The Magic of Differential Forms and Why Physicists Don't Use Them
Description
Under the direction of Dr. Tim Magee. Vector calculus is the standard for performing calculations in many areas of physics, including electrodynamics. While mathematicians and physicists alike have always questioned whether or not there existed a method of calculation which could truly encapsulate the complexities of our physical world, about 20 years after Maxwell’s equations on electrodynamics were published there finally came a bit of a breakthrough in the form of a concept called differential forms. It’s been discovered that differential forms actually work quite well with vector calculus, the ways of “translating” between vector calculus and differential forms have become standardized and differential forms allow physicists to represent electrodynamic calculations in a much more elegant way that vector calculus prevents. Despite the benefits and amazing progress that’s been made in applying differential forms, mathematicians face obstacles in standardizing its use. As a lot of mathematical physicists have found, many students are not introduced to differential forms until much later in their education and therefore find it difficult to adjust. This leaves room to address the benefits of differential forms in studying physics and suggest ways that the topic could be introduced earlier to students.
The Magic of Differential Forms and Why Physicists Don't Use Them
Dana Science Building, 2nd floor
Under the direction of Dr. Tim Magee. Vector calculus is the standard for performing calculations in many areas of physics, including electrodynamics. While mathematicians and physicists alike have always questioned whether or not there existed a method of calculation which could truly encapsulate the complexities of our physical world, about 20 years after Maxwell’s equations on electrodynamics were published there finally came a bit of a breakthrough in the form of a concept called differential forms. It’s been discovered that differential forms actually work quite well with vector calculus, the ways of “translating” between vector calculus and differential forms have become standardized and differential forms allow physicists to represent electrodynamic calculations in a much more elegant way that vector calculus prevents. Despite the benefits and amazing progress that’s been made in applying differential forms, mathematicians face obstacles in standardizing its use. As a lot of mathematical physicists have found, many students are not introduced to differential forms until much later in their education and therefore find it difficult to adjust. This leaves room to address the benefits of differential forms in studying physics and suggest ways that the topic could be introduced earlier to students.