課程資訊

Calculus (general Mathematics) (a)(1)

106-1

MATH1201

201 101A1

09

4.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1061MATH1201_09

The course will cover the following topics.
1. Functions and Models
2. Limits and Derivatives
3. Differentiation Rule
4. Applications of Differentiation
5. Integrals
6. Applications of Integration
7. Techniques of Integration
8. Differential Equations
9. Parametric Equations and Polar Coordinates

After completing this course, students should be well versed in the mathematical language needed for applying the concepts of calculus to numerous applications in science and engineering. They should also be well prepared for courses in differential equations, linear algebra, or advanced calculus.

Students should be skilled in high school math.
Students should attend and participate actively in lectures as well as discussion sections.
Office Hours

Textbook: James Stewart, Calculus Early Transcendentals, 8th edition.

數學知識網站: http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal
免費線上數學繪圖軟體 Desmos Calculator: https://www.desmos.com/calculator

(僅供參考)

 No. 項目 百分比 說明 1. Midterm Exam 35% Nov 4 (Sat) 9:00-11:30 2. Final Exam 35% Jan 6 (Sat) 9:00-11:30 3. Homework and quizzes 30% There will be weekly homework and 6 quizzes (10/6, 10/18, 11/1, 11/22, 12/6, 12/27).

 課程進度
 週次 日期 單元主題 第1週 09/13, 09/15 1.4 Exponential Functions
1.5 Inverse Functions and Logarithms
2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function

2.4 The Precise Definition of a Limit
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes 第3週 09/27, 09/29 2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function
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

3.6 Derivatives of Logarithmic Functions
3.8 Exponential Growth and Decay (も)
3.9 Related Rates 第6週 10/18, 10/20 3.10 Linear Approximations and Differentials
3.11 Hyperbolic Functions (も)
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem

4.4 Indeterminate Forms and L'Hospital's Rule
4.5 Summary of Curve Sketching 第8週 11/01, 11/03 4.7 Optimization Problems
4.9 Antiderivatives

5.2 The Definite Integral (online course)
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
5.5 The Substitution Rule

6.1 Areas Between Curves
6.2 Volume
6.3 Volumes by Cylindrical Shells 第11週 11/22, 11/24 6.5 Average Value of a Function
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution

7.5 Strategy for Integration
7.8 Improper Integrals (online course) 第13週 12/06, 12/08 8.1 Arc Length (online course)
8.2 Area of a Surface of Revolution (online course)

10.2 Calculus with Parametric Curves (online course)
10.3 Polar Coordinates

9.1 Modeling with Differential Equations 第16週 12/27, 12/29 9.3 Separable Equations
9.4 Models for Population Growth