ME-P1 Proof by Mathematical Induction




























































































































Summation notation or Sigma Notation







































































































Why we need proof by mathematical induction







































































































Proof by Mathematical Induction: Mathematical Dominoes







































































































Proof by induction partial sums worked examples







































































































Proof by Induction Divisibility proofs





















ME-V1 Introduction to vectors
– V1.1 Introduction to vectors




























































































































Vectors Introduction







































































































Adding Vectors Graphically







































































































Vectors Multiplying by a scalar







































































































Vectors in 2D and 3D Shapes







































































































Vectors in linear combinations







































































































Vectors in component form







































































































Adding Vectors in component form







































































































Vectors multiplying by a scalar in component form





















– ME-V1.2 Further Operations with Vectors




























































































































Vectors finding the magnitude







































































































Vectors finding the unit vector







































































































Finding direction of a vector







































































































Defining a vector between 2 points







































































































Vector Revision part 1







































































































The dot product part 1







































































































The dot product part 2







































































































The dot product part 3







































































































The scalar product or dot product of a vector revisited





















































































