Taylor series | Chapter 10, Essence of calculus
Taylor polynomials are incredibly powerful for approximations, and Taylor series can give new ways to express functions. Early access to future series: ...
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When I first learned about Taylor series, I definitely didn’t appreciate how important they are. But time and time again they come up in math, physics, and many fields of engineering because they’re one of the most powerful tools that math has to offer for approximating functions. One of the first times this clicked for me as a student was not in a calculus class, but in a physics class. We were studying some problem that had to do with the potential energy of a pendulum, and for that you need an expression for how high the weight of the pendulum is above its lowest point, which works out to be proportional to one minus the cosine of the angle between the pendulum and the vertical. The specifics of the problem we were trying to solve are beyond the point here, but I’ll just say that this...
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When I first learned about Taylor series, I definitely didn’t appreciate how important they are. But time and time again they come up in math, physics, and many fields of engineering because they’re one of the most powerful tools that math has to offer for approximating functions. One of the first times this clicked for me as a student was not in a calculus class, but in a physics class. We were studying some problem that had to do with the potential energy of a pendulum, and for that you need an expression for how high the weight of the pendulum is above its lowest point, which works out to be proportional to one minus the cosine of the angle between the pendulum and the vertical. The specifics of the problem we were trying to solve are beyond the point here, but I’ll just say that this...
