微積分
Calculus
| 節 | 週二 |
|---|---|
7 15:30–16:20 | 微積分 YX216（陽明） 2 節連堂 |
8 16:30–17:20 |
* 根據陽明交大上課時間表所列
極限、連續、三角函數、指數函數、對數函數、連鎖律、隱微分、L'Hopital's Rule、極值、導函數、定積分、積分技巧。Limit, Continuity, Trigonometric Function, Exponential Function, Logarithmic Functions, The chain rule, Implicit Differentiation, L'Hopital's Rule, Extreme Values, Antiderivatives, Definite Integral, Integration methods.
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教導學生函數的極限與連續、常見函數(多項式、指數、對數、三角函數)之微分與積分方法,以及如何應用微分、積分技巧解決日常生活中可能遭遇的問題。The aim of this course is to teach students the limit and continuity of a function, differentiation and integration of common functions (such as: polynomial, exponential, logarithmic, and trigonometric functions), and how to use the techniques of differentiation and integration to solve the questions and problems in daily living life.
紙筆測驗4次,每次佔總成績25%。請務必準時參與考試,缺考者不得以任何理由要求補考。1.Test 1(25%) 2.Test 2(25%) 3.Test 3(25%) 4.Test 4(25%)
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| 週次 | 主題 |
|---|---|
| 第 1 週 | 新生入學輔導週(不上課) |
| 第 2 週 | 中秋節(放假一天) |
| 第 3 週 | * 課程簡介(Introduction) * The Concept and Computation of Limit |
| 第 4 週 | * Continuity * Limits Involving Infinity* Continuity * Limits Involving Infinity * Derivative |
| 第 5 週 | * Derivative * Power Rule * Product and Quotient Rules* Power Rule * Product and Quotient Rules * Chain Rule |
| 第 6 週 | 測驗一(Test 1) |
| 第 7 週 | * Chain Rule * Derivatives of Trigonometric Functions * Exponential and Logarithmic Functions* Derivatives of Trigonometric Functions * Exponential and Logarithmic Functions |
| 第 8 週 | * Implicit Differentiation * Inverse Trigonometric Functions * Mean Value Theorem |
| 第 9 週 | 測驗二(Test 2) |
| 第 10 週 | * Linear Approximation * Newton''''s Method * Indeterminate Forms * L''''Hopital''''s Rule* Linear Approximation * Newton''s Method * Indeterminate Forms * L''Hopital''s Rule |
| 第 11 週 | * Maximum and Minimum Values * Increasing and Decreasing Functions * Concavity |
| 第 12 週 | * Overview of Curve Sketching * Optimization * Related Rates |
| 第 13 週 | 測驗三(Test 3) |
| 第 14 週 | * Antiderivatives * Definite Integral |
| 第 15 週 | * Fundamental Theorem of Calculus * Integration by Substitution |
| 第 16 週 | * Integration by Parts * Trigonometric Techniques of Integration |
| 第 17 週 | 測驗四(Test 4) |
| 第 18 週 | 彈性補充教學 - 成績查詢 & 問題討論 |
Robert T. Smith & Roland B. Minton, "Calculus," Fourth Editon, ISBN 978-0-07-131656-9.
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