Transcription of 2A1VectorAlgebraandCalculus - Information Engineering …
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2A1VectorAlgebraandCalculus - Information Engineering …
12A1 Vector Algebra and Calculus8 Lectures MT 2013 Stephen RobertsRev Oct sjrob/Teaching/VectorsOverviewMany of you will know a good deal already aboutVector Algebra how to add and subtractvectors, how to take scalar and vector products of vectors, and something of how to describegeometric and physical entities using vectors. This coursewill remind you about that good stuff,but goes on to introduce you to the subject ofVector Calculuswhich, like it says on the can,combines vector algebra with give you a feeling for the issues, suppose you were interested in the temperatureTof water ina river. TemperatureTis ascalar, and will certainly be a function of a position vectorx= (x , y , z)and may also be a function of timet:T=T(x, t).
1 a 1 a 2 3 a k a i j Figure 1.2: Vector components. In a Cartesian coordinate frame we write a = [a1,a2,a3] = [x2 −x1,y2 −y1,z2 −z1] or a = [ax,ay,az] as sketched in Figure 1.2. Defining ˆıı,ˆ , kˆ as unit vectors in the x,y,z directions ˆı = [1,0,0] ˆ = [0,1,0] kˆ = [0,0,1]
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