MTH623 Lessons 1-21 by Aziz Raaj

• The word tensor has its root tensus in Latin, meaning stretch or tension.
• J. W. Gibbs in (1884) developed the concept of dyadics (object with two parts or elements) and polyadics (an object comprising of many elements) which are actually tensors in modern sense but only different by names.

Why we need tensors?

• A scalar is a physical quantity that is represented by a number at a particular point in space. For example, mass, density and temperature.
• A vector is a tool to keep track of two pieces of information, typically magnitude and direction, for a physical quantity. For example position, force and velocity.

Why we need tensors?

In short: A scalar is a quantity whose specification requires just one number. On the other hand, a vector is a quantity whose specification requires three numbers, namely its components with respect to some basis. Scalars and vectors are both special cases of a more general term called a tensor.