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# Lecture 2 - ENGR-1100 Introduction to Engineering Analysis...

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Lecture 2 Notes courtesy of: Professor Yoav Peles ENGR-1100 Introduction to Engineering Analysis

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Office Hours Professor: Nelson J. Tacy Email: [email protected] JEC-7043 T, W, F: 1:00 - 2:30 GTA: Carlos Alberto Gonzales Calderson Email: [email protected] JEC-4034 W, R: 7:00 - 10:00 GTA: Fan Zhang Email: [email protected] JEC-2001 T: 12:30 – 3:30
Homework Assignment (due next class) From handout Set 3.2 Problems 3f and 6a Set 3.3 Problems 1d, 2d, 4c and 6c

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Lecture outline Vectors Unit vector Dot product
Scalar and vectors A scalar quantity is completely described with only a magnitude (a number). -Examples: mass, density, length, speed, time, temperature. A vector quantity has both a magnitude and a direction and obeys the parallelogram law of addition. -Examples: force, moment, velocity, acceleration.

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Vector arithmetic If u , v , w are vectors in 2- or 3-space and k and l are scalar, then the following relationships hold: (a) u + v = v + u (b) u + 0 = 0 + u = u (c) k ( l u ) =( kl ) u (d) ( k + l ) u = k u + l u (e) ( u + v ) + w = u + ( v + w ) (f) u + (- u ) = 0 (g) k ( u + v ) = k u + k v (h) 1 u = u
From the Theorem of Pythagoras it follows that the length of a vector is : The norm of a vector (the length of a vector) x y (v 1 ,v 2 ) v v 1 v 2 v = v 1 2 + v 2 2

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Three dimensional space (a 1 ,a 2 ,a 3 ) a z x y a 1 a 2 a 3 a = a 1 2 + a 2 2 + a 3 2
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Lecture 2 - ENGR-1100 Introduction to Engineering Analysis...

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