Maths - Partial Differentiation

Small Increments:

If z=f(x,y) then d z = ∂ z d x + ∂ z d y
∂ x ∂ y

Rates of Change:

We can express the above expression as a rate of change with respect to some extra dimension 't'.

d z = ∂ z d x + ∂ z d y
d t ∂ x d t ∂ y d t

Implicit functions:

Or if we use one of the existing dimensions such as 'x':

d z = ∂ z + ∂ z d y
d x ∂ x ∂ y d x

Change of variables

Or we can change to a new set of variables (u,v):

∂ z = ∂ z ∂ x + ∂ z ∂ y
∂ u ∂ x ∂ u ∂ y ∂ u

 

∂ z = ∂ z ∂ x + ∂ z ∂ y
∂ v ∂ x ∂ v ∂ y ∂ v

 


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cover us uk de jp fr ca Schaum's Outline of Theory and Problems of Tensor Calculus - I'm finding this hard going, it starts off with as review of linear algebra, matrix notation, etc. It redefines a lot of conventions which are hard to relearn, such as superscrips instead of subscripts to identify elements, and a summation convention, then it goes into coordinate transformations. I cant find any definition of what a tensor is. I think this book is aimed at people who already have some knowledge of the subject.

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