Physical Sciences and Mathematics Commons^™

2017: "From Sea To Shining Sea: Looking Ahead With The National Park Service", Abhay Gupta '18, James Wei '18, Istvan Kovach '18, Shyam Sai '18, Darius Hong '18

Distinguished Student Work

There is a natural inclination for humanity to view the Earth as our steadfast, never-changing home. After all, it seems as permanent as the ground beneath our feet. However, nothing could be further from the truth, especially in today’s rapidly changing climes. Global temperatures are on the rise, and with them comes an increase in sea levels, wildfires, and hurricanes, three serious, expensive issues. Unfortunately for the National Park Service (NPS), who guard ninety-seven coastal units, coastlines are especially vulnerable to such problems. Thus, the NPS must take extra precautions and expenditures to maintain and protect them. With limited budget, …

2017: "Park2vec: A Vector Representation Of Our National Parks’ Climate Change Susceptibility", William Tong '17, Ankit Agarwal '17, George Moe '17, Aakash Lakshmanan '17

Distinguished Student Work

With over 400 units, between them covering almost 850 million acres of carefully preserved land, the National Park Service (NPS) acts as steward to the nation’s natural treasures. In the move to the Twenty-First century, the NPS faces numerous looming challenges, particularly those related to a rapidly changing climate. It was our task to strategize with the Service in addressing three such issues, leveraging our experience in mathematical modelling and data analysis to aid them in the quest to protect and to preserve.

The first problem under consideration was determining the risk associated with sea-level change for five different coastal …

2016: "Analysis Of The Effectiveness Of Varying Car-Sharing Business Models", William Tong '17, Sachin Govind '16, Ankit Agarwal '17, David Xu '16, George Moe '17

Distinguished Student Work

A continually evolving field, the automotive industry consistently introduces a number of innovative technologies and services to ease the problem of transportation. One such service is termed Car-sharing. Car-sharing allows users to rent vehicles and use them for a short period of time without worrying about the additional costs associated with maintenance, fuel, and pollution, presenting a simple alternative to owning a car. Still an emerging concept, Car-sharing requires a great deal more analysis to fully understand the nuances and implications behind its implementation.

1. Coffee, Ruth Dover

Differential Equations

Newton’s Law of Cooling.

3: Drugs And De's, Ruth Dover

Differential Equations

Making a connection between discrete recursion and differential equations.

2. Population, Ruth Dover

Differential Equations

Introduction to logistic population growth.

4. Dragging Along, Ruth Dover

Differential Equations

More information on air drag.

1. Measuring Speed, Ruth Dover

More on Derivatives

Tables of values to measure rates.

2. Intro To Concavity, Ruth Dover

More on Derivatives

Looking at changes in ƒ’ to understand concavity.

3. Derivatives Of Exponential Functions, Ruth Dover

More on Derivatives

Exploring the derivative of exponential functions.

Limits3, Ruth Dover

Limits

Algebraic techniques for functions with holes.

More Limits, Ruth Dover

Limits

No abstract provided.

Limits2, Ruth Dover

Limits

More on limits, both algebraic and graphical, including one-sided limits.

Limits5, Ruth Dover

Limits

Limits and continuity.

Limits1, Ruth Dover

Limits

A basic idea to limits and notation.

Limits4, Ruth Dover

Limits

An introduction to limits as something goes to infinity.

Rate Of Change 1, Ruth Dover

A Simple Introduction to Rates

No abstract provided.

Rate Of Change 4, Ruth Dover

A Simple Introduction to Rates

No abstract provided.

Rate Of Change 3, Ruth Dover

A Simple Introduction to Rates

No abstract provided.

Bc 1 Rate Of Change Activity Sheet Teacher Notes, Ruth Dover

A Simple Introduction to Rates

Before beginning this section of handouts, students will be introduced to a variety of vocabulary words often associated with calculus. These words will be used in an intuitive sense only and will not have been formally defined. Vocabulary should include graphical terms such as continuous, increasing, decreasing, maximum and minimum points, concave up, concave down, and point of inflection. In addition, discussion of the concept of "rate of change" should begin. It should be mentioned that many quantities change – population, cost, and temperature, to name just a few. All that is specifically required at this point can be related …

Rate Of Change 2, Ruth Dover

A Simple Introduction to Rates

No abstract provided.

Approximations 1, Ruth Dover

Integrals

Measuring distance and accumulation.

Approximations 4, Ruth Dover

Integrals

Trapezoidal Rule.

Approximations 3, Ruth Dover

Integrals

Understanding Riemann sum approximations, including technology.

Approximations 2, Ruth Dover

Integrals

Drawing rectangles and calculating Riemann sums.

1. Monotonic Sequences, Ruth Dover

Series

Practice with monotonic sequences.

Series 08, Ruth Dover

Series

More on error.

Series 07, Ruth Dover

Series

Where did the Lagrange error bound come from?

3. Upper Bounds, Ruth Dover

Series

Understanding upper bounds and a proof of the divergence of the harmonic series.

Series 10, Ruth Dover

Series

Extra stuff to show more ways to work with series.