A Sense of Doubt blog post #2599 - 2017 HEY MOM Reprint - Studying Calculus

A Sense of Doubt blog post #2599 - 2017 HEY MOM Reprint - Studying Calculus

This is what I was doing on this day five years ago. I was studying for a calculus test.

So as I often do, I went back and grabbed THIS DATE from a prior year. I reviewed and noticed that I had not pulled from 2017 very often.

And so...

The study rooms in SANGREN at WESTERN MICHIGAN UNIVERSITY were awesome.

I miss those rooms.

I would often make musical mixes when I was studying there, though probably not when studying for a test.

Wow. Seems like another lifetime ago.

Here's today's reprint. Thanks for tuning in.

Blog Vacation Two 2022 - Vacation II Post #36

I took a "Blog Vacation" in 2021 from August 31st to October 14th. I did not stop posting daily; I just put the blog in a low power rotation and mostly kept it off social media. Like that vacation, for this second blog vacation now in 2022, I am alternating between reprints, shares with little to no commentary, and THAT ONE THING, which is an image from the folder with a few thoughts scribbled along with it. I am alternating these three modes as long as the vacation lasts (not sure how long), pre-publishing the posts, and not always pushing them to social media.

Here's the collected Blog Vacation I from 2021:

Saturday, October 16, 2021

A Sense of Doubt blog post #2433 - BLOG VACATION 2021 COLLECTED

ORIGINALLY PUBLISHED IN:

Friday, March 31, 2017

Hey, Mom! Talking to My Mother #633 - Studying Calculus - Exam #2

Hey, Mom! Talking to My Mother #633 - Studying Calculus - Exam #2

Hi Mom,

Studying for a Calculus test that I have today at 1 p.m.

These pictures are from my study session yesterday.

Up top, that's music by Brian Eno on the monitor. I included the video below.

The other picture has James Blake music playing, just FYI.

I work on my Musical Mondays posts while I study.

I am not sure how well I will do on this exam.

But the good news is that I have improved a great deal in the last two years.

I passed the second mastery test last week on the first try. I conquered those limits and derivatives.

This week's test is worth more points and is over not just derivatives but applying that knowledge to real work problems: analyzing functions, optimization, related rates, and so on.

A good take away is that when I made my study guide I went back to the problems that scared me the most in my first run of Calculus, the one right after you died, when I took a hardship withdrawal. I came up against problems in that course by exam #3 that I could not even begin to fully understand let alone complete correctly. So I put those problems on my study guide practice exam, and guess what? They are actually pretty easy.

I would say "wish me luck," Mom, but I don't need to. You're right here with me. All the time.

Thanks.

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Reflect and connect.
Have someone give you a kiss, and tell you that I love you.
I miss you so very much, Mom.
Talk to you tomorrow, Mom.
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- Days ago = 635 days ago
- Bloggery committed by chris tower - 1703.31 - 6:39

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- Bloggery committed by chris tower - 2203.31 - 10:10

- Days ago = 2463 days ago

- New note - On 1807.06, I ceased daily transmission of my Hey Mom feature after three years of daily conversations. I plan to continue Hey Mom posts at least twice per week but will continue to post the days since ("Days Ago") count on my blog each day. The blog entry numbering in the title has changed to reflect total Sense of Doubt posts since I began the blog on 0705.04, which include Hey Mom posts, Daily Bowie posts, and Sense of Doubt posts. Hey Mom posts will still be numbered sequentially. New Hey Mom posts will use the same format as all the other Hey Mom posts; all other posts will feature this format seen here.

Hey, Mom! Talking to My Mother #983 - Pi Day (a day later) - Review - Calculate Pi

Colorado Rockies - 3/14/2017 - calculate Pi to... well that's a lot of digits ...

Hey, Mom! Talking to My Mother #983 - Pi Day (a day later) - Review - Calculate Pi

Hi Mom,

I am working on a longer post charting my trip last weekend with Liesel, but it's not done yet. I took the time to copy over all this text and the imagery from WIRED that provides a nice review of how Pi is calculated, which is something I was doing just a year ago.

How did I have time to go to a class almost every day plus teaching two additional courses in Michigan? Are days longer there? Or isn't the time a constant, like Pi, but rather there's some change in how I use it? I still do not have this issue sussed, but like sussing Pi, it's a work in progress.

That's the thought for today.

Now, calculate Pi.

Oh yeah, and the picture up top. I had this from last year as the Colorado Rockies worked out Pi to, well, a lot of digits. I never shared the photo but isn't it cool?

