National Taiwan Normal University Course Outline
Spring , 2023

@尊重智慧財產權,請同學勿隨意影印教科書 。
Please respect the intellectual property rights, and shall not copy the textbooks arbitrarily.

I.Course information
Serial No. 2635 Course Level Undergraduate
Course Code MAU0181 Chinese Course Name 微積分乙(二)
Course Name Calculus B (II)
Department Department of Mathematics
Two/one semester 1 Req. / Sel. Req.
Credits 3.0 Lecturing hours Lecture hours: 3
Prerequisite Course Prerequisite course: 【MAU0180 Calculus B (I)】
Comment
Course Description
Time / Location Mon. 6-7 Gongguan S3-04, Thur. 6 Gongguan S3-04
Curriculum Goals Corresponding to the Departmental Core Goal
1. Improve understanding of basic concepts of mathematical analysis College:
 1-1 Equipped with professional mathematics competences
 2-1 Being able to communicate and express mathematically
 3-3 Being willing to work collaboratively
2. Improve the ability of logical reasoning and induction College:
 1-2 Being able to reason and induct with mathematical logic
 2-2 Possessing the competences of transferring and contextualizing theories in mathematics and mathematics education
 3-1 Being able to seek out answers with the attitudes of patience, diligence, concentration, and curiosity
3. Improve mathematical and critical thinking skills College:
 1-3 Being able to think mathematically and critically
 1-4 Possessing the abilities to propose and solve questions in advanced mathematics
 1-5 Being able to use mathematics as tools to learn other subjects
 3-2 Possessing the abilities to think independently, criticize, and reflect
 4-3 Possessing a variety of beliefs regarding mathematics values and mathematics learning
4. Enhance professional knowledge and attitude towards truth College:
 1-6 Possessing the capacities to view elementary mathematics from an advanced viewpoint
 2-4 Possessing the competences of lifelong learning
 3-5 Having good taste for mathematics
 4-1 Being knowledgeable and being able to self-develop in the profession
 4-2 Possessing a consistent and firm attitude toward pursuing truths
 4-4 Possessing global views from both scientific and humanistic perspectives, and being able to appreciate the values of other knowledge fields

II. General Syllabus
Instructor(s) Daniel Spector/ 司靈得
Schedule

一、無窮級數
(1) 級數的意義及其斂散性質
(2) 冪級數、Taylor級數、Maclaurin級數

二、向量值函數
(1) 平面曲線、參數方程式
(2) 極坐標、圓柱坐標、球面坐標

三、多變數函數的微分
(1) 多變數函數的極限與連續
(2) 偏導數
(3) 方向導數與梯度 (多變數函數的鏈鎖法則)
(4) 切平面與法平面
(5) 多變數函數的極值 (Lagrange 乘子法、最小平方法)

四、多變數函數的積分
(1) 二重和三重積分的意義與應用
(2) 二重和三重積分的計算   (變數代換法、Fubini定理)
 

Instructional Approach
Methods Notes
Formal lecture 以上課講授為主,並輔以習題研討。
Problem-based learning 每週排定習演和討論時間。
Grading assessment
Methods Percentage Notes
Midterm Exam 40 % 命題形式包括問答題,計算題和証明題。
Final exam 40 % 命題形式包括問答題,計算題和証明題。
other: 20 %  
Required and Recommended Texts/Readings with References

教科書:
1. J. Hass, C. Heil, P. Bogacki, M. Weir , and G. Thomas : University Calculus , early transcendentals

參考書目:
2. R. Larson and B.H. Edward  : Calculus
3. S. Salas, E. Hille, and G. Etgen :  Calculus, one and several variables
4. Stewart, Calculus, early transcendentals
5. G. Thomas, Calculus
 

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