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Physical Sciences and Mathematics Commons™
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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
The Use Of Calculus To Determine Efficient Fertilizer Levels For Crop Production, Cole Loadholtz
The Use Of Calculus To Determine Efficient Fertilizer Levels For Crop Production, Cole Loadholtz
Undergraduate Journal of Mathematical Modeling: One + Two
For this project, I wanted to incorporate calculus into agriculture and environmental science methods. More in detail, the problem used asked for the maximum levels of nitrogen (N) and phosphorus (P) that would be best for a current crop yield. This allowed incorporating partial derivatives, and critical points to find the maximum values for the equation. The results show that in order to demonstrate maximum crop yield production, the levels of nitrogen (N) and phosphorus (P) were to be both at 2, with the correct corresponding units. The drawback from this problem is that although the problem showed effective nitrogen …
Optimization Of Handicap Ramp, Tyler Schilling
Optimization Of Handicap Ramp, Tyler Schilling
Undergraduate Journal of Mathematical Modeling: One + Two
The objective of this project is to minimize the cost of building a handicap ramp. This is done by introducing an equation that represents the total cost of the construction, including labor and materials. Variables are then defined in terms of block length l, allowing for an equation with one variable to be graphed and derived. This equation then undergoes the first derivative test to find a value of l that would create a minimum output for cost. This value is then compared to the physical constraints of the project allowing for a realistic minimum cost to be found. …
Minimizing Container Weight, Ibrahim Alomran
Minimizing Container Weight, Ibrahim Alomran
Undergraduate Journal of Mathematical Modeling: One + Two
Increased globalization has resulted in increased competition in the shipping industry. Since large carriers control over 70% of the total shipping industry, small carriers are left with only 30% of the market share to compete for. Ultimately, profit margins for small carriers have become very minimal. There is, therefore, need to develop a strategy that will aid in optimizing the profits of carriers. The goal of this paper is to develop a model that will help determine the minimum weight for a particular container design. The validity of the model is important in the sense that minimum container weight will …
Optimization Of A Fuel Cell, Eduardo Gines
Optimization Of A Fuel Cell, Eduardo Gines
Undergraduate Journal of Mathematical Modeling: One + Two
Fuel cells are devices that generate energy from a chemical reaction that takes place inside the cell. The main parts of these devices are two electrodes and an electrolyte solution. The project consists of determining the area of the electrodes for the fuel cell at which the cell produces its maximum amount of power. This was done with the performance curve of the fuel cell which was in terms of voltage vs current density. The performance curve was turned into terms of power density vs current density, and through this curve the maximum power was determined by identifying the maximum …
Optimum Gear Ratios For An Electric Vehicle, Scott Parkinson
Optimum Gear Ratios For An Electric Vehicle, Scott Parkinson
Undergraduate Journal of Mathematical Modeling: One + Two
The goal of this project is to determine the optimal gear ratios for a vehicle containing a four-speed transmission. This vehicle is required to reach a speed of 30 m/s in the minimum time possible. Equations for the velocity at each shift point were found. An equation for the total time that the vehicle took to reach 30 m/s was then derived and equations for the times spent in each gear were found through integration of the provided formula for acceleration. The optimal gear ratios were then found by taking the partial derivatives of the total time equation with respect …
Optimization Of A Pressure-Treating Process, Josean Velez
Optimization Of A Pressure-Treating Process, Josean Velez
Undergraduate Journal of Mathematical Modeling: One + Two
A company that pressure-treats wood wants to minimize its annual cost without using more than 250 days of operation per year. In addition, they want to find the corresponding value of time, batches and cost for each category. We develop an expression in terms of boards per batch to model the total cost of the treatment process. We then take the derivative and use Newton's Method to find the number of boards per batch that minimizes total cost.
Optimization Of A Chemical Reaction Train, Bahar Sansar
Optimization Of A Chemical Reaction Train, Bahar Sansar
Undergraduate Journal of Mathematical Modeling: One + Two
This project consists of the optimization of a chemical reactor train. The reactor considered here is the continuous stirred tank reactor (CSTR), one of the reactor models used in engineering. Given the design equation for the CSTR and the cost function for a reactor, the following values are determined; the optimum number of reactors in the reaction train, the volume of each reactor and the total cost.