Calculus › Section J · Infinite series › Topic J.7
Taylor polynomials and approximation
Polynomials are the only functions a computer really loves: add and multiply and you are done. Taylor polynomials imitate a complicated function near a point, matching its value, slope and curvature, and they come with a guaranteed error bound.
In this topic
- Imitating a function
- Matching derivatives forces the coefficients
- The Taylor polynomial
- Worked example: eˣ at the origin
- Taylor's inequality: a guaranteed error bound
- Worked example: sin x by hand
- Applied: the pendulum's small swings
- Degrees of accuracy
- Common mistakes to avoid
- Key takeaways
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Standards: 10 (BC)