微積分及演習

臺北科技大學 114-2 學期課程，課號 355573。

課程大綱

本課程希望在一學年中，能使學生對微分及積分有充分的瞭解、培養邏輯推理、啟發思考創造、強化計算演繹並注重應用與作圖，以建立同學未來學習工程數學及相關專業課程之數學基礎，充分達到學以致用的目的。課程內容包括：1.極限與連續，2.導數及其應用，3.不定積分與定積分，4.超越函數及其反函數，5.積分法則，6.不定型與瑕積分，7.定積分的應用，8.空間幾何與向量微積分，9.偏導數，10.重積分。

課程進度

第 1 週 7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 7.4 Integration of Rational Functions by Partial Fractions 第 2 週 7.5 Strategy for Integration 7.6 Approximate Integration 7.7 Improper Integrals 第 3 週 9.1 Curves Defined by Parametric Equations 9.2 Calculus with Parametric Curves 9.3 Polar Coordinates 第 4 週 9.4 Calculus in Polar Coordinates 9.5 Conic Sections 9.6 Conic Sections in Polar Coordinates 第 5 週 10.1 Sequences 10.2 Series 10.3 The Integral Test and Estimates of Sums 第 6 週 10.4 The Comparison Tests 10.5 Alternating Series and Absolute Convergence 第 7 週 10.6 The Ratio and Root Tests 10.7 Strategy for Testing Series 第 8 週 10.8 Power Series 10.9 Representations of Functions as Power Series 10.10 Taylor and Maclaurin Series 第 9 週 期中考 第 10 週 9.1 Plane Curves and Parametric Equations 9.2 Parametric Equations and Calculus 9.3 Polar Coordinates and Polar Graphs 9.4 Area and Arc Length in Polar Coordinates 第 11 週 10.8 Power Series 10.9 Representations of Functions as Power Series 10.10 Taylor and Maclaurin Series 第 12 週 12.1 Functions of Several Variables 12.2 Limits and Continuity 12.3 Partial Derivatives 第 13 週 12.4 Tangent Planes and Linear Approximations 12.5 The Chain Rule 12.6 Directional Derivatives and the Gradient Vector 第 14 週 12.7 Maximum and Minimum Values 12.8 Lagrange Multipliers 13.1 Double Integrals over Rectangles 第 15 週 13.2 Double Integrals over General Regions 13.3 Double Integrals in Polar Coordinates 第 16 週 13.5 Triple Integrals 第 17 週 13.6 Triple Integrals in Cylindrical Coordinates 13.7 Triple Integrals in Spherical Coordinates 第 18 週 期末考

評量方式

期中考 30% 期末考 30% 平時成績 40% (含作業、小考、課堂表現) 選課前可先參考上學期上課規定 https://docs.google.com/document/d/17QuuEF8P_Du8xu1PI1eXsNsbmglpIaJD3CBv_jc7i3M/edit?usp=sharing

教材

【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】 使用外文原文書：是 Essential Calculus Metric Version Early Transcendentals (custom solution, 2e) Stewart Reference: Thomas' Calculus, thirteen edition in SI units (global edition), by Thomas, Weir, Hass