Hamman’s Study Diary

May 8, 2007

End of Spring 2007!

Filed under: CIV 211, CSC 213, MAT 211, PHY 106, SEN 261, Spring 2007 — Hamman @ 2:44 pm

run “SPRING 2007  -terminate”

“The semester, she has ended”!

I just completed my last exam on Physics, and this marks the end of my semester. I hope to be more consistent in blogging my next semester here… Until then…

“Good night out there, whatever you are”

April 2, 2007

Last week Friday…

Filed under: MAT 211, Spring 2007 — Hamman @ 12:02 pm

Internet was down, so I couldn’t post Friday’s stuff…

We started section 6 of chapter 14

  • Directional derivatives
  • Gradients

March 28, 2007

Test yesterday

Filed under: MAT 211, Spring 2007 — Hamman @ 12:05 pm

It didn’t go well 😦

March 26, 2007

Chain rule

Filed under: MAT 211, Spring 2007 — Hamman @ 8:11 am

Last week Friday, we revisited the chain rule from Calculus II, bu this time extending it to 2-D and 3-D. We also learnt about the use of diagramming techniques in getting out a chain rule for multivariate functions.

March 23, 2007

Practice exercises

Filed under: MAT 211, Spring 2007 — Hamman @ 8:05 am

Yesterday, we did a lot of practice questions in class, very helpful for learning different techniques of solving 2-D and 3-D differentials. There was also some good news that the test coming up today will now take place on Tuesday!

March 21, 2007

Differentiation on more than one variable

Filed under: MAT 211, Spring 2007 — Hamman @ 8:20 am

We now moved naturally from limits to differentiation for two and three variables. Today, we covered topics on…

  • Differentiability of multi-variate functions
  • Differentials of multi-variate functions
  • Local linear approximations

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.

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

March 14, 2007

Test review and next chapter

Filed under: MAT 211, Spring 2007 — Hamman @ 8:31 am

We got back our test papers back from the mid-term exam. We went through solutions and corrections, and will now be getting into the next chapter on partial derivatives and 4-space! I love 4-space!

4-D Cube

Image source: http://www.geocities.com/CapeCanaveral/7997/

February 21, 2007

Arc length and parametrization

Filed under: MAT 211, Spring 2007 — Hamman @ 12:05 pm

Yesterday, we did a brief revision of arc length (from Calculus II), and then its representation in vector-valued functions. Then we were off to how to change parameters of a function.

  • Arc length
  • Smooth parametrization
  • Arc length of a parameter
  • Change of parameter
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