INTRODUCTION TO MULTIVARIABLE CALCULUS |
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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.

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

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

Topic 1. Parametric and Polar Curves

1.2 Polar coordinates

1.3 Calculus in polar coordinates

Lecture notes: T1-1-3

Topic 2. Vectors and Vector-Valued Functions

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

Topic 3. Functions of Several Variables

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

Topic 4. Multiple Integration

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

Topic 5. Vector Calculus

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