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課程名稱

微積分(二)實習

Course Name

RECITATION OF CALCULUS (2)

課程敘述

內容包含部分積分法;三角積分, 三角積分;三角代換法, 瑕積分;多變數函數, 多變數函數的極限與連續;偏導數, 偏導數;切平面及線性迫近, 鏈導法則;方向導數及梯度向量, 多變數函數的極大,極小;二重積分, 疊積分;一般區域上的二重積分, 極座標的二重積分;數列, 數列;級數, 積分檢定;比較檢定, 交錯級數;絕對收斂,比值、根值檢定, 冪級數;冪級數函數展開式, 泰勒級數,馬克勞林級數。

Course Description

Topics include the Integration by Parts, Trigonometric Integrals, Trigonometric Substitution, Improper Integrals, Functions of Several Variables, Limits and Continuity, Partial Derivatives, Tangent Planes and Linear Approximations, The Chain Rule, Directional Derivative and Gradient Vector, Maximum and Minimum Values, Double Integrals over Rectangles, Iterated Integrals, Double Integrals Over General Regions, Double Integrals in Polar Coordinates, Triple Integrals, Triple Integrals, Change Variables in Double Integrals, Sequences, Series, Series, The Comparison, Alternating Series, Absolute Convergence and the Ratio and Root Tests, Power Series, Representations of Functions as Power Series, Taylor and Maclaurin Series.