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Potentials and Gauge Symmetry in Electromagnetism

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

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

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

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

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

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

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

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

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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