Most of the mathematics that gives physics students trouble is not hard. It is unmotivated. Somebody wrote \(\nabla \times \vect{B}\) on a board without ever saying what question a curl was invented to answer, and from that point on it is a symbol you manipulate rather than an idea you have.
These lessons go the other direction. Each one starts with a concrete problem somebody actually had, follows the reasoning that produced the tool, and only then writes down the notation.
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Planned
Nothing here is written yet. The rough order I intend to work through:
- Vectors and coordinates — why we bother with different coordinate systems and how to move between them without losing track of what is physical
- Derivatives as rates — the physics reading of calculus, where \(\deriv{x}{t}\) is a thing you can see rather than a rule you apply
- Integrals as accumulation — adding up infinitely many small contributions, and why that is the same operation as area
- Taylor series — why “just approximate it as linear” is the single most used move in physics
- Linear algebra — matrices as things that do something to vectors
- Differential equations — how to read one before you try to solve it
- Fourier analysis — decomposing a signal into frequencies, which is most of what spectroscopy is
If one of these would be useful to you sooner rather than later, tell me at s.stockton@tcu.edu and I will bump it up the list.