ?CHAPTER 4 THE INDEFINITE INTEGRALS5 N) y" R% ]+ f5 K$ Q( ~( m& ^
Section 4-1 Antiderivative and The Indefinite Integrals, ]: P% L2 ^$ r: k+ }( f) r
Section 4-2 Integration by Changing Variables* L8 R0 }7 G% [) y& ?2 r
Section 4-3 Integration by Parts
0 K! N7 W1 }. wSection 4-4 The Trigonometric Integrals
9 h5 P( S" B: |- {2 R6 V* vSection 4-5 The Integration by Partial Fractions) z$ x- ?' |4 Q, ~, h" `8 s
Section 4-6 Trigonometric and Half-Angle Substitution3 o3 i, p9 ^6 W5 ]# |
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CHAPTER 5 THE DEFINITE INTEGRALS8 r' v. R) `, \: \: l2 R
Section 5-1 Areas and the Definition of Definite Integral' b; q* c+ p3 P4 L' g; `
Section 5-2 The Fundamental Theorem of Calculus
7 Z. b5 b) D f, @8 q. n7 K: YSection 5-3 The Approximate Integration- \" ` N& C1 u* o% L% k: f
Section 5-4 The Improper Integrals 1 y" Z, u# T( u" S7 b+ k
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CHAPTER 6 APPLICATIONS OF INTEGRATION
" R5 ]8 A8 H* O$ }Section 6-1 Areas between Curves
' E" y) L$ E: @7 V& F+ L& |! jSection 6-2 Areas in Polar Coordinates+ v! f0 I: n( f. G
Section 6-3 Arc Length4 J( \( F/ y1 o- W6 K
Section 6-4 Volumes and The Volumes of Revolution
8 e/ a$ D6 f: Y' K8 f; q& h: ?2 USection 6-5 Area of a Surface of Revolution
5 F( d- @8 e, ?$ u' t) Q8 R' ]Section 6-6 Centroid of A Plane Region# t7 b9 D' z8 x8 ]6 N
Section 6-7 Work and The Problems of The Engineering
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CHAPTER 7 PARTIAL DERIVATIVES
* l$ ` r1 N; b b8 WSection 7-1 Limits and Continuity' a) b% V, E# J" _/ r& @: h
Section 7-2 Partial Derivatives W/ X0 g1 W4 T% T2 [
Section 7-3 The Differentials and Chain Rules* F! f3 n/ Q& D
Section 7-4 Extrema of Functions of Two Variables* d) B3 M& p. T: ~3 G
Section 7-5 Directional Derivatives, Gradient and Tangent Plane+ U$ T- n8 f: x! E0 d5 O2 L" P$ y8 J
; z, `4 ^2 q; F+ K+ {& rCHAPTER 8 MULTIPLE INTEGRALS5 X* W ]5 t) ]
Section 8-1 Integrals over a Rectangle4 s0 C7 f" ~ i! Q' x
Section 8-2 Integrals over a Region
3 j0 ^0 Y1 {' Y, G( oSection 8-3 Three-Dimensional Iterated Integrals( o1 u' x: z% c7 `( v
Section 8-4 Multiple Integration in Polar, Cylindrical and Spherical Coordinates
' j, D. k( m% O x5 DSection 8-5 Applications of Multiple Integrals2 K+ Q9 z1 f& a- ^8 B; y& B
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