查詢教學大綱與進度

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

113-3 353109 微積分 1 3.0 3 ▲ 林尚文大學部重補修 34 0 上學期C班

學年期	課號	課程名稱	階段	學分	時數	修	教師	班級	人	撤	備註
113-3	353109	微積分	1	3.0	3	▲	林尚文	大學部重補修	34	0	上學期C班

教學大綱與進度：

教師姓名林尚文

Email shangwen5435@gmail.com

最後更新時間 2025-06-21 16:30:17

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 1 6/23 Overview 1.1 Four Ways to Represent a Function. 1.2 Mathematical Models: A Catalog of Essential Functions. 1.4 The Tangent and Velocity Problems. 2 6/25 1.5 The Limit of a Function. 1.6 Calculating Limits Using the Limit Laws. 1.7 The Precise Definition of a Limit. 1.8 Continuity 3 6/26 2.1 Derivatives and Rates of Change 2.2 The Derivative as a Function. 2.3 Differentiation Formulas. 4 6/30 2.4 Derivatives of Trigonometric Functions. 2.5 The Chain Rule. 2.6 Implicit Differentiation 5 7/1 2.7 Related Rates. 2.8 Linear Approximations and Differentials. 3.1 Maximum and Minimum Values. 3.2 The Mean Value Theorem. 6 7/2 3.3 How Derivatives Affect the Shape of a Graph. 3.4 Limits at Infinity; Horizontal Asymptotes. 3.5 Summary of Curve Sketching. 3.6 Optimization Problems. 7 7/3 3.7 Newton’s Method. 3.8 Antiderivatives. Review 8 7/8 期中考 9 7/9 4.1 Areas and Distances. 4.2 The Definite Integral. 4.3 The Fundamental Theorem of Calculus 4.4 Indefinite Integrals and the Net Change Theorem. 10 7/10 4.5 The Substitution Rule. 5.1 Areas Between Curves. 5.2 Volumes. 5.3 Volumes by Cylindrical Shells. 5.4 Work 5.5 Average Value of a Function. 11 7/15 6.1 Inverse Functions. 6.2 The Natural Logarithmic Function 6.3 The Natural Exponential Function. 6.4 General Logarithmic and Exponential Functions. 12 7/16 6.5 Exponential Growth and Decay. 6.6 Inverse Trigonometric Functions. 6.7 Indeterminate Forms and l’Hospital’s Rule. 13 7/17 7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonoetric Substitutions 14 7/21 期末考

評量方式與標準期中考 30% 期末考 30% 平時成績 40% (含數學會考、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

課程對應SDGs指標 SDG4：優質教育（Quality Education）
SDG17：夥伴關係（Partnerships for the Goals）

課程是否導入AI AI2：鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools）

備註

教師姓名	林尚文
Email	shangwen5435@gmail.com
最後更新時間	2025-06-21 16:30:17
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	1 6/23 Overview 1.1 Four Ways to Represent a Function. 1.2 Mathematical Models: A Catalog of Essential Functions. 1.4 The Tangent and Velocity Problems. 2 6/25 1.5 The Limit of a Function. 1.6 Calculating Limits Using the Limit Laws. 1.7 The Precise Definition of a Limit. 1.8 Continuity 3 6/26 2.1 Derivatives and Rates of Change 2.2 The Derivative as a Function. 2.3 Differentiation Formulas. 4 6/30 2.4 Derivatives of Trigonometric Functions. 2.5 The Chain Rule. 2.6 Implicit Differentiation 5 7/1 2.7 Related Rates. 2.8 Linear Approximations and Differentials. 3.1 Maximum and Minimum Values. 3.2 The Mean Value Theorem. 6 7/2 3.3 How Derivatives Affect the Shape of a Graph. 3.4 Limits at Infinity; Horizontal Asymptotes. 3.5 Summary of Curve Sketching. 3.6 Optimization Problems. 7 7/3 3.7 Newton’s Method. 3.8 Antiderivatives. Review 8 7/8 期中考 9 7/9 4.1 Areas and Distances. 4.2 The Definite Integral. 4.3 The Fundamental Theorem of Calculus 4.4 Indefinite Integrals and the Net Change Theorem. 10 7/10 4.5 The Substitution Rule. 5.1 Areas Between Curves. 5.2 Volumes. 5.3 Volumes by Cylindrical Shells. 5.4 Work 5.5 Average Value of a Function. 11 7/15 6.1 Inverse Functions. 6.2 The Natural Logarithmic Function 6.3 The Natural Exponential Function. 6.4 General Logarithmic and Exponential Functions. 12 7/16 6.5 Exponential Growth and Decay. 6.6 Inverse Trigonometric Functions. 6.7 Indeterminate Forms and l’Hospital’s Rule. 13 7/17 7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonoetric Substitutions 14 7/21 期末考
評量方式與標準	期中考 30% 期末考 30% 平時成績 40% (含數學會考、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
課程對應SDGs指標	SDG4：優質教育（Quality Education） SDG17：夥伴關係（Partnerships for the Goals）
課程是否導入AI	AI2：鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools）
備註