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L01_Index___Summation_Notations

# L01_Index___Summation_Notations - CE507 Lecture 1 1 Index...

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CE507 Lecture 1 Index and Summation Notations 1. Index Notation The conventional Coordinate System (right-handed) will now be renamed as: A point ( ˆ ) xyz r ,, = becomes ( 123 ˆ ) xxx x The symbol “ i x "’ stands for 12 x x , or 3 x (i=1,2 or 3). 1 is the first (or ) coordinate 2 is the second (or ) coordinate 3 is the third (or ) coordinate ix iy iz = = = Figure 1. Coordinate Representation 1. Double Subscript : ij a will mean: 11 12 13 21 22 23 31 32 33 aaa 2. ij a is thus an element of the matrix 3. Triple Subscript : ijk a will now have the subscripts i, j and k all range from 1 to 3, or a total of 27 elements:

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2. Summation Notation An expression 11 1 12 2 13 3 ax ax ax + + or 3 1 ij j j ax = will be denoted by ij j . Convention: The repetition of an index (subscript or superscript) in a term will mean a summation from 1 to 3 w.r.t the repeated index. An index that is summed out is called a free dummy index.
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L01_Index___Summation_Notations - CE507 Lecture 1 1 Index...

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