Category: Mathematics

Plant Capacity Factor

Plant Capacity Factor

Plant Capacity Factor

12/26/18

“How can we determine the potential used by a power-plant during a given period of time?”

 

Power plants are capable of generating a certain amount of energy. But only so much of it actually gets used. The ratio of energy used/potential energy is known as the Plant Capacity Factor. A simple way to conceive of the plant capacity factor is to think about the amount you can study in an hour compared to how much you study. Although you might be able to study a lot in an hour, the amount you actually study determines your efficiency!

 

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How Heat Transfer is Used to Model Climate Change

How Heat Transfer is Used to Model Climate Change

How Heat Transfer is Used to Model Climate Change

12/16/18

“How is Heat Transfer Used to Model Climate Change?”

 

Heat Transfer is one of the foundational course for a Mechanical Engineer. But internal combustion engines and HVAC are not the only things that the theory can be applied to. Climate Scientists will use many of the same Heat Transfer equations when designing climate models. In this way, Heat Transfer is Used to Model Climate Change.

 

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Climate Change Model Verification

Climate Change Model Verification

Climate Change Model Verification

12/15/18

“How can we verify climate change models?”

 

Climate models are extremely useful for helping us predict the impacts of climate change. But how can we verify them? Well, what if we were to map their mathematical functions to historical data and see if they accurately predict temperature rises? If it turns out to be correct, then the model has a good chance of being valid. This Climate Model Verification, often known as hindcasting, gives our methods validity for future policy work.

 

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Climate Change Modeling

Climate Change Modeling

Climate Change Modeling

12/14/18

“How can we create models for the future climate?”

 

We seem to hear about the predictions of the future climate all the time in the media. Whether it be a warning if we go 2 degrees centigrade above pre-industrial levels or the ever-increasing rate of global warming. But how do we actually obtain this information? Well, people from a variety of different academic disciplines come together to make mathematical models that take in a variety of complex terrestrial processes and their interactions with each other and then layer it on to a physical model of the earth to produce a simulation of what will happen. This is known as Climate Change Modeling and is one of the most important tools that humans have to make policy goals.

 

Image credit http://www.gfdl.noaa.go

Column Space

Column Space

Column Space

12/11/18

“What is the space spanned by the linearly independent columns of a matrix?”

 

Matrices are likely to have at least a few linearly independent columns. The span of this space will result in a vector space known as a Column Space. The dimension of the column space is equivalent to the number of linearly independent vectors.

 

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Onto Functions

Onto Functions

Onto Functions

12/10/18

“What happens when all of the mappings in a linear transformation have at least one output?”

 

Sets of numbers can be changed around in linear transformations. And if every number maps onto at least one other number, then the function is Onto.

 

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Vector Spaces

Vector Spaces

Vector Spaces

12/09/18

“How can we represent a set of vectors?”

 

Vectors are one of the most important aspects of Linear Algebra. But in order to have a true set of vectors, they must be closed under vector addition and scalar multiplication. This is known as a Vector Space and is vital for a true understanding of Linear Algebra.

 

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