微積分甲(一)

This course is basically given in English. Students need to learn the skill of writing and reading mathematical expressions and arguments in English. The goal of this course is to obtain the following abilities, 1. Computational Skills: the accuracy and appropriateness of their use of fundamental calculus techniques, including calculating limits, derivatives, and integrals 2. Logic: the capacity to appropriately link supporting reasons to the main conclusions, demonstrating coherence, relevance, and logical progression in their arguments 3. Application: the capacity to select relevant skills learned in class and apply them effectively to solve problems, supported by logical and appropriate reasoning

高中數學 * If student is a foreign student, the background of mathematics is different from students who passed Taiwanese Entrance Exam for the university. So Please consult us as soon as possible if you are worried about it.

無備註

Lectures will be given using Lecture Slide and Blackboard Explanation in English. Lecture Slide will be uploaded on E3 system at latest one day before the lecture. The details will be provided in the first lecture.

Exams: 期中考 (Midterm Exams) 40%, 微積分會考 (Final Exam) 30% Attitudes: Attendance + Small Weekly Quiz 10% Reports: 20%

• Functions and Models

  ◆1.3 New Functions from Old Functions 1.4 Exponential Functions 1.5 Inverse Functions and Logarithms

  講授：

  3

  備註：◆ 為選教內容,不列入微積分會考考試範圍。

• Limits and Derivatives

  2.2 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws 2.4 The Precise Definition of a Limit 2.5 Continuity 2.6 Limits at Infinity; Horizontal Asymptotes 2.7 Derivatives and Rates of Change 2.8 The Derivative as a Function

  講授：

  8

• Differentiation Rules

  3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions 3.4 The Chain Rule 3.5 Implicit Differentiation 3.6 Derivatives of Logarithmic Functions ◆3.7 Rates of Change in the Natural and Social Sciences ◆3.8 Exponential Growth and Decay ◆3.9 Related Rates 3.10 Linear Approximations and Differentials ◆3.11 Hyperbolic Functions

  講授：

  8

  備註：◆ 為選教內容,不列入微積分會考考試範圍。

• Applications of Differentiation

  4.1 Maximum and Minimum Values 4.2 The Mean Value Theorem 4.3 How Derivatives Affect the Shape of a Graph 4.4 Indeterminate Forms and L’Hospital's Rule 4.5 Summary of Curve Sketching 4.7 Optimization Problems ◆4.8 Newtons Method 4.9 Antiderivatives

  講授：

  7

  備註：◆ 為選教內容,不列入微積分會考考試範圍。

• Integrals

  5.1 Areas and Distances 5.2 The Definite Integral 5.3 The Fundamental Theorem of Calculus 5.4 Indefinite Integrals and the Net Change Theorem 5.5 The Substitution Rule

  講授：

  6

• Applications of Integration

  6.1 Areas Between Curves 6.2 Volumes 6.3 Volumes by Cylindrical Shells 6.5 Average Value of a Function

  講授：

  3

• Techniques of Integration

  7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 7.4 Integration of Rational Functions by Partial Fractions ◆7.5 Strategy for integration ◆7.7 Approximate Integration 7.8 Improper Integrals

  講授：

  7

  備註：◆ 為選教內容,不列入微積分會考考試範圍。

• Further Applications of Integration

  8.1 Arc Length 8.2 Area of a Surface of Revolution ◆8.3 Applications to Physics and Engineering ◆8.4 Applications to Economics and Biology ◆8.5 Probability

  講授：

  3

  備註：◆ 為選教內容,不列入微積分會考考試範圍。

• Parametric Equations and Polar Coordinates

  10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 10.4 Areas in Polar Coordinates

  講授：

  4

Calculus (Early Transcendentals), James Stewart, 9th Edition

地點

SA239

時間

The details for Office Hour will be announced in the first lecture.

聯絡方式

y.chino@math.nctu.edu.tw chino@nycu.edu.tw * The second address is also available but not frequently checked, so the first one would be safer if you need my reply.