教學大綱與進度

課程基本資料：

學年期	課號	課程名稱	階段	學分	時數	修	教師	班級	人	撤	備註
111-1	305760	微積分	1	3.0	3	▲	林尚文	材資一乙	54	1	◎

教學大綱與進度：

教師姓名	林尚文
Email	shangwen5435@gmail.com
最後更新時間	2022-09-12 12:11:52
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，11.級數。 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, 11.Infinite Series.
課程進度	W1 1.1 Four Ways to Represent a Function 1.2 Mathematical Models: A Catalog of Essential Functions 1.3 New Functions from Old Functions W2 1.4 Exponential Functions 1.5 Inverse Functions and Logarithms 2.1 The Tangent and Velocity Problems W3 2.2 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws 2.4 The Precise Definition of a Limit W4 2.5 Continuity 2.6 Limits at Infinity; Horizontal Asymptotes 2.7 Derivatives and Rates of Change W5 2.8 The Derivative as a Function 3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions W6 3.4 The Chain Rule 3.5 Implicit Differentiation 3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions 3.7 Rates of Change in the Natural and Social Sciences W7 3.8 Exponential Growth and Decay 3.9 Related Rates 3.10 Linear Approximations and Differentials 3.11 Hyperbolic Functions W8 4.1 Maximum and Minimum Values 4.2 The Mean Value Theorem 4.3 What Derivatives Tell Us about the Shape of a Graph 4.4 Indeterminate Forms and l’Hospital’s Rule 4.5 Summary of Curve Sketching 4.6 Optimization Problems W9 Midterm W10 4.6 Optimization Problems 4.7 Newton’s Method W11 4.8 Antiderivatives 5.1 The Area and Distance Problems 5.2 The Definite Integral W12 5.3 The Fundamental Theorem of Calculus 5.4 Indefinite Integrals and the Net Change Theorem W13 5.5 The Substitution Rule 6.1 Areas Between Curves W14 6.2 Volumes 6.3 Volumes by Cylindrical Shells W15 6.5 Average Value of a Function 7.1 Integration by Parts 7.2 Trigonometric Integrals W16 7.3 Trigonometric Substitution 7.4 Integration of Rational Functions by Partial Fractions 7.5 Strategy for Integration W17 7.6 Approximate Integration 7.7 Improper Integrals W18 Final
評量方式與標準	期中考 30% 期末考 30% 平時成績 40% (含作業、小考、課堂表現)
使用教材、參考書目或其他	【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)
課程諮詢管道	1.MS Teams 中可發訊息給老師 2.電子郵件：shangwen5435@gmail.com
備註	因應疫情遠距上課方式： 1.每次上課會以Teams直播並錄影，每節課發起一次會議，標題為“日期_節次”，比方說“0705_1”，請同學加入正確的會議。 2.課前會將課程投影片上傳到Teams(檔案→課程投影片)，同學可以自行下載(但避在Teams中開啟並更改檔案)。 3.課堂中主要討論投影片內容，並適時在投影片上畫重點或是補充計算過程，課後會另外把包含筆跡的投影片上傳到Teams(檔案→課程投影片(筆跡))。 4.課堂中會有課堂問題─MS快速表單讓同學填答，或是將計算過程拍照上傳。規定時間內完成可獲的平時積分。 團隊連結： https://teams.microsoft.com/l/team/19%3ai6wZEdh5WseqgNvF6ESeXMRTtGzWHJDKJ4YqaBC9bLQ1%40thread.tacv2/conversations?groupId=07d6d0fc-038f-4454-bda3-482fe2ba59fe&tenantId=dfb5e216-2b8a-4b32-b1cb-e786a1095218 團隊代碼： qnvv0tj