FROM - https://www.wired.com/story/this-pi-day-calculate-the-value-of-pi-for-yourself

• RHETT ALLAIN
• SCIENCE
• 03.14.18
• 12:00 AM

THIS PI DAY, CALCULATE THE VALUE OF PI FOR YOURSELF

ROBERT GRESHOFF/GETTY IMAGES

IT IS ONCE again Pi Day (March 14—which is like the first digits of pi: 3 and 14). Before getting into this year's celebration of pi, let me just summarize some of the most important things about this awesome number.

• Outside the US, Pi Day should probably be July 22 (22/7)—this fraction is a surprisingly good estimate of pi.
• You can find the value of pi with a mass and a spring.
• The value of pi is related to the local gravitational field.
• You can find the value of pi using random numbers (this one is my favorite).
• And finally—there is a relationship between pi, e, 1, 0 and i (the imaginary number).

But today, I am going to calculate pi with a numerical integral. What does that even mean? Let me start with an example—how do you find the area of a half-circle?

The area of a circle is pi times the radius squared. This is half of a circle with a radius of 1 (no units) such that it would have an area of pi/2. If I find the area with some other method, I can just multiply this area by 2 and get pi. That's the plan.

But how do you find the area of some shape—or any shape for that matter? This is where calculus comes in handy. I can find the area of the half circle by adding up the area of a bunch of rectangles. It turns out that it's pretty easy to find the area of a rectangle. Let me just draw a few rectangles in that half-circle so you can see what I mean.

The area of each of these skinny rectangles can be found with the formula "base times height." A rectangle has a height of "y" and a base of "dx" where the dx is just some arbitrary length along the x-axis. I can find the actual value of the height because the top of the rectangle hits the circle where this height can be found from the equation of a circle.

Now I just need to add up all these rectangles—boom, that's the area of half a circle. I can write this as a sum of areas like this:

But wait! Isn't this a poor approximation to the actual area of a circle (half-circle)? Yes, that is indeed true—but it really depends on the width of these tiny area rectangles. In fact, if I take the limit as the width (dx) goes to zero then I will get the exact area. This is actually the definition of the integral in calculus—but I will save that for another day. Instead we will do a numerical calculation by simply adding up the area of a bunch of rectangles. You could of course do this by hand—but it might get boring. Instead, let's do this with a computer program. Yup.

Here is numerical calculation in python. You can go ahead and run the code by pressing the "play" button, but I will give some code comments below.

You can change the code if it makes you happy—here are a few things to consider.

• This is a numerical calculation. That means the program only deals with numbers. Technically, the area should have units of m2 or something like that but not here. Only numbers.
• For loops in python, it includes everything that is tab-indented as part of the loop. Once you dedent, it's no longer in a loop.
• Line 18 should look weird because it is. If you consider this to be an algebraic equation, the A should cancel since it is on both sides of the equation—but this is not an equation. In python (and most other languages), the "=" means "make equal to". This line takes the old value of A, adds the new stuff and then makes it the new value of A.

This initial calculation has a dx of 0.1. That means there will be just 20 rectangles to add up and get the area of the half-circle. With this, I get an approximate pi value of 3.10452—which is clearly not exact pi. Of course I can make a better estimate by making smaller width rectangles. You should try this by changing the code above (hint: change the value for dx). However, since I can't let this go here is a plot of the value of pi for different step sizes.

Perhaps that's not the best plot—but it's good enough for now. If you want to check out the code for this plot, here you go. But in the end, the value does approach the expected value of pi. This method might not get you one million digits of pi, but maybe you at least can learn something about integration.


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Reflect and connect.

Have someone give you a kiss, and tell you that I love you, Mom.

I miss you so very much, Mom.

Talk to you tomorrow, Mom.

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- Days ago = 985 days ago

- Bloggery committed by chris tower - 1803.15 - 10:10

NEW (written 1708.27) NOTE on time: I am now in the same time zone as Google! So, when I post at 10:10 a.m. PDT to coincide with the time of your death, Mom, I am now actually posting late, so it's really 1:10 p.m. EDT. But I will continue to use the time stamp of 10:10 a.m. to remember the time of your death, Mom. I know this only matters to me, and to you, Mom.

Hey, Mom! Talking to My Mother #658 - Calculus Final Exam Today! (F'(x) = musical accompaniment)

Hey, Mom! Talking to My Mother #658 - Calculus Final Exam Today! The Fundamental Theorem of Calculus (F'(x) = musical accompaniment)

Hi Mom,

The final FINAL studying.

But unlike you, I do not shut myself in the bathroom with no windows with the fan on. :-)

Here's some of what I am studying and the music accompaniment.

More content tomorrow, though it's gonna be a week that's light on original content.













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+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Reflect and connect.

Have someone give you a kiss, and tell you that I love you.

I miss you so very much, Mom.

Talk to you tomorrow, Mom.

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

- Days ago = ## days ago

- Bloggery committed by chris tower - date - time

NOTE on time: When I post late, I had been posting at 7:10 a.m. because Google is on Pacific Time, and so this is really 10:10 EDT. However, it still shows up on the blog in Pacific time. So, I am going to start posting at 10:10 a.m. Pacific time, intending this to be 10:10 Eastern time. I know this only matters to me, and to you, Mom. But I am not going back and changing all the 7:10 a.m. times. But I will run this note for a while. Mom, you know that I am posting at 10:10 a.m. often because this is the time of your death.

Hey, Mom! Talking to My Mother #633 - Studying Calculus - Exam #2

Hey, Mom! Talking to My Mother #633 - Studying Calculus - Exam #2

Hi Mom,

Studying for a Calculus test that I have today at 1 p.m.

These pictures are from my study session yesterday.

Up top, that's music by Brian Eno on the monitor. I included the video below.

The other picture has James Blake music playing, just FYI.

I work on my Musical Mondays posts while I study.

I am not sure how well I will do on this exam.

But the good news is that I have improved a great deal in the last two years.

I passed the second mastery test last week on the first try. I conquered those limits and derivatives.

This week's test is worth more points and is over not just derivatives but applying that knowledge to real work problems: analyzing functions, optimization, related rates, and so on.

A good take away is that when I made my study guide I went back to the problems that scared me the most in my first run of Calculus, the one right after you died, when I took a hardship withdrawal. I came up against problems in that course by exam #3 that I could not even begin to fully understand let alone complete correctly. So I put those problems on my study guide practice exam, and guess what? They are actually pretty easy.

I would say "wish me luck," Mom, but I don't need to. You're right here with me. All the time.

Thanks.

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Reflect and connect.

Have someone give you a kiss, and tell you that I love you.

I miss you so very much, Mom.

Talk to you tomorrow, Mom.

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

- Days ago = 635 days ago

- Bloggery committed by chris tower - 1703.31 - 6:39

Hey, Mom! Talking to My Mother #604 - Calculus Video Resources part one

Hey, Mom! Talking to My Mother #604 - Calculus Video Resources part one

Hi Mom,

Guess what?

I have video homework.

I think a lot about your own studies and what it would be like for you if you were in school now. You were such an over-achiever. I use you as my standard for excellence. I can never do as much homework as you did. The way you listened to recorded lectures multiple times, the way you re-copied notes multiple times, all the extra work you did with work books and whatnot. I can only imagine how amazing it would be if you could look at videos, too. Wow.

My teacher ha asked for additional videos for Calculus and why they were helpful for which she will award some extra credit.

How about this? I added a few extra here on this page plus all those she shared. I will continue to share extra ones in future blog entries.

I like videos especially for problems like the optimization and related rates problem. I just watched a related rates video and was impressed with the mnemonic for related rates work: DREDS: diagram, label rates, find equation, take derivative, substitute specific information.

I also liked the tricks for memorizing the unit circle, which I had already worked on with a tutor.

I have watched most of these videos, but I have created this entry so I can make sure I watch them all and maybe more than once. I would like to find more examples.

But my professor asked for extra videos on the chain rule.

I like KHAN Academy quite a lot. I have referenced its services quite a lot for many different problems and math issues.

KHAN ACADEMY

KHAN ACADEMY ON YOU TUBE

So, my first example is Khan. It has great graphics and the explanations are clear and easy to understand.

Is the power of videos that people would rather watch videos to learn than to read the text book?

I am old school, so I still like the text books, but I may be a dinosaur.

Presentation is everything. So I also like Math BFF. Good presentation and nice scripting. Good graphics. I like the writing on a the camera lens effect. I wish I could make a video that looked like that.

I also like that Math BFF's Nancy did a good wrap up at the end with a "quick quiz." She closed with a trig problem. Nice. :-)

I like Math BFF's presentation. I also like that she explained when you do and do not need to use the chain rule. This is similar for when to use the Quotient rule and when not to use it. I was discussing with my tutor Anthony on how we both try to turn quotients into products to avoid the quotient rule, but his mnemonic -- BDT-TDB/B^2 -- makes it easier for me to remember.

I plan to watch more. These are my two go to choices - Math BFF and Khan Academy.

That's all for today, Mom. Lots of studying, and I plan to do tons of chain rule over spring break and catch up on homework I missed.

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CHAIN RULE VIDEOS






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Here's another example of a video from Khan Academy, Mom.



So, I made a playlist for all the video resources posted by my professor, Doctor Koelling. It's here:

YOU TUBE PLAYLIST FOR CALCULUS RESOURCES KOELLING

HERE'S THE VIDEO LINK (It's the same as the first video and in the listed videos below)





VIDEOