Exploring Multivariable Calculus in Real-World Applications

Jane Tu Jane Tu

Guardians

Driving Questions

  1. How can Multivariable Calculus concepts be applied to analyze and solve real-world problems?
  2. What insights can be gained by using techniques like vector calculus, partial derivatives, and 3D modeling in practical contexts?

Project Introduction

Disciplines/Subjects: Mathematics, Multivariable Calculus, Applied Mathematics

Key Themes: Multivariable Calculus, Real-World Modeling, Advanced Mathematical Techniques


This project empowers learners to explore real-world phenomena using advanced Multivariable Calculus techniques. Learners choose a topic of personal interest and apply concepts such as vector calculus, gradient fields, and optimization to create detailed mathematical models. For example, one project analyzed constrained utility optimization in economics using Lagrange multipliers, providing insights into consumer behavior and market dynamics. Another explored the modeling of piano string vibrations, employing wave equations to simulate realistic sound mechanics. By utilizing tools like Mathematica and Python for data visualization and computation, learners deliver comprehensive reports and presentations showcasing the intersection of mathematics and practical applications.

Core Competency

Habits of mind: Curiosity, Continuous Learning, Strive for Excellence

Transferable skills: Modeling, Interpreting Data/Information to Make Valid Claims, Organizing and Representing Information

Content Knowledge:

Understanding advanced Multivariable Calculus concepts such as vector calculus, partial derivatives, and gradient flows.

Applying these concepts to analyze and model real-world phenomena.

Using technological tools for data analysis, visualization, and documentation.

Developing comprehensive exploration reports that communicate findings effectively.

Team Members1