Ch_03 - Vector I - Summary

Ch_03 - Vector I - Summary - Chapter 3 Vector Differential...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 3 Vector Differential Calculus
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Table of Contents 1. Vector Algebra in 2-Space and 3-Space 2. Inner Product (Dot Product) 3. Vector Product (Cross Product) 4. Vector and Scalar Functions and Fields. Derivatives 5. Curves, Tangents, Arc Length, Curvature, Torsion 6. Curves in Mechanics. Velocity and Acceleration 7. Gradient of a Scalar Field. Directional Derivative 8. Divergence of a Vector Field 9. Curl of a Vector Field Appendix A-1 Types of Derivative A-2 Orthogonal Curvilinear Coordinates
Background image of page 2
Vector Differential Calculus 1. Vector Algebra in 2-Space and 3-Space 1.1. Scalar and Vector Scalar mole fraction, concentration, Thermodynamic state function, , Tp Vector velocity, shear stress, heat/mass flux, Transport properties Arrow or directed line segments Initial point P to terminal point Q Length (magnitude) or norm : || aa Unit vector: a vector of length 1. Zero vector (no magnitude): 0 Notation boldface with direction and magnitude (exception 0 -vector ) 123 [ , , ] aaa a in 3D 1.2. Equality of Vectors Notation boldface with direction and magnitude (exception 0 -vector ) ab (same length and direction) 1.3. Components of Vectors Cartesian coordinate system [ , , ] a 222  a 12 1 ax x  , 22 1 ay y , 32 1 az z Position vector [, , ] xyz r 111 (, ,) Px y z Qx y z a
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Vector Differential Calculus 1. Vector Algebra in 2-Space and 3-Space 1.4. Vector Addition, Scalar Multiplication Scalar multiplication () 0 ck c k   aa a a0 Vector Addition  ab ba ( )   uv w u vw cc c ab a b (commutative law) (associative law) (distributive law) 123 [ , , ] a c a c a a 112 233 [ , , ] ababab   Geometric representation 1.5. Unit Vectors; , , i j k , , ijk are the unit vector in the positive directions of the axis of a Cartesian coord. 1 2 3 [, , ] aaa a a a  ai j k [1, 0, 0] i , [0, 1, 0] j , [0, 0, 1] k Position vector r with coordinate system [ , , ] xyz x y z ri j k Basis , , Components , , Representation position vector r Space Time vector in fluid motion ( , , , ) ( , , , ) ( , , , ) ( , , , ) xyzt  uu ij k u v uv w v w w i j k r  :, , Px y z
Background image of page 4
Vector Differential Calculus 1. Vector Algebra in 2-Space and 3-Space 1.6. Vector Space 3 R Linear combination of a and b 12 cc ca b Linear combination of given vectors (1) (2) ( ) ,, , n aa a 1( 1 ) 2( 2 ) () nn c  a and if and only if the only solution of 1 ) 2 ) c a0 is 0 n c   , then the given vectors (1) (1) ( ) , n a are called “ linearly independent ”. Let C divide by BA in : ( 1 ) If midpoint, 1/2  11 1 2 ) (1 ) 0 OB OA c c c   cb b ab a b bc a b 1 0  Any three vectors with common origin be on a straight line lmn  c0 0  with 22 2 0 .
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/27/2011 for the course CHEM 101 taught by Professor Suh during the Spring '11 term at University of Toronto.

Page1 / 55

Ch_03 - Vector I - Summary - Chapter 3 Vector Differential...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online