MathReview

MathReview - Exam 1 Review Session Week 05 Day 2 8.02...

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Exam 1 Review Session Week 05, Day 2 Class 13 1 1 PMR - 8.02 Math (P)Review: Outline Hour 1: Vector Review (Dot, Cross Products) Review of 1D Calculus Scalar Functions in higher dimensions Vector Functions Differentials Purpose : Provide conceptual framework NOT teach mechanics 2 PMR - Vectors • Magnitude and Direction • Typically written using unit vectors: • Unit vector just direction vector: ˆˆ ˆ ˆˆˆ x yz x y z = ++ = + + ri j kx y z G r r = ⇒= r rr r G G Length = 1 3 PMR - Dot (Scalar) Product • How Parallel? How much is r along s ? • Ex: Work from force. How much does force push along direction of motion? r G s G cos r θ ( ) cos sr ⋅= rs G G Note: If r , s perpendicular 0 = G G dW = Fd s JJG G 4 PMR - Cross (Vector) Product • How Perpendicular? • Direction Perpendicular to both r , s r G s G sin s () sin ×= GG Note: If r , s parallel 0 Which perpendicular? Into or out of page? Use a right hand rule. There are many versions. 5 PMR - Review: 1D Calculus • Think about scalar functions in 1D: Think of this as height of mountain vs position f x x 6 PMR - Derivatives How does function change with position? dx df '( ) slope xa df fa dx = == f x x x a = Rate of change of at ? f =
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Exam 1 Review Session Week 05, Day 2 Class 13 2 7 PMR - By the way… Taylor Series • Approximate function? Copy derivatives!
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This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.

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MathReview - Exam 1 Review Session Week 05 Day 2 8.02...

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