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Intermediate Mathematics · 6 Topics
Taylor Series for Physics
From the general formula to quantum perturbation theory — the series that makes all of physics tractable.
1
The Taylor Formula
Derivatives, the general formula, and why any smooth function is locally a polynomial
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2
Common Maclaurin Series
The six series every physicist knows: sin, cos, eˣ, ln(1+x), binomial, and geometric
Interactive
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3
Convergence & Error Bounds
When does a Taylor series converge, and how large is the truncation error?
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4
Small-Angle Approximations
How $\sin\theta \approx \theta$ and $\cos\theta \approx 1 - \theta^2/2$ make hard problems tractable
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5
Binomial Series & Relativity
How $(1+x)^\alpha \approx 1 + \alpha x$ connects Newton to Einstein and recovers classical physics
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6
Harmonic Approximation
Why every stable equilibrium looks like a spring, and how this drives phonons, molecules, and QFT
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