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欢迎光临丁云龙老师教学网页
- p+ C9 C7 r% `9 U chttp://csm01.csu.edu.tw/0166/2007Ting/index.htm
9 e: n# d! i6 ^; t3 b: ^0 }! j1. 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 d6 ^; f! y% u2 z8 y
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' c: \5 F$ K3. 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
& d1 p9 ~, _3 a1 T# F4. 限于人力、时间等因素，此教学网页暂不设置讨论区8 F# P) g; @' d4 c2 a8 q, w1 l
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CHAPTER 1 LIMITS OF FUNCTIONS
# S) A( l; x9 J3 L5 M. vSection 1-1 Limits
: [; V$ H2 _ f+ s- y9 j% MSection 1-2 One-Sided Limit
2 F( _" `4 e8 H5 NSection 1-3 Continuity E* b1 U3 P; \
Section 1-4 A Limit at Infinity and Infinite Limit
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CHAPTER 2 DERIVATIVE
5 Y$ b) {" I, E# i5 T! NSection 2-1 Definition of Derivative% @# T4 \. S! {' U/ _
Section 2-2 The Rule of Differentiation9 A5 u; X9 A" V! M- w
Section 2-3 Chain Rule and Implicit Differentiation
; B0 f/ G, M0 P2 |4 y' a, kSection 2-4 Derivatives of Exponential and Logarithmic F
5 y$ e. P' W4 _" z$ cSection 2-5 Numerical Approximate –Differentials
$ q7 c7 z v+ d ~" x- cSection 2-6 Derivatives of Trigonometric Functions6 b$ }1 Z3 ~* l$ k
Section 2-7 Derivatives of Inverse Trigonometric F
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# n; N, [" d y' h6 ~CHAPTER 3 APPLICATIONS OF DERIVATIVES
8 x c' A) P( Q% q' FSection 3-1 The Mean Value Theorem and its Applications! L- h- ~( ^$ Q
Section 3-2 Increasing and Decreasing Functions
6 g8 n" p$ n$ l" W& a! o5 r! m. xSection 3-3 Maximum and Minimum Values
- X8 S& \: |( ?Section 3-4 The Max -Min Problems
8 n8 y$ J c5 }$ y$ R7 E( [Section 3-5 Concavity and Points of Inflection
h% q$ i9 Z$ U: jSection 3-6 Asymptotes4 d+ }/ t; q( N/ E0 [
Section 3-7 Sketching curve
) U" O# P3 ^: A" VSection 3-8 L' Hopital's Rule
7 Q( J2 A1 _$ A, {4 Z: lSection 3-9 Taylor Series1 x3 W4 B. Y4 q% B9 @( \' \% \
Section 3-10 Applications In Marginal Analysis# {$ u. K2 ]( r6 j; V8 B
Section 3-11 Elasticity* m' b% u) y A8 v5 O2 _
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CHAPTER 4 THE INDEFINITE INTEGRALS
: u8 V: c" X( i3 z+ f0 fSection 4-1 Antiderivative and The Indefinite Integrals6 h9 l. f+ U# G7 K. O
Section 4-2 Integration by Changing Variables
2 \& V# @' C4 n$ f0 ?7 nSection 4-3 Integration by Parts
[% A5 B1 a; P$ {) k6 M' USection 4-4 The Trigonometric Integrals
8 e& k& ~' ~* i# @: x' QSection 4-5 The Integration by Partial Fractions) |; v: s$ R& L$ q$ L% ^% A# M3 v O
Section 4-6 Trigonometric and Half-Angle Substitution% V( `5 `, h/ u7 t" O
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CHAPTER 5 THE DEFINITE INTEGRALS& u) [/ B# ]$ ]. g- s8 Y* `6 ~
Section 5-1 Areas and the Definition of Definite Integral
; }9 `: S7 q4 q4 |# E1 _Section 5-2 The Fundamental Theorem of Calculus
- }+ R7 F( C" k9 H7 O' i9 b! I1 ~Section 5-3 The Approximate Integration8 G/ ~/ t' G1 m; x
Section 5-4 The Improper Integrals 8 }5 [9 Q" I, z# t' t
8 n. `& _( y0 YCHAPTER 6 APPLICATIONS OF INTEGRATION
- Y$ H; F1 w# } B- i# N# qSection 6-1 Areas between Curves6 l/ H- o) X, g3 z' Q9 Z
Section 6-2 Areas in Polar Coordinates% S7 h3 K. s3 O/ Z
Section 6-3 Arc Length; Q* d7 H$ E4 s
Section 6-4 Volumes and The Volumes of Revolution
( q+ D' y- M! ]Section 6-5 Area of a Surface of Revolution
+ E. B# z/ Q# i6 z1 ZSection 6-6 Centroid of A Plane Region! h2 x4 Q4 `% S% L4 j' e' k8 X: v+ Y
Section 6-7 Work and The Problems of The Engineering2 z* l8 J2 o, ?' U0 Z% b9 n
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CHAPTER 7 PARTIAL DERIVATIVES
5 w1 k5 u7 R* o, l l _Section 7-1 Limits and Continuity
9 C9 K) T# Z- ?" o% }Section 7-2 Partial Derivatives
3 p* M1 e6 ^ k' s* G" K, C% p* P9 ySection 7-3 The Differentials and Chain Rules0 `# J) `; s1 t$ c
Section 7-4 Extrema of Functions of Two Variables* f, K: \, q1 I
Section 7-5 Directional Derivatives, Gradient and Tangent Plane
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CHAPTER 8 MULTIPLE INTEGRALS
6 G5 [; f. a/ f- x4 o0 eSection 8-1 Integrals over a Rectangle; p2 g1 I1 o$ b- g' S
Section 8-2 Integrals over a Region
0 V8 Y- Y( ]1 i( }/ B! {9 h* dSection 8-3 Three-Dimensional Iterated Integrals
6 Y. [, l" K: o' w# |Section 8-4 Multiple Integration in Polar, Cylindrical and Spherical Coordinates6 c% o4 j9 I- ?& m* q/ v3 p! G
Section 8-5 Applications of Multiple Integrals
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发表于 2008-11-30 02:38:09
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