16.21 Techniques of Structural Analysis and sig Spring 2003 Unit #2 -Mathematical aside: Vectors indicial notation and summation convention Indicial notation In 16.21 we'll work in a an euclidean three-dimensional space R3 Free index: A subscript index Oi will be denoted a free inder if it is not repeated in the same additive term where the index appears. Free means that the index represents all the values in its range Latin indices will range from 1 to, (i,j, k, . = 1, 2, 3), greek indices will range from 1 to 2,(a, B, y,...= 1, 2) Examples 1. ail implies a11, a21, a31.(one free index) 2. ayB implies 191, T132, 291, 2y2(two free indices) 3. ai; implies a11, a12, a13, a21, a22, a23, a31, a32, a33(two free indices implies 9 valu b=016.21 Techniques of Structural Analysis and Design Spring 2003 Unit #2 - Mathematical aside: Vectors, indicial notation and summation convention Indicial notation In 16.21 we’ll work in a an euclidean three-dimensional space R3. Free index: A subscript index ()i will be denoted a free index if it is not repeated in the same additive term where the index appears. Free means that the index represents all the values in its range. • Latin indices will range from 1 to, (i, j, k, ... = 1, 2, 3), • greek indices will range from 1 to 2, (α, β, γ, ... = 1, 2). Examples: 1. ai1 implies a11, a21, a31. (one free index) 2. xαyβ implies x1y1, x1y2, x2y1, x2y2 (two free indices). 3. aij implies a11, a12, a13, a21, a22, a23, a31, a32, a33 (two free indices implies 9 values). 4. ∂σij + bi = 0 ∂xj 1