Partial Fraction Decomposition Lecture

These flashcards cover key vocabulary and concepts related to partial fraction decomposition from the lecture notes.

Partial Fraction Decomposition

A method to break down rational functions into simpler fractions for easier analysis.

Rational Function

A function of the form $f(x) = \frac{P(x)}{Q(x)}$ where $P(x)$ and $Q(x)$ are polynomials and $Q(x) \neq 0$.

Proper Rational Function

A rational function where the degree of the numerator is less than the degree of the denominator.

Improper Rational Function

A rational function where the degree of the numerator is greater than or equal to the degree of the denominator, requiring polynomial division.

Distinct Linear Factors

Case where the denominator can be expressed as a product of linear factors of the form $Q(x) = (x - r_1)(x - r_2) \cdots (x - r_n)$.

Repeated Linear Factors

Case where the denominator contains the same linear factor raised to a power, expressed as $P(x) = \frac{Q(x)}{(x - a)^n}$.

Integration of Rational Functions

The process of finding the integral of a rational function, often facilitated by partial fraction decomposition.

Coefficients

In the context of partial fractions, these are the constants, such as $A$ and $B$, that need to be determined during decomposition.

Setup Step in Decomposition

The initial stage where the rational function is expressed as a sum of simpler fractions.

Equate Coefficients

The method used in solving for unknowns in the decomposition by setting like terms equal to each other.