微積分講義 陳隆奇
**版權保留**
本課程配合 952 電子系一年甲班
一.教材與成績:
本 講 義 取 自 :James Stewart: Calculus 5thed,International Student Edition
評分標準:平時考(每週一次,自選十次成績之總和):30%
期中考:30%
期末考:40%.
二.內容 ( 儘可能的按照此內容上課， 但須配合學生的吸收狀況而 稍有更改， 所以會定期的增加或更改教材內容):
§ Improper Integrals.
§ Act Length.
§ Area of Surface of Revolution.
§ Parametric Equations and Polar Coordinates * Curve Defined by Parametric Equations.
* Calculus with Parametric Curves.
* Polar Coordinates.
* Areas and lengths in Polar Coordinates.
§ Infinite Sequence and Series
* Sequences.
* Series.
* The Integral Test and estimates of Sums.
* The comparison Tests.
* Alternating Series.
* Absolute Convergence and the Ratio and Root Tests.
* Power Series.
* Representations of Functions as Power Series.
* Taylor and Maclaurin Series.
* The Binomial Series.
* Applications of Taylor Polynomials.
( 以上為期中考範圍 )
§ Vectors and the Geometry of Space.
* Vectors.
* The Dots Product.
* The cross product.
* Equations of Lines and Planes.
§ Vector Function
* Vector Functions and Space Curve.
* Derivatives and Integrals of Vector Functions.
§ Partial Derivatives
* Functions of several variables, limits and Continuity.
* Partial Derivatives.
* Tangent Planes and Linear Approximations.
* The Chain Rule
* Directional Derivatives and the Gradient Vector
* Maximum and Minimum values
* Lagrange Multipliers.
§ Multiple Integrals
* Double Integrals over Rectangles.
* Iterated Integrals.
* Double Integrals over General Regions.
* Double Integrals in Polar Coordinates.
* Surface Area.
* Triple Integrals in Cylindrical and Spherical Coordinates.
§ Vector Calculus
* Vector Fields.
* Line Integrals.
* The fundamental Theorem for Line integrals.
* Green＇s Theorem.
* Curl and Divergence.
* Parametric Surfaces and Their Areas.
* Surface Integrals.
* Stokes＇ Theorem.
* The divergence Theorem.
註: 黑字為一定會教到的內容, 紅字為希望能教到的內容.
