Key information


This course is going to be very different from what you have been used to with math classes before. You are expected to do preparation work at home before coming to class. Here’s the break down of the process:

  1. At home: Students watch assigned YouTube videos from Prof. Rob Ghrist of the University of Pennsylvania.
    1. While watching, it is important that you take notes of concepts you don’t understand.
    2. (Optional) Try to read in the textbooks/notes about the concepts you don’t understand.
  2. In class:
    1. Prof. Son will go through the concepts that you don’t understand on the board.
    2. You will work through worksheets and together with Prof. Son, you will learn how to solve problems.

Materials and references

No textbook is required. We will follow the University of Pennsylvania’s guide ( However, a physical copy of this book is not required.

Required materials

You will find useful information (including a breakdown of the playlists) on the website of Prof. Rob Ghrist of UPenn, who developed the materials course:

Additional References

The following books are highly recommended. If you find the style of the videos doesn’t fit you and would love to have something concrete to read, they are your friends.

  1. Active Calculus: Multivariable by Schlicker et al. 2018 edition. (

  2. Thomas’ Calculus: Early Transcendentals by Hass, Heil, et al. \(14^{th}\) edition.

  3. Calculus Early Transcendental by Stewart. \(8^{th}\) edition.

  4. Anything you can find on Google would work. Calculus is a subject that people have written about so much. So, there’s no excuse for not having access to the knowledge.

  5. 3-D grapher:

  6. Very good graphers:,

Course description

How do we describe the trajectory of a space shuttle? How is the human body affected by scuba diving to different depths for different lengths of time? The mathematics required to describe most real life systems involves functions of more than one variable. The concepts of the derivative and integral from a first course in calculus must therefore be extended to higher dimensional settings. In this course students will be guided through the essential ideas of multivariable calculus, including partial derivatives, multiple integrals and vector calculus, and their applications. These mathematical tools are used extensively in the physical sciences and engineering, and in other areas including economics and computer graphics.

Learning objectives

After the course, students are expected to:

  • Be confident in handling functions of two or more variables and familiar with how they can be represented graphically

  • Understand the key concepts of multivariable calculus, including partial derivatives, the gradient vector, multiple integrals, line and surface integrals, the divergence and curl of a vector function

  • Know how such derivatives and integrals are calculated and some of their uses

  • Be able to apply these ideas to real world problems

  • Have improved analytic, computational and problem solving skills


During the course, students are expected to compute their own percentage points based on the following scheme. The instructor is not responsible for providing the running percentage.

Form of assessment Weight
Weekly homework 40%
Daily quizzes 10%
Midterm 20%
Final 30%

The following is the non-negotiable letter grade breakdown. It is based on common practice in the United States for standard courses such as Calculus.

Letter Grade Percentage
A [93,100]
A- [90,93)
B+ [87,90)
B [83,87)
B- [80, 83)
C+ [77,80)
C [73,77)
C- [70,73)
D+ [67,70)
D [60, 66)
F [0,60)

Core content

  1. Introduction
  • Functions of two variables
  • Graphs in three dimensions, surfaces and level curves
  • Functions of three or more variables
  • Limits and continuity
  • Vectors (review)
  1. Partial Derivatives
  • Partial derivatives
  • Tangent planes, linear approximations and differentials
  • Chain rule
  • Directional derivatives and gradient vectors
  • Extrema and optimization
  • Lagrange Multipliers
  1. Multiple Integrals
  • Double integrals
  • Double integrals in polar coordinates
  • Triple integrals
  • Triple integrals in cylindrical and spherical coordinates
  • Applications of multiple integrals
  1. Vector Calculus
  • Vector functions and their derivatives
  • Vector fields
  • Line integrals
  • The fundamental theorem of line integrals
  • Green’s Theorem
  • Parametric surfaces and surface integrals
  • Curl and divergence
  • Divergence Theorem
  • Stokes Theorem

Late assignments

  • 15% of the possible total mark will be deducted for every 24 hrs (or part of 24 hrs) after the deadline. Work more than 2 days late will not be accepted.
  • Except for exceptional circumstances (see definition), I will not extend the deadlines.

Time expectations

Some materials require time to be accustomed to. Some students are quicker than others. However, on average, you should expect 10-15 hours per week (including class time) on the materials in order to know the subject relatively well.

Collaboration & Plagiarism

Plagiarism is the act of submitting the intellectual property of another person as your own. It is one of the most serious of academic offenses. Acts of plagiarism include, but are not limited to:

  • Copying, or allowing someone to copy, all or a part of another person’s work and presenting it as your own, or not giving proper credit.

  • Purchasing a paper from someone (or a website) and presenting it as your own work.

  • Re-submitting your work from another course to fulfill a requirement in another course.

Further details can be found in the Code of Academic Integrity [link].

Learning Support

In addition to your course instructors, there are other resources available to support your academic work at Fulbright, including one-on-one consultations with learning support staff, supplementary workshops, and both individual and group tutoring and mentoring in course content, language learning, and academic skills. If you would like to request learning support, please contact Fulbright Learning Support (


Mental health and wellbeing are essential for the success of your academic journey. The Fulbright Wellness Center provides various services including counseling, safer community, and accessibility services. If you are experiencing undue personal or academic stress, are feeling unsafe, or would like to know more about issues related to wellbeing, please contact the Wellness Center via or visit the Wellness Center office on Level 5 of the Crescent campus.

For more information, pleaes check

Tentative Course Schedule

The following schedule will be updated as we go so that students will know what to watch/read before/after class.

Week Topcs Watch
1 lines, planes, surfaces, coordinates, vectors; dot, cross, & scalar triple products Vol 1: Chapters 1,2,3,4
2 intro to vector calculus Vol 1: Chapters 5,6,7,8
3 motivating matrices, matrix algebra, linear systems, & row reduction, inverses, linear transformation Vol 1: Chapters 9,10,11,12,13, 14
4 multivariate functions & partial derivatives, derivatives as linear transformations Vol 2: Chapters 1, 2, 3, 4
Break Tet (Feb 5 - 23)
5 derivatives as linear transformations, chain rule, derivative rules, inverse theorem Vol 2: Chapters 5, 6, 7, 8
6 gradients, tangents, & linearization, multivariate Taylor expansion Vol 2: Chapters 9, 10, 11, 12, 13
7 Applications: Optimization Vol 2: Chapters 14, 15, 16, 17, 18
8 Integrals, Riemann sums Vol 3: Chapters 1, 2, 3, 4, 5
9 Applications: Mass & Probability Vol 3: Chapters 6, 7, 8, 9, 10, 11, 12
10 Changing coordinates Vol 3: Chapters 13, 14, 15, 16, 17, 18
11 Path integrals Vol 4: Chapters 1, 2, 3, 4, 5
12 Differential forms & Fundamental theorems Vol 4: Chapters 6, 7, 8, 9, 10, 11, 12