Physical Sciences and Mathematics Commons^™

2016: "Maximizing Customer Convenience With Hill Climbing", Ankit Agarwal '17, William Tong '17, Robert Lou '17, George Moe '17

Distinguished Student Work

As technology advances and the pace of life quickens, companies are expected to continually provide better services, be more accessible, and respond to requests faster. While such expectations have led to the rapid growth of retail stores and service locations throughout the United States, delivery services have arguably been the most influenced by these rising demands.

Amazon.com is an online storefront that has seen tremendous growth throughout its lifetime, and it only continues to grow. Founded in 1994 as an online bookstore, the digital retailer eventually expanded its services to include technology, home goods, and even eBooks. Amazon’s response to …

2016: Himcm International Mathematics Modeling Contest: National Outstanding Paper, Suchet Kumar '19, Tommy Vadakumchery '19, Nathan Kim '19, Bert Cao '19

Distinguished Student Work

In the modern business world, maximizing profits is the highest priority. Businesses, especially small ones, should try to save money whenever possible. Along with cutting wages, removing competition, and increasing advertising and production, efficiency of company sites can save money. For example, a cheap 50 ft. by 100 ft. warehouse costs $35,000, but when coupled with the costs of maintenance and wages, increasing the number of warehouses significantly increases costs.

Clearly, warehouses are expensive, making it necessary to place them in optimal locations. In this problem, we attempt to reduce the number of warehouses while shipping to the entirety of …

05: Rats Grapher, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

RatsGrapher.nb graphs rational functions and labels all holes and asymptotes.

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.