Definition of a sequence and definition of a series. Introduces the concept of the convergence or divergence of a series using basic examples.

Introduces the concept of an alternating series and the Alternating Series test before utilizing this method to determine the convergence of such a series.

Introduces the Limit Comparison Test and utilizes this method to determine the convergence of a series.

Worked example of solving an inequality statement with a denominator . Explanation of why multiply both sides of inequality by denominator squared given.

Verifies distributive property of the dot product

Proof of some basic properties of the dot product.(i) Dot product of perpendicular vectors,(ii) Dot product of parallel vectors, (iii) Dot product of a vector with itself, and (iv) Commutative property of the dot product

Proof of vector ab = vector b minus vector a explained

Explains the calculation of the power of a complex number using the exponential form to finally deduce De Moivre's Formula

Introduces Newton' Method and explains the procedure for finding a root

Defines negative vector and shows why vector ba is equal to vector -ab. Defines position vector and states that a vector which starts at the origin can be expressed in terms of its end point only, i.e.as a single letter vector.