微積分甲(一)

The purpose of this course is to introduce to our students the basic concepts of Differential Calculus and integral Calculus.

高中數學

無備註

Due to the spreading of the Covid 19, we will temporarily conduct the course lecture online. Starting from the week of September 20, I will prepare video-recordings of my own weekly lectures on the morning of Tuesday and the afternoon of Friday. The video-records will then be uploaded to the E-3 System of NYCU by the same day (or the next day if technical computer problem may arise). So, in summary, the recorded lectures will be provided via the E-3 system. During the time in which we are not able to meet in actual classroom, each student should check one's e-mail account frequently. Important updates about the course will be announced frequently during each typical week of the semester. Also, if the situation of the Covid 19 turns better, we may switch our teaching back to classroom meetings. This depends on the changing regulations of the society and the NYCU.

Homework: 10% Mid-Term ONE: 30% Final Exam: 30% 微積分會考: 30% Please note that we expected to have all Exams to be conducted in classrooms on Campus of NYCU, though the course lectures will temporarily be conducted online. Also, the time schedules for all the three exams is listed as below: Mid-Term ONE at November 5, 2021 , Friday, 13:20-15:10 in actual classrooms. Final Exam at January 7, 2022, Friday, 13:20-15:10 in actual classrooms. 微積分會考時間訂於 2022 年 1 月 5 日(三)下午 15:30~17:30 Since we have to separate the class and assign students to several different classrooms during each of the three Exams, the actual classroom-arrangements will be announced later.

• Functions and Models

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

  講授：

  3

• 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

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  7

• 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

• 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 10.3 Polar Coordinates 10.4 Areas in Polar Coordinates

  講授：

  4

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

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