Electromagnetic Field Theory

Vector Calculus

SCALAR CALCULUS

…Since scalars are just numbers (integers), it follows ordinary algebraic identities…

Let us consider A and B be two scalar quantities,

  • Addition of two scalars will result in a scalar $$C=A+B$$
  • Subtraction of two scalars will result in a scalar $$C=A-B$$
  • Multiplication of two scalars will result in a scalar $$C=A×B$$
  • Division of two scalars will result in a scalar $$C=A/B$$

Scalar Algebra:

Scalar Addition:

Since Scalar is just a number, Scalar addition is equivalent to simple addition of two numbers.

Let us consider A, B and C be scalar quantities,

  • Scalar Addition is commutative $$A+B=B+A$$
  • Scalar Addition is associative $$A+(B+C)=(A+B)+C$$
  • Scalar Addition is distributive $$C(A+B)=CA+CB$$

Scalar Subtraction:

Scalar subtraction is equivalent to simple subtraction of two numbers.

  • Scalar Subtraction is anti-commutative $$A-B=-(B-A)$$
  • Scalar Subtraction is associative $$A-(B-C)=(A-B)-C$$
  • Scalar Subtraction is distributive $$C(A-B)=CA-CB$$

Scalar Multiplication:

Scalar multiplication is equivalent to simple multiplication of two numbers.

  • Scalar Multiplication is commutative $$AB=BA$$
  • Scalar Multiplication is associative $$A(BC)=(AB)C$$
  • Scalar Multiplication is distributive $$C(A+B)=CA+CB$$