INTRODUCTION TO MULTIVARIABLE CALCULUS


Course Outline / Syllabus


We have 25 classes in total in Spring 2017.

Homework will be assigned through the online WeBWorK system located at https://webwork.math.ust.hk/webwork2/.

FYI: WeBWorK is an open-source Online Homework System for mathematics and science courses.

Please note that students can seek help at Math Support Center (MSC). For more information, please go to MSC webpage.

Here is a poster of Math Support Center.


The Midterm Exam (for ONE HOUR) is scheduled on March 25, 2017 (Saturday).

You will be informed of the time and venue in due course.


Grading Policy: 10% Homework + 30% Midterm Exam + 60% Final Exam.



Teaching Schedule


Class 1 - 3
Topic 1. Parametric and Polar Curves

1.1 Parametric equations
1.2 Polar coordinates
1.3 Calculus in polar coordinates
Lecture notes: T1-1-3


Class 4 - 10
Topic 2. Vectors and Vector-Valued Functions

2.1 Vectors in the plane
2.2 Vectors in three dimensions
2.3 Dot products
2.4 Cross products
2.5 Lines and curves in space
2.6 Calculus of vector-valued functions
2.7 Motion in space
2.8 Length of curves
2.9 Curvature and normal vectors
Lecture notes: T2-1-2
Lecture notes: T2-3-4
Lecture notes: T2-5-6
Lecture notes: T2-7-8
Lecture notes: T2-9


Class 11 - 17
Topic 3. Functions of Several Variables

3.1 Planes and surfaces
3.2 Graphs and level curves
3.3 Limits and continuity
3.4 Partial derivatives
3.5 The chain rule
3.6 Directional derivatives and the gradient
3.7 Tangent planes and linear approximation
3.8 Maximum/minimum problems
Lecture notes: T3-1
Lecture notes: T3-2
Lecture notes: T3-3
Lecture notes: T3-4
Lecture notes: T3-5
Lecture notes: T3-6
Lecture notes: T3-7
Lecture notes: T3-8


Class 18 - 21
Topic 4. Multiple Integration

4.1 Double integrals over rectangular regions
4.2 Double integrals over general regions
4.3 Double integrals in polar coordinates
4.4 Triple integrals
Lecture notes: T4-1
Lecture notes: T4-2
Lecture notes: T4-3
Lecture notes: T4-4


Class 22 - 25
Topic 5. Vector Calculus

5.1 Vector fields
5.2 Line integrals
5.3 Conservative vector fields
5.4 Green's Theorem
Lecture notes: T5-1
Lecture notes: T5-2
Lecture notes: T5-3
Lecture notes: T5-4