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Dr. Naser Abu-Zaid; Lecture notes on Electromagnetic Theory(1); Ref:Engineering Electromagnetics; William Hayt& John Buck, 7th & 8th editions; 2012 Preliminary material (mathematical requirements) Vector Analysis Vector algebra: Vector Calculus: Addition; Subtraction; Multiplication Differentiation; Integration Vector: A quantity with both magnitude and direction. (Force F 10N to the east). Scalar:A quantity that does not posses direction, Real or complex. (Temperature T 20o . Vector addition: 1) Parallelogram: A B A A B B 2) Head to Tail: B A A B B Chapter One A 1

Dr. Naser Abu-Zaid; Lecture notes on Electromagnetic Theory(1); Ref:Engineering Electromagnetics; William Hayt& John Buck, 7th & 8th editions; 2012 Vector Subtraction: A B A B B A B A B B Multiplication by scalar: B k A A 2A B 0.5A B 3A 0.5A A A 3A Commulative law: A B B A Associative law: A B C A B C Equal vectors: A B if A B 0 (Both have same length and direction) Add or subtract vector fields which are defined at the same point. If non vector fields are considered then vectors are added or subtracted which are not defined at same point (By shifting them) Chapter One B 2A 2

Dr. Naser Abu-Zaid; Lecture notes on Electromagnetic Theory(1); Ref:Engineering Electromagnetics; William Hayt& John Buck, 7th & 8th editions; 2012 THE RECTANGULAR COORDINATE SYSTEM y x , y , z are coordinate Right Handed System variables (axis) which are mutually perpendicular. x z Out of page z z 3 P 1,2,3 A point is located by its x , y and z coordinates, or as the intersection of three constant surfaces (planes in this case) y 2 y x 1 Chapter One x 3

Dr. Naser Abu-Zaid; Lecture notes on Electromagnetic Theory(1); Ref:Engineering Electromagnetics; William Hayt& John Buck, 7th & 8th editions; 2012 z z 3 P 1,2,3 surface (plane) y x 1 Surface (plane) y 2 Three mutually perpendicular surfaces intersect at a common point Chapter One x surface (plane) 4

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