微積分甲(一)

本課程目標是希望讓剛接觸微積分的學生能了解微積分的基本精神並且知道如何使用微積分到更高等的數學或者其他相關領域。 The goal of this course is to make the freshmen understand the spirit of the calculus.

高中數學 Precalculus

無備註

所有跟此課程有關的公告,將會post在課程網頁 All announcements will be posted on the course webpage. 助教可能會提供各次小考的相關訊息以及解法 TAs might provide answer sheet of quiz.

小考30%:每週一,四上課時小考十分鐘。範圍以回家作業為主。 期中考40%:學期中將會有三次期中考,每次比重皆佔學期成績20%。期末計分方式將捨棄最低分的那一次。 微積分會考30% 附註:本課程沒有回家作業,但是大部分的考題將會從習題以及上課內容出,請同學們抓緊時間做練習並且準備好考試。本課程學期末不調分。 更多訊息請詳見授課教師的課程網頁https://yihsuan_lin.updog.co/Teaching/2019Calculus.html Quiz 30%: Every Monday and Thursday, there will be 10 minutes quiz during the class. The range of the quiz is from the weekly homework assignment. Midterm 40%: There will be 3 midterms. The lowest score will be dropped in the end of semester. Calculus Final Exam 30%. PS: There is no homework of this course. The problems of quiz and midterms will be considered from the context of the class and the assigned homework. For further information, we refer students to https://yihsuan_lin.updog.co/Teaching/2019Calculus.html

• Functions and Models

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

  講授：

  4

• 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

• 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：

  8

• 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

• 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

• Parametric Equations and Polar Coordinates

  10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves

  講授：

  3

Calculus (Early Transcendentals), James Stewart, 8th Edition

地點

Instructor's office is at SA228. TAs' office is TBA.

時間

林奕亘老師的會談時間於每週二上午10am-12pm,或者是使用email預約會唔時間 The instructor's (Yi-Hsuan Lin) office hours are arranged during 10am-12pm, every Tuesday. 助教的會談時間還未決定 The office hours of TAs are TBA.

聯絡方式

Refer the course webpage