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Demo01VectorCalc

# Demo01VectorCalc - ECE 3030 Electromagnetic Fields and...

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ECE 3030: Electromagnetic Fields and Waves Fall 2009 DEMO 1 INSTRUCTOR NOTES: Vector Calculus Reminder: Don’t do Workshop or Homework items! Date: Tuesday 9/1 1. Do a quick review of notation: unit vectors: ˆ x, ˆ y, ˆ z , or ˆ i, ˆ j, ˆ k , or ˆ a x , ˆ a y , ˆ a z , or a x , a y , a z ( sometimes bold ). We will use the “hat” notation: ˆ x, ˆ y, ˆ z . coordinate positions: ( x, y, z ), or ( r, φ, z ), or ( r, θ, φ ) ( never bold ) full vectors: E, E , ~ E, E . We will use the “over arrow” notation: ~ E . differential lengths: d , d x , d y , d z , d s . Use d s for length. differential areas: ~ d a = d x d y~ z , ~ d S , ~ d A , dA . Use ~ d a for area. differential volume: d V ( never a vector) differential vectors: ~ d , ~ d x , ~ d y , ~ d z , or d x ˆ x , d y ˆ x , or d z ˆ z , ~ d S , ~ d a , ~ d A 2. Review r.h. orthogonal coordinate systems (draw each): Cartesian (or rectangular): ( x, y, z ); vector field: ~ A = A x ˆ x + A y ˆ y + A z ˆ z differential examples: ~ d s = d x ˆ x , ~ d a = d x d y ˆ z , d V = d x d y d z y x z x z ( ) z y x , , y P r & Figure 1: Cartesian coordinate system. y x z x z y z ˆ x ˆ y ˆ Figure 2: Local unit vectors in the Cartesian coordinate system. Cylindrical: ( r, φ, z ); vector field: ~ A = A r ˆ r + A φ ˆ φ + A z ˆ z differential examples: d s = d x , or ~ d s = d r ˆ r , ~ d s = r d θ ˆ θ , ~ d s = d z ˆ z ~ d a = r d φ d z ˆ r , d V = r d r d φ d z y x z φ r z ( ) z r , , φ Figure 3: Cylindrical coordinate system. y x z φ r z z ˆ r ˆ φ ˆ Figure 4: Local unit vectors in the Cylindri- cal coordinate system. CORNELL UNIVERSITY c WES SWARTZ (09/8/7) 1–1

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ECE 3030: Electromagnetic Fields and Waves Fall 2009 DEMO 1 INSTRUCTOR NOTES: Vector Calculus Spherical: ( r, θ, φ ); vector field: ~ A = A r ˆ r + A θ ˆ θ + A φ ˆ φ differential examples: d s = dr , d s = r d θ , d s = r sin θ d φ , ~
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Demo01VectorCalc - ECE 3030 Electromagnetic Fields and...

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