Tag: 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!

 

Image credit Wikipedia.org

 

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.

 

Image credit singularityhub.com

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.

 

Image credit d2vlcm61l7u1fs.cloudfront.net

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.

 

Image credit http://3.bp.blogspot.com

Block Diagrams for Controls Systems

Block Diagrams for Controls Systems

Block Diagrams for Controls Systems

12/08/18

“How can we represent control process graphically?”

 

Control systems are a bedrock of modern day technology. However, sometimes it would be easier to see their processes if visualized. This can be done by using Block Diagrams, which shows each component of the control system in its natural order.

Matrix Transposition

Matrix Transposition

Matrix Transposition

12/05/18

“How can we flip rows and columns of a matrix?”

 

When doing Linear Algebra, there are times where we may want to flip the rows and columns. This can be accomplished through Matrix Transposition. A matrix that has undergone transposition is known as a transposed matrix. If we multiply the transposed matrix by the original matrix then we arrive at the identity matrix.

 

Photo credit http://3.bp.blogspot.com

 

 

The Span of a Matrix

The Span of a Matrix

The Span of a Matrix

12/03/18

“How can we represent all possible combinations of a matrix?”

 

Matrices are great for representing groups of numbers. But sometimes we would like to see all possible results. We can do this using the Span of a Matrix, using weighted values for each part.