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Potentials and Gauge Symmetry in Electromagnetism
Finally wrapping up our dive into the different representations of Maxwell's equations, we arrive at the vector potential forms. Unlike...
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Maxwell’s Equations: Differential and Integral Forms
What are the big ideas behind Maxwell's equations? In this post, we uncover the Vector Calculus that gives their two...
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Convergence and Complex Taylor Series
Infinite series are up there with some of the coolest functions in math. They're at the heart of Calculus with...
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Vectors vs. Complex Numbers: Intro to Complex Differentiation
An example of a linear transformation, the angle with which we'll be looking at complex numbers and vectors alike.Credit: All...
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Infinitesimals Vs. Limits In Calculus
Credit: [Contemporarycalculus.com] When I was learning Calculus on my own, I decided to skip limits. Sounds stupid, I know, but...
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Algebra Needs Complex Numbers
If you've been following along with my earlier posts on the complex number system then you've gotten a taste of...
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Imaginary Numbers and Real Math
All math is connected. But as mathematicians go deeper and deeper into the weeds the results they find grow increasingly...
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Imaginary Apples and Oranges
What is the sum of 3 apples and 4 oranges? This classic statement highlights the difficulties in comparing the incomparable....
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The Mystery of the Complex Plane
Think about when you learned algebra for the first time. On that seemingly uneventful day of middle school, the letter...
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