The calculation of the height of rocket as a function of time, t.

Given an equation that gives the height traveled by a model rocket as a function of time, finding the maximum height and the time corresponding to the maximum.

model rocket

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Partial Derivative Problems with Solutions

Below are the partial derivative problems that I worked out.  Some we did in class and some were homework.  Just remember that if you take a derivative with respect to x, for example, all of the other variable are treated like constants.

partial deriv with solns

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Getting Ready for the Final

Much of this is a repeat of what I said in class, but in more detail and some changes.

H Calc guidance for Final  This is a revised edition at 11:30 pm, 5/3.

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Partial derivative hw with worked out examples

When a function is defined in terms of two variable, say x and y, you can assume one of them stays constant and see how the function changes when the other one changes.  That is called taking the partial derivative.

An example might be, if a company making a product has a profit that is simultaneously a function of labor costs and material costs, sometimes it is beneficial to analyze the profit to see how the rate of change of profit varies with the changes of each of the variables separately.  This could answer the question, for example,: “Assume the cost of the materials stay constant, how would the profit vary with the change in labor costs.”

The variable that is assumed to stay constant is treated like a regular constant when taking the derivative “with respect to” the other variable.  See some worked out problems in the following two links to further clarify this explanation.  Note the special symbol used to denote the Partial derivative.

partial deriv probs pg 1

partial deriv pg 2

Do the odd numbered problems for homework.

partial deriv hw 4 19 16

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Benoit Mandelbrot and Fractals

In class we saw a YouTube, “Hunting the Hidden Dimension,” a NOVA special on Fractals.

I am including the link so that those who missed the video will be able to make it up.  There will be up to 10 points on the final based on this video.   The video presents ideas of mathematics unlike anything you’ve learned in any math course, and gives a glimpse of where math and science is headed.

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HW 4/13

Do the two problems for homework, understanding that for the first one you need to find the volume of rotation, and the second one, you only have to evaluate an integral– old stuff.

hw 4 13 16

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Volume of rotation 4/12/16

Classwork:  vol of rotation 4 12 16

Homework:  HW 4 12 16

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