微積分甲(一)

This is the first semester of a one-year calculus course, covering differentiation and integration for functions of a single variable. You will learn how derivatives describe instantaneous rates of change, with applications to slopes, velocity, and optimization problems. You will also learn how antiderivatives and integrals describe the accumulation of small quantities, with applications to area and displacement. Throughout the semester, you will explore the meanings of limits, derivatives, and antiderivatives, and develop the skills needed to compute and apply them effectively.

高中數學 High School Mathematics

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The lecture will be delivered in English. Important announcements will be posted on the course website. https://jupiter.math.nycu.edu.tw/~chlin/2026FGECS10001/2026FGECS10001.html

Quizzes 20% Midterms 25%*2 Joint exam 30%

• 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 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 ◆4.7 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 The Areas and Distance Problems 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

  備註：◆ 為選教內容，不列入微積分會考考試範圍。

• 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

  備註：◆ 為選教內容，不列入微積分會考考試範圍。

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

地點

SA336

時間

Appointments by email

聯絡方式

jephianlin@gmail.com