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

 

T2B: Wed 03:30PM-04:20PM, Rm 2302 (Lift 17-18)

 

 

 

 

 

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

 
  1. The grading is based on studentsŐ performance in assessment tasks.

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