Real Numbers
Real Numbers
Real numbers are the numbers that are either rational or irrational, i.e., the set of real numbers is the union of the sets Q and H. If the set of real numbers is denoted by R , then
Algebra
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http://course-notes.org/Algebra
Complex Numbers
Complex Numbers
Complex numbers are the numbers with the format a + b i, where a and b are real numbers and
i ² = - 1. If we denote the set of complex numbers by C, then
Binomial Theorem
The binomial theorem is a useful formula for determining the algebraic expression that results from raising a binomial to an integral power. It provides one with a quick method for finding the coefficients and literal factors of the resulting expression.
The binomial theorem is stated as follows:
Infinite Series
Given a geometric progression { an } = a1, a2, a3, ...., an , ...., if the absolute value of the common ratio, | r | , is less than 1, the corresponding geometric series Sn = a1 + a2 + a3 + .... + an + ...
Geometric Progression
A geometric progression is a sequence in which each term (after the first) is determined by multiplying the preceding term by a constant. This constant is called the common ratio of the arithmetic progression. A geometric progression can be defined as follows:
Arithmetic Progression
An arithmetic progression is a sequence in which each term (after the first) is determined by adding a constant to the preceding term. This constant is called the common difference of the arithmetic progression. An arithmetic progression can be defined as follows:
Sequence Series
A sequence is a function whose domain is the set of positive integers
{ 1, 2, 3, ... }. The functional values or range elements are called the terms of the sequence. A sequence can be defined as follows:
Mathematical Induction
The principle of mathematical induction is stated as follows:
Cramer's Rule
Given the system of equation;
Then
Determinants
A matrix with the same number of columns as rows is called a square matrix. The determinant is a real number which is associated with each square matrix having real number entries.
ex.
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