Course title |
微積分甲下 Calculus (general Mathematics) (a)(2) |
Semester |
108-2 |
Designated for |
DEPARTMENT OF BIOMEDICAL ENGINEERING |
Instructor |
蔡國榮 |
Curriculum Number |
MATH1202 |
Curriculum Identity Number |
201E101A2 |
Class |
05 |
Credits |
4.0 |
Full/Half Yr. |
Full |
Required/ Elective |
Required |
Time |
Wednesday 8,9,10(15:30~18:20) Friday 1,2(8:10~10:00) |
Room |
新202 |
Remarks |
本課程以英語授課。統一教學.大二以上限20人.三10為實習課. Restriction: within this department (including students taking minor and dual degree program) The upper limit of the number of students: 110. |
Ceiba Web Server |
http://ceiba.ntu.edu.tw/1082MATH1202_05 |
Course introduction video |
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Table of Core Capabilities and Curriculum Planning |
Table of Core Capabilities and Curriculum Planning |
Course Syllabus
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Please respect the intellectual property rights of others and do not copy any of the course information without permission
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Course Description |
Our main course page would be on NTU COOL.
https://cool.ntu.edu.tw/courses/804
This course will be conducted in English.
As a continuation of the course MATH1201 Calculus A (1), in which Calculus on functions of a single (real) variable is discussed, this course turns to an introduction (and applications) of multivariable (mainly 2- and 3-variable) Calculus, which is the foundation for various disciplines in Science and Engineering.
Topics to be discussed include the definitions of directional, partial derivatives and double, triple, line, surface integrals (together with their geometric meanings), the method of Lagrange Multipliers in resolving extreme-value problems with constraints in mutlivariables, and Green's, Stokes', Divergence Theorem, which can be regarded as multivariable version of the Fundamental Theorem of Calculus.
Finally, to complete the discussion on limits of a function or a (infinite) sum of functions in the course of the study of Calculus, the definitions of limits of sequences and series are also introduced, which provide the theoretical basis of the introduction of a `power series'. `Power series' is a generalisation of polynomials and can be used to represent elementary as well as more general functions, which paves the way for more advanced analysis of functions, necessary in practical applications.
Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides discussion sections in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants. |
Course Objective |
Students would be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. "Calculus A (1) and (2)" provide a basis for studying advanced courses such as Engineering Mathematics, Mathematical Analysis and Differential Equations. |
Course Requirement |
Prerequsites : Calculus A (I), basic trigonometry, vectors, determinants of 2x2 and 3x3 matrices, knowledge in linear algebra will be useful but not necessary |
Student Workload (expected study time outside of class per week) |
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Office Hours |
Mon. 14:00~16:00 |
Designated reading |
Textbook:
James Stewart, Calculus Early Transcendentals, 8th edition.
The course will be supplemented by the instructor's lecture notes.
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References |
J. Marsden, A Tromba, Vector Calculus (4th Edition),
S. Lang, Calculus of Several Variables (3rd Edition)
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Grading |
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Week |
Date |
Topic |
Week 1 |
2/19,2/21 |
Vector Functions |
Week 2 |
2/26,2/28 |
Curves : Arclength and Curvature |
Week 3 |
3/04,3/06 |
Functions of Several Variables I : Partial derivatives and Continuity |
Week 4 |
3/11,3/13 |
Functions of Several Variables II : Linear approximations, Chain rule, Directional derivatives |
Week 5 |
3/18,3/20 |
Lagrange Multipliers |
Week 6 |
3/25,3/27 |
Double Integrals I : Definitions |
Week 7 |
4/01,4/03 |
Reading week |
Week 8 |
4/08,4/10 |
Double Integrals II : Centre of Mass, Moments, Surface Areas |
Week 9 |
4/15,4/17 |
Triple Integrals : Volumes and Change of variable formula |
Week 10 |
4/22,4/24 |
Line Integrals I : Vector fields, FTC |
Week 11 |
4/29,5/01 |
Line Integral II : Green's Theorem |
Week 12 |
5/06,5/08 |
Surface Integrals I : Cuvl and Div |
Week 13 |
5/13,5/15 |
Surface Integrals II : Stokes' and Divergence Theorems |
Week 14 |
5/20,5/22 |
Sequences and Series I : Definitions, Ratio and Root Tests |
Week 15 |
5/27,5/29 |
Sequences and Series II : Integral test, Comparison test, Alternating series test |
Week 16 |
6/03,6/05 |
Power series and Taylor's theorem |
Week 17 |
6/10,6/12 |
Second Order Differential Equations (✽) |
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