Math2013-L2
Multivariable Calculus
Course
Outline-Fall 2018
1.
Instructor
Name: Prof. Hai
Zhang
Contact
Details:
Office: Room
3442 Email:
haizhang@ust.hk
Office hour:
Tue Thu 9AM-10AM or by just stop by.
2.
Teaching Assistant
Name: Mr. Ping
Liu
Contact
Office: 3209B
Email: pliuah@connect.ust.hk
3.
Meeting Time
and Venue
Lectures:
Date/Time/Venue:
Tue Thu 12:00PM-01:20PM,
Rm 2502 (Lift 25-26)
Tutorials (by
Ping Liu):
Date/Time/Venue:
T2A: Th 09:30AM-10:20AM,
G009A, CYT Bldg |
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T2B:
Wed 03:30PM-04:20PM, Rm 2302 (Lift 17-18) |
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4.
Course
Description
Credit
Points:
4
Prerequisite: MATH1020 /MATH1014 /MATH1024; or AL Applied Mathematics/Pure Mathematics
Exclusion: Math2010, Math2011, Math2021.
Brief
Information/synopsis:
Differentiation in several variables with discussion on geometry,
maximum & minimum. Integration in several variables with physical
applications and vector analysis
5.
Reference
Major
reference: lecture notes written by Prof. Tsz-Ho Fong
(available on canvas)
Lecture
slides will be posted on canvas after class
Recommended
references:
Chapters
on multivariable of the following textbooks:
1)
Calculus for Scientists and Engineers, by Briggs, Cochran, Gillett
2)
ThomasŐ Calculus, by Thomas, Weir
3)
Calculus: Early Transcendentals, by Stewart
4)
Calculus of Several Variables, by Adams
6.
Intended Learning Outcomes
Upon
successful completion of this course, students should be able to:
No. |
ILOs |
1 |
to demonstrate the understanding and skills
in reading, interpreting and communicating mathematical contents which are
integrated into other disciplines or appear in everyday life; |
2 |
to gain ability to model real-world
situations and to use mathematics to help develop solutions to practical problems; |
3 |
to articulate the understanding of more
advanced mathematical concepts and quantitative skills to support the study
of other disciplines |
4 |
to explain clearly concepts from
multi-variable calculus, e.g. able to compute partial derivatives of
multivariate functions and double integrals |
5 |
to develop mathematical maturity to
undertake higher level studies in mathematics and related fields |
7.
Assessment
Scheme
a.
Examination
duration: Midterm exam 2 hrs; Final exam 3 hrs
b.
Percentage of
coursework, examination, etc.:
Assessment |
|
10% by Webwork |
|
30% by midterm
exam |
|
60% by final
exam |
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8.
Learning
Activities
In mathematics, new concepts continually rely
on the mastery of old ones; it is therefore essential that you thoroughly
understand each new topic before moving on. Our classes are an important
opportunity for you to ask questions; to make sure that you are understanding
concepts correctly. Speak up!! ItŐs your education at stake. Make every effort
to resist the temptation to put off work, and to fall behind. Try to do
mathematics every single day. (I do.) Class attendance is probably your best
way to insure that you will keep up with the material, and make sure that you
understand all of the concepts. I will not be taking attendance; I expect that
you will simply see the wisdom of attending class, for yourselves.
9.
Homework
There are two homework components: WebWork
and Problem Sets. WebWork will be posted on the
website
http://webwork.math.ust.hk/webwork2.
Each WebWork assignment consists of elementary questions to help
students grasp the basic concepts and techniques covered in the lecture. To
avoid lagging behind, students are advised to complete the relevant problems
right after each lecture (DonŐt leave them until a few days before the
deadlines).
Weekly problem
sets, each of which contains about 8-12 problems, will be posted on Canvas.
They will not be collected or graded, and selected solutions will be posted as
soon as they are ready. Students are expected to work seriously on these
problems. In both Midterm and Final Exams, substantial amount of the problems
will be based on them.
10. Exam
The Midterm Exam will be given in around Week 6-8 subject to availability of
rooms. The midterm is different (in both problem set and exam time) from the
one in the Session L1. The Final Exam will take place at the end of the
semester arranged by ARRO. In both exams, HKEAA approved calculators are allowed but they are rarely
needed. A list of formulae prepared by the
instructor will be provided in each exam and this list will also posted at
least one week before each exam. Students are not allowed to bring their own formula
sheets
11. Course Schedule (Tentative)
Week |
Topics |
1 |
vectors, lines, planes, curves in three
dimensional space |
2 |
Functions of several variables, continuity, partial derivatives |
3 |
Chain rule, directional derivative,
gradient |
4 |
Tangent plane, total differential |
5 |
Maxima/minima, Lagrange multiplier |
6 |
Double integrals, rectangular and polar
coordinates |
7 |
Triple integrals, cylindrical and spherical
coordinates, change of variable |
8 |
Vector fields, line integrals, conservation
of vector fields |
9 |
Curl operator, GreenŐs theorem |
10 |
Parametric surfaces, surface integrals |
11 |
Surface flux, Divergence theorem |
12 |
Stokes theorem |
13 |
Flexible week: catch up
class/review/optional material |