# 14.2: Arithmetic

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Arithmetic in the mathematical sense, not the elementary sense. Most of the material in this section is from other Libretexts sources.

• 14.2.1: Powers and Roots
Multiple sections on powers including the Binomial theorem and roots.
• 14.2.2: Partial Fractions
Decompose a ratio of polynomials by writing the partial fractions. Solve by clearing the fractions, expanding the right side, collecting like terms, and setting corresponding coefficients equal to each other, then setting up and solving a system of equations. The decomposition with repeated linear factors must account for the factors of the denominator in increasing powers. The decomposition with a nonrepeated irreducible quadratic factor needs a linear numerator over the quadratic factor.
• 14.2.3: Matrices and how to use them
Matrices are a system to organize numbers to make transforms easier, including solving a system of equations.
• 14.2.4: Combinations and Permutations
A permutation is a (possible) rearrangement of objects.
• 14.2.5: Complex Numbers
The connection between a complex number and complex exponential (De Moivre's theorem), and how this allows a complex number to be visualized in the Cartesian plane.
• 14.2.6: Sequences and Series
The topic of infinite series may seem unrelated to differential and integral calculus. In fact, an infinite series whose terms involve powers of a variable is a powerful tool that we can use to express functions as “infinite polynomials.” We can use infinite series to evaluate complicated functions, approximate definite integrals, and create new functions.
• 14.2.7: Power Series
A power series (in one variable) is an infinite series. Any polynomial can be easily expressed as a power series around any center c, although most of the coefficients will be zero since a power series has infinitely many terms by definition. One can view power series as being like "polynomials of infinite degree," although power series are not polynomials.

14.2: Arithmetic is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by LibreTexts.