Class Information
- Instructor: Hyosang Kang ([email protected], E7-G11)
- Class hours and classroom: check the portal system website
Course Description
This course extends mathematical analysis from single variable functions to functions of multiple variables. We will explore key concepts including partial derivatives, multiple integrals, and their applications. By the end of this course, you will be equipped to model and solve complex problems involving multivariable functions, laying a strong foundation for advanced studies and practical applications in various scientific and engineering fields.
Course Objectives
- Mathematical Literacy: Develop the ability to read and write complex mathematical contexts accurately and fluently, enabling precise communication and understanding of multivariable calculus concepts.
- Problem Design: Acquire skills to design and formulate original problems using precise mathematical terminology, fostering creativity and deeper comprehension of mathematical theories.
- Computational Proficiency: Gain competence in using computational tools such as Matlab, Python, and Go to solve mathematical questions effectively, enhancing problem-solving capabilities and practical application of theoretical knowledge.
Course Operation and Grading
- In-class Group Activity (30%)
- Flip-Learning Style: This course employs a flip-learning approach where students must watch video lectures before each class. The in-class sessions will focus on discussions of the topics covered in these lectures.
- Active Engagement: Students are required to participate actively in these discussions, guided by the instructor. Group scores will be based on the quality and timeliness of questions and discussions, as well as attendances.
- Project (40%)
- Python-based Submissions: After each chapter, students must submit projects completed using Python. All works should be uploaded to the designated location, which will be announced in class.
- Objective Flexibility: Some projects will be open-ended, allowing groups to create any output they desire. Other projects will be collaborative and completed during class time.
- Written Report (30%)
- Report Requirements: Each project requires a summary of the work done and the related mathematical topics. Reports must be written in English, adhere to a formal format, and demonstrate professional detail.
| Grade |
Score |
Grade |
Score |
Grade |
Score |
Grade |
Score |
| A+ |
90-100 |
B+ |
65-74 |
C+ |
40-49 |
D+ |
15-24 |
| A0 |
80-89 |
B0 |
55-64 |
C0 |
30-39 |
D0 |
5-14 |
| A- |
75-79 |
B- |
50-54 |
C- |
25-29 |
D- |
1-4 |
Weekly Schedule
| Class |
Topics |
Class |
Topics |
| 1 |
Orientation |
15 |
Applications of differentiation |
| 2 |
Vectors |
16 |
Project: Heat flow |
| 3 |
Matrices |
17 |
Taylor series |
| 4 |
Project: CAPTCHA |
18 |
Optimization |
| 5 |
Sequence |
19 |
Project: Gradient descent |
| 6 |
Series |
20 |
Definite integrals |
| 7 |
Project: Calculator |
21 |
Multiple integrals |
| 8 |
Functions and graphs |
22 |
Project: Crofton formula |
| 9 |
Limits and continuity |
23 |
Line integrals |
| 10 |
Project: Drawing graphs |
24 |
Surface integrals |
| 11 |
Differentials |
25 |
Project: Maxwell’s equations |
| 12 |
Theorems on differentials |
26 |
Green and Stokes theorem |
| 13 |
Project: Spring oscillation |
27 |
Divergence theorem |
| 14 |
Partial derivatives |
28 |
Project: Areas of polygons |
Course Policies
- Mandatory Submissions: If a group misses submitting any project output or report, all members of the group will fail the course. It is crucial to adhere to deadlines and ensure all required materials are submitted on time.
- Plagiarism: Any act of plagiarism will result in an immediate failure of the course for all involved parties. Plagiarism includes copying code, reports, or any other academic dishonesty. All work submitted must be original and properly cited if referencing external sources.