lecture01

lecture01 - MATH 100 Introduction to Multivariable Calculus...

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2006 Fall MATH 100 Lecture 1 1 MATH 100 Introduction to Multivariable Calculus 13.1 Rectangular coordinate in 3-space 13.2 Vectors 13.3 Dot product 13.4 Cross product 13.5 Vectors and parametric equation of lines 13.6 Planes in 3-space 13.7 Quadratic surface 13.8 Cylindrical / Spherical coordinates Available at http://www.math.ust.hk/malwu
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2006 Fall MATH 100 Lecture 1 2 13.1 Rectangular coordinate in three-dimensional space Three-dimensional space (3-space) () {} R z y x z y x R = , , : , , 3 where R = set of real numbers R x x = : 0 , 0 , ( ) { } R y x y x = , : 0 , , The x -axis The xy -plane
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2006 Fall MATH 100 Lecture 1 3 Distance Formula is ) , , ( and ) , , ( points o between tw distance The 2 2 2 1 1 1 z y x z y x () ( ) 2 2 1 2 2 1 2 2 1 z z y y x x d + + = Ex. 13.1 Two points (4,-1,3) and (2,3,-1) have distance 6 36 )) 1 ( 3 ( ) 3 1 ( ) 2 4 ( 2 2 2 = = + + = d Meanwhile, the mid-point between the two points is ) 1 , 1 , 3 ( )) 1 ( 3 ( 2 1 ), 3 1 ( 2 1 ), 2 4 ( 2 1 = + + +
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2006 Fall MATH 100 Lecture 1 4 Surface in 3-space () { } 1 : , , 2 2 2 = + + z y x z y x ( ) { } 2 : , , x y z y x = { } 1 : , , 2 2 = + z x z y x Sphere Cylinder Parabola
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lecture01 - MATH 100 Introduction to Multivariable Calculus...

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