Multivariable Calculus

Math 2110Q § 003

Fall 2017

Project information

As stated in the syllabus, every student is required to submit a short paper on some topic that extends the topics discussed in the lecture.

Specifically, the paper can be submitted **alone or with one other student.**

The paper must be **single spaced** and between **two and five complete pages** in length.

The paper can be submitted for review or final grading at any point during the regular semester but will not be accepted during exam week.

The paper will recieve a letter grade (A - F) upon final submission.

Project topics

Here is a list of potential topics, feel free to propose you're own.

- Applications of the cross and dot products to physics
- The cross product and an n-dimensional Pythagorean theorem
- Limits and continuity for functions of several variables
- Quadratic approximations and Taylor series for functions of two variables
- Linearization in higher dimensions
- Differentiability of multi-variable functions
- When does Clairaut's theorem not apply?
- The method of Lagrange multipliers finding extrema relative to constraints
- The Jacobian and change of variables for a functions of two variables
- Applications of multiple integrals
- Fubini's theorem and when it fails
- TNB Frames and curvature for space curves
- Deriving Keplar's laws of planetary motion
- Using parametric equations to connect straight tracks of railroad
- A history of calculus
- The projects given in Stewart
- Section 14.4
- Section 14.7
- Section 14.8
- Section 15.6
- Section 15.8
- Section 16.8

- The physical applications of curl and divergence
- The mathematics of the Ekman Transport - Chris Dubiel