CALCULUS 3 PROJECT 2

In this project, our team of engineers was to evaluate several different features of a mountain range, and provide our friends, who are planning to hike in these mountains, answers to their questions.

Mathematica was the primary software used to write the code and provide results. Some of the answers we had to provide our friends involved creating graphs of the mountain range, the hiking path, a topological map, and evaluating several complicated integrals to learn about specific properties of the mountain range.

Calculus 3 Project 2: About

The Music Mountains

To be able to do most of the project, we first had to create the mountain range. By combining 10 radially symmetric functions with different weights, centers, and heights, the mountain range defined as a single multivariable function, seen in this graph, was created.

Topographic Map of The Music Mountains

I used a contour plot, with specific lines being added at certain output values of the function describing the music mountains, to create the outlines present in the topographic map. After coloring it in, it looks much more useable as an actual topographic map, which will help our friends navigate around the music mountains.

Gradient Vector Field in the Music Mountains

By using the same contour plot, but superimposing the gradient of the function describing the music mountains instead of coloring it in, the areas where the slope of the mountains is very large show up as large arrows and vice versa for small slopes. This is useful to our friends so they can know where to hike if they want an easier hike or a more challenging hike.

Our Friend's Hiking Path

After choosing a hiking path, superimposed on the graph of the music mountains in blue and with dots highlighting the hourly progress and overall duration of their trip, our friends wanted to know a couple of things about their chosen path.

Elevation During the Hike

The main thing they wanted to know was how long they might be above 10000 ft, so as to avoid any major altitude sickness and thin air. The graph above shows their elevation as a function of time, and highlights the durations of their hike that they will spend above 10000 feet in elevation.

Elevation Rate of Change

They also wanted to know what their steepest ascent and descent were, so as to be prepared for those conditions. The graph above shows the elevation rate of change with respect to time, and the steepest ascent and descent can be seen in dark red and blue respectively.

Calculus 3 Project 2: Work