When in doubt before a calculus test, take bomb selfies for a confidence boost

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When in doubt before a calculus test, take bomb selfies for a confidence boost

Scans from my little interactive calculus book :)

My flight got cancelled due to a raging typhoon, so I decided to whip out my past books and start studying for the math placement tests coming up. And here I thought that my days with the AP and SATS were over.

Helpful little study sheet. Follow @Studious-Steminist for more!

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“What do we do when we encounter double integrals? First, we cry. When we are done crying, we solve.”

—
Multivariable calculus professor

|| 6.21.15 || Trying something new with my calc notes. Not sure if I like it, but it was worth a try.

calculus gothic

-The limits keep getting farther and farther away. Where are they going? Where did they start? Will they ever stop?

-The unit circle tells us to bow before it. All hail the unit circle. All hail.

-You have been scribbling the integral symbol and the summation symbol for so long. You can’t write 3′s or capital S’s normally anymore. It is a reflex, muscle memory.

-Piles of math homework surround you as you become a machine, cranking out more math problems as you hone your skills. You build your own castle out of math homework. It is never-ending.

-Trigonometry rids us of our sins. and cosines. and tangents.

I don’t even math

**Boy:**I want to be a derivative so I can be tangent to your curves ;)**Girl:**I'm the Weierstrass function.

“Isn’t it refreshing not to use a calculator? Doing math by hand cleanses your spirit. It’s wholesome.”

—
Calculus professor

|| 7.6.15 || Wasn’t sure what to do with that empty space. Maybe I’ll doodle in it a little later…

We’re allowed to use a cheat sheet for tomorrow’s calculus exam. Enough said.

The Gaussian Integral is a beautiful integral for which the area between the e^(-x^2) and the x-axis from negative infinity to positive infinity perfectly equals the square root of pi. Image sources: 1, 2.

Mathematics = beauty.

“Feel the algebra. Feeeeeel the algebra.”

—
Calculus teacher

|| 6.15.15 || Early morning calculus, still going over the very basics, continuity and vertical and horizontal asymptotes.

reviewing some calculus basics… the book calculus for dummies is great so far!

This is my favorite setup for studying for a calc exam. I use an HDMI cord to turn the TV into a second monitor which I use for Khan Academy and other video tutorials. I typically have my textbook open on my laptop screen for examples and problems to try out. I use the coffee table as a desk and will use a couch cushion as a seat if the floor gets too uncomfortable!

** The exponential function** is more complicated in the complex plane. On
the real axis, the real part follow the expected exponential shape, and
the imaginary part is identically zero. However, as the imaginary part
changes, the exponential varies sinusoidally, with a period of 2π in the
imaginary direction.

In this plot, you can see the main branch on the real axis (*y*=0), and part of each branch on either side. This plot runs from -2π..2π in the y-direction and from -3..3 in the x-direction. Diagram of the real part of exponential function in the complex plane. The surface is given by:

The colour in the density plot (right) runs from red (large negative values), through green (nearly zero) to blue (large positive values) Please note that the this colour scheme is non-linear (it is based on the Arctan function and therefore emphaseses changes near zero more), and thus a given change in hue does NOT necessarily reflect a similar change in value, although at the same magnitude, the changes should be identical. Diagram of the real part of exponetial function in the complex plane, as the operand approaches infinity. The plot is given by:

The plot below shows the absolute value of the real part as the operand approaches infinity:

The colouring of the density plots is different to the graphs above. It runs from green (small), through blue and red to yellow (large). It is highly non-linear and changes near zero give a larger hue shift than large values.

The plot below shows the imaginary part of the exponetial function as the operand approaches infinity. This plot is given by:

Note that the orientation of the surface graph below is different to provide a better view of the structure of the function.

The plot below shows the absolute value of the imaginary part as the operand approaches infinity:

The colouring of the density plots is different to the graphs above. It runs from green (small), through blue and red to yellow (large). It is highly non-linear and changes near zero give a larger hue shift than large values.