"Wisdom begins in wonder" – Socrates
Category: Mathematics
Bond Value
01/29/26
“How can we estimate the current value of a bond?”
Entities take out bonds for all kinds of reasons, ranging from infrastructure development to trade balancing. Financial institutions want to know how much a potential bond might be worth. To accomplish this, people can estimate the present value of the bond’s final worth and the present value of the bond payments to arrive at the Bond Value. Bond values are fundamental for quantifying a bond’s appeal.
Uniform Amount per Interest Period
01/25/26
“How can we calculate equal payments per interest period under compound interest?”
Finance and interest move the investment world, whether it’s paying for infrastructure materials or the operations of a non-profit. Sometimes, when people take out a loan or investment, there will be an equal payment amount per interest period, even when there is compound interest involved. This Uniform Amount per Interest Period is a mix of paying off the interest and the principal amount.
Hydrographs
08/03/25
“How can we graph the amount of water predicted to arrive over time?”
Water comes in and out of zones. Sometimes, we may want to graph how this will change over time. One way to accomplish this is to plot the volume of water on the y axis and the time duration on the x axis to make a Hydrograph. We can use hydrographs to plot both water inflowing to and outflowing from an area to predict how much storage is needed.
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Hydrological Routing
08/02/25
“How can we predict how the volume of water will move through a confined body over time?”
Water is a dynamic system that can move through confined physical bodies such as streams or storage units. Sometimes, we may want to model how the volumes of water will move throughout confined bodies. This task, known as Hydrological Routing, is vital for designing stormwater management systems and implementing flood controls.
Decision Matrix
04/24/25
“How can we evaluate a series of options for action implementation?”
A Decision Matrix evaluates a series of options by integrating and ranking all pertinent criteria. Each criterion is given a score multiplied by a weight based on how vital a criterion is for selecting an option and then summed to form a final decision score. The system with the highest score is selected.
Boundary Conditions
04/08/25
“Why do we sometimes have to provide constraints to solve a problem?”
Some problems in technical subjects can sometimes have an infinite number of theoretical solutions. We can apply constraints known as Boundary Conditions to limit ourselves to feasible solutions to the problem. Examples of boundary conditions can range from limiting potential well drilling to areas outside of environmentally protected zones to solving differential equations for only a certain known range.
Parametric Insurance
02/04/25
“Can we have insurance that only pays out when a certain threshold is reached?”
Insurance usually pays out when a loss is incurred. But a special type of insurance, Parametric Insurance, pays out after reaching a certain threshold. Example parameters for disaster parametric insurance include earthquake magnitude size, wind speed, or flood level.
Multivariate Regression
09/01/24
“How can we perform regression with multiple variables?”
We can use regression to determine the relationship between an input variable and an output variable. But what if we have multiple variables in either the input or output? Well, we use a technique called Multivariate Regression.
Why Calculus Can Be Used to Optimize Solar and Wind Energy Area Combinations
06/19/24
“Why can calculus be used to optimize solar and wind energy area combinations?”
Solar panels and wind turbines can be used in combination for power generation. However, given a constricted area, how can we find the optimal breakdown for solar and wind? Well, if we use calculus, we can see what would be the highest amount of energy generated through area constraints. This is Why Calculus Can Be Used to Optimize Solar and Wind Energy Area Combinations.
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