Implicit Function Theorem.wmv

The Implicit Function Theorem is discussed and proved using the local linear space of differentials. Here we discuss implicit functions defined by a function on R^3. This theorem is useful in the theory of Manifolds. It allows sub-manifolds to be defined and allows lower dimensional manifolds to be embedded in the original manifold M3. The equation of state in Thermodynamics defines an implicit function and a sub-manifold of a Thermodynamic state space. A simplified notation for partial derivatives is introduced and the three dimensional Taylor expansion formula and the implicit function formula are written in this new notation.

Category:

Education

Tags:

• Implicit
• Function
• Theorem
• Manifolds
• Equation
• of
• State
• Thermodynamics
• Linear
• Space
• Differentials
• Embedding
• Sub-Manifolds
• State.

[PianoOnDemand]

Thank you, there are not many online resources for Implicit and Inverse Function Theorems. Very well presented!

[crisis87]

Hi, what did you study to be able to understand these theorems?

[sk8hack]

I like the partial derivative notation, it gives a shorter representation