Hamman’s Study Diary

March 16, 2007

Limits and partial derivatives

Filed under: MAT 211, Spring 2007 — Hamman @ 4:04 pm

Today we got into finding the limits of functions having two variables (functions having many approaches to values other than the number line approaches from the left or right) That is, we now get into limits of graphs in 2-D and 3-D!

Then we were introduced to partial derivative, their notations, and examples/methods on how to compute them.

We finished off with second-order partial derivatives and mixed derivatives.


Heat reservoirs and isometrics

Filed under: PHY 106, Spring 2007 — Hamman @ 1:24 pm

We learnt about heat and cold reservoirs. The main topic was the derivation of the formula for work done by a gas. Plus we touched on the Ideal gas equation, and some different isometrics involved in the gas equation.

  • Isobaric
  • Isovolumetric
  • Isothermal
  • Adiatic
  • Free expansion
  • Cyclic

We also learnt about a new kind of differentiation coming from path-dependant quantities, that would be different from path-independant ones.

A new look at the domain of a function

Filed under: MAT 211, Spring 2007 — Hamman @ 8:09 am

Yesterday, we started off into the abstract world of 4-space.

The idea is that the domain of a function in 1 variable is actually a number line, or a linear graph. The domain of functions with 2 variables can be thought of as curves, and 3 variables as surfaces.

We then move into level surfaces (sort of like contour maps), a fascinating look at how the domain of a 4-space function can be represented by 3-D curves and surfaces! Amazing!

So at least we can represent 4-D functions in terms of their domains, just as we can represent the domain of 3-D functions using level surfaces, and then think about the z-dimension separately.

Image source: http://en.wikipedia.org/wiki/Fourth_dimension

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