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 - Bailey Skrtich and Kevin Spichiger
- The Jacobian and change of variables for a functions of two variables
- Applications of multiple integrals
- Fubini's theorem and when it fails - Xinba Li
- 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

For typing your papers

Feel free to use your favorite word processor for typing this paper as many have built in "drag and drop" mathematics. If you want to use something to similar to my preferred way of producing type mathematics I recommend using LaTeX. Specifically, trough the online platform Overleaf. While the learning curve can be steep, this quickly becomes the fastest and prettiest way to typeset mathematics. An example can be found here. For determining how to do something in the language of LaTeX, a quick Google search usually is the answer. Detexify can help you determine the commands for symbols you may need.