微積分

臺北科技大學 115-1 學期課程，課號 362975。

課程大綱

Course Description This course aims to provide students with a solid understanding of differential and integral calculus. It is designed to cultivate logical reasoning, inspire creative thinking, strengthen computational and deductive skills, and emphasize practical applications and graphing techniques. The goal is to build a strong mathematical foundation for future studies in engineering mathematics and related professional courses, ultimately achieving the objective of applying what is learned in real-world contexts. Course topics include: 1. Limits and Continuity 2. Derivatives and Their Applications 3. Indefinite and Definite Integrals 4. Transcendental Functions and Their Inverses 5. Integration Techniques 6. Indeterminate Forms and Improper Integrals 7. Applications of Definite Integrals 8. Solid Geometry and Vector Calculus 9. Partial Derivatives 10. Multiple Integrals 11. Series 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

Week 1 Definition of Functions and Limits Week 2 Techniques for Finding Limits and Infinite Limits Week 3 Continuity of Functions Week 4 Definition and Computation of Derivatives Week 5 Chain Rule Week 6 Implicit Differentiation and Higher-Order Derivatives Week 7 Derivatives of Trigonometric, Inverse Trigonometric Functions, Exponential and Logarithmic Functions Week 8 Extrema of Functions and Mean Value Theorem Week 9 Midterm Exam Week 10 Concavity, Curve Sketching, and Applications of Extrema Week 11 Introduction of Indefinite Integrals Week 12 Integration of Substitution Week 13 Fundamental Theorem of Calculus and Definite Integrals Week 14 Integration Techniques: Integration by Parts Week 15 Integration Techniques: Trigonometric Substitution Integration, Integral of Rational Functions and Partial Fractions Week 16 Final Exam Week 17~18 Flexible Self-Directed Learning

評量方式

Midterm Exam: 25% Final Exam: 25% Mathematics Proficiency Test: 10% Regular Performance: 35% (including class participation, homework, quizzes, etc.) Flexible Self-Directed Learning Project 5% Deductions (There is no limit to point deductions): Tardiness: 1 point per instance (遲到 -1/堂課) Unexcused Absence: 1 point per class session (曠課 -1節)) Sleeping in Class (head down): 2^n points for the nth offense Using Phone/Tablet Without Permission: 2^n points for the nth offense 打瞌睡(或趴著睡覺)或划手機或戴耳機 -2^n/第n次 請假請依學校規定，病假要有相關單據證明。

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: Calculus，2e, Huei-Lin Hong, Cheh-Chih Yeh，高立圖書 Reference: 1. Calculus 5e, James Stewart 2. Calculus, 6e, Larson, Hostetler and Edwards. 3. Calculus, Tan 4. Thomas' Calculus, Thomas, Weir and Hass. 5.微積分, 第四版, 洪揮霖著，高立圖書 6. 微積分， 林晶璟，劉國安編著，新頁圖書