微積分
Calculus
| 節 | 週二 |
|---|---|
7 15:30–16:20 | 微積分 YX216 2 節連堂 |
8 16:30–17:20 |
* 根據陽明交大上課時間表所列
本課程將教導學生學習函數的極限與連續、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。課程內容包含: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。 This course will teach students to learn about the limits and continuity of functions, the differentiation and integration methods of common functions (polynomials, exponentials, logarithms, trigonometric functions), and how to apply differentiation and integration techniques to solve problems that may be encountered in daily life. The course content includes: limits, continuity, trigonometric functions, exponential functions, logarithmic functions, chain rule, implicit differentiation, L’Hopital’s Rule, extrema, derivative functions, definite integrals, and integration techniques.
無 None
本課程第一週在排定之上課教室上課,會簡介本學期課程內容、說明上課方式與成績評定規則,請務必出席。第二週起採"線上上課、課堂考試"的方式進行。每週上課內容請參閱陽明交大E3數位教學平台,課程的各項公告事項也會統一在E3系統中發佈。 The first week of this course will be held in the scheduled classroom. We will introduce the course content for this semester, explain the teaching method and grading rules, so please be sure to attend. Starting from the second week, we will adopt the method of “online classes and in-class exams”. Please refer to the E3 platform for the content of each week’s class. All announcements for the course will also be uniformly released on the E3 system.
筆試測驗3次,每次各佔總成績34%、33%、33%。請務必準時參與考試,缺考者不得以任何理由要求補考。 Three tests, each accounting for 34%, 33%, and 33% of the total grade respectively. Please be sure to participate in the exams on time. Those who miss the exam will not be allowed to request a make-up exam for any reason.
| 週次 | 主題 |
|---|---|
| 第 1 週 | - 課程簡介(Introduction) - 1.1 A Brief Preview of Calculus - 1.2 The Concept of Limit - 1.3 Computation of Limits |
| 第 2 週 | - 1.4 Continuity and Its Consequences - 1.5 Limits Involving Infinity; Asymptotes - 2.1 Tangent Lines and Velocity |
| 第 3 週 | - 中秋節放假 |
| 第 4 週 | - 2.2 The Derivative - 2.3 Computation of Derivatives: The Power Rule - 2.4 The Product and Quotient Rules |
| 第 5 週 | - 2.5 The Chain Rule - 2.6 Derivatives of Trigonometric Functions |
| 第 6 週 | - 測驗一(Test 1) |
| 第 7 週 | - 2.7 Implicit Differentiation - 2.8 The Mean Value Theorem |
| 第 8 週 | - 3.1 Linear Approximations and Newton's Method - 3.2 Maximum and Minimum Values - 3.3 Increasing and Decreasing Functions |
| 第 9 週 | - 3.4 Concavity and the Second Derivative Test - 3.5 Overview of Curve Sketching |
| 第 10 週 | - 3.6 Optimization - 3.7 Related Rates - 4.1 Antiderivatives |
| 第 11 週 | - 測驗二(Test 2) |
| 第 12 週 | - 4.2 Sums and Sigma Notation - 4.3 Area - 4.4 The Definite Integral |
| 第 13 週 | - 4.5 The Fundamental Theorem of Calculus - 4.6 Integration by Substitution - 6.1 The Natural Logarithm |
| 第 14 週 | - 6.2 Inverse Functions - 6.3 The Exponential Functions - 6.4 The Inverse Trigonometric Functions |
| 第 15 週 | - 6.5 The Calculus of the Inverse Trigonometric Functions - 7.1 Review of Formulas and Techniques - 7.2 Integration by Parts |
| 第 16 週 | - 測驗三(Test 3) |
Robert T. Smith & Roland B. Minton, "Calculus," Fourth Editon, ISBN 978-007-132537-0
- 地點
- 陽明交大-陽明校區-生醫工程館411室。
- 時間
- 請事前透過Email或電話向老師約定時間。
- 聯絡方式
- Email: whsung@nycu.edu.tw。 Tel: 67910(校內分機)。