Colin James Physics - Mathematics data.

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Last updated: 25th June 2013.

Greek alphabet.
Integrals - Algebraic functions.
Integrals - Hyperbolic functions.
Integrals - Trigonometrical functions.
Series and sequences.
Trigonometry.
Vector algebra (laws).

Laws of Vector Algebra.

Table 1 - Laws of Vector Algebra.

In the following equations A, B and C are vectors (having both magnitude and direction) and m and n are scalars (numbers - having magnitude but no direction).

1.	A + B = B + A	Commutative Law for Addition.
2.	A + (B + C) = (A + B) + C	Associative Law for Addition.
3.	mA = Am	Commutative Law for Multiplication.
4.	m(nA) = (mn)A	Associative Law for Multiplication.
5.	(m + n)A = mA + nA	Distributive Law.
6.	m(A + B) = mA + mB	Distributive Law.

Table 2 - Laws of Algebra.

In the following equations m, n and p are scalars (numbers - having magnitude but no direction).

1.	m + n = n + m	Commutative Law for Addition. (Subtraction is not commutative e.g. (3 - 2) is not equal to (2 - 3))
2.	m + (n + p) = (m + n) + p = m + n + p	Associative Law for Addition.
3.	mn = nm	Commutative Law for Multiplication. (Division is not commutative e.g. (3/2) is not equal to (2/3))
4.	m(np) = (mn)p = (mnp)	Associative Law for Multiplication.
5.	(m + n)p = mp + np	Distributive Law (multiplication is distributive over addition).
6.	m(n + p) = mn + mp	Distributive Law (multiplication is distributive over addition).

The parallels between vector algebra and ordinary algebra allow us to treat vector equations in the same way as ordinary algebraic equations.

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