微積分

臺北科技大學 115-1 學期課程，課號 362892。

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。 This course aims at developing comprehension of Derivation and Integral、activating capabilities of Logic Inference and Induction、enlightening confidence and independence、strengthening calculating abilities with an emphasis on its application and diagram、furnishing a sound basis for future specialty. The content includes: 1.Limits and Continuity, 2.Derivative and Application, 3.Indefinite and Definite Integral, 4.Transcendental Functions and their Inverses, 5.Techniques of Integration, 6.Indeterminate Forms and Improper Integral, 7.Application of Integration, 8.Basic Vector Analysis, 9.Partial Derivative, 10.Multiple Integration.

課程進度

1st Semester Week 01 Functions and Models Week 02 Limits and Derivatives Week 03-04 Differentiation Rules Week 05-06 Inverse Functions Week 07-08 Applications of Differentiation Week 09-10 Integrals Week 11-12 Fundamental Theorem of Calculus Week 13-14 Techniques of Integration Week 15 Improper Integrals Week 16 Series & Taylor series 2nd Semester Week 01-02 Applications of Integration Week 03-04 Parametric Equations Week 05-06 Polar Coordinates Week 07-08 Vector & the Geometry of Space Week 09-10 Directional Derivatives & Gradient Vector Week 11-12 Partial Derivatives Week 13-14 Double Integrals Week 15-16 Triple Integrals

評量方式

Midterm Exam (around 9th week) 30-35% Final Exam (around 18th week) 30-35% Others (Homework, Exercise in-class & Attendance, etc.) 20-30% Uniform examination: 10%

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 Textbook James Stewart, Essential Calculus (Metric Version) Early Transcendental (2e), Taiwan exclusive, 2022. Reference J. Hass, C. Heil, P. Bogacki, M. D. Weir, G. B. Thomas, University Calculus Early Transcendentals,4e