1. Continuum Mechanics (MTH487)
Lecture 2
Instructor
Dr. Junaid Anjum

2. Recap Notation : Summation Convention: Kronecker delta:
1. Scalar variables are written as italic letters
2. Vectors are written as boldface italics
3. SECOND and HIGHER ORDER TENSORS are designated by UPPERCASE FONTS. Additionally matrices are shown in calligraphic form to differentiate them from tensors
Summation Convention:
Kronecker delta:
Permutation symbol:

3. Recap
ε-δ identity :

4. Quiz…
Expand the following expressions
(b)

5. Quiz…
Expand the following expressions
(c)

6. Quiz…
Expand the following expressions
(d)

7. Quiz…
If and show that

8. Aims and Objectives Tensor Algebra Vector addition
Scalar multiplication
Scalar (dot) product
Cross product
Triple scalar product (box product)
Triple cross product

9. Tensor Algebra …. Vector addition Scalar multiplication
Dot (scalar) product

10. Tensor Algebra ….
Vector (cross) product

11. Tensor Algebra ….
The triple scalar product (box product)

12. Tensor Algebra ….
The triple cross product

13. Quiz… Write expressions for: Addition of vectors
Multiplication of a vector by a scalar
Dot (scalar) product of two vectors
Triple scalar product (box product)
Triple cross product

14. Solution… Write expressions for: Addition of vectors
Multiplication of a vector by a scalar
Dot (scalar) product of two vectors
Cross product of two vectors
Triple scalar product (box product)
Triple cross product

15. Quiz…
Let the vector v be given by where a is an arbitrary vector, and is a unit vector. Express in terms of the base vectors , expand and simplify.

16. Quiz…
Show that
(i) (ii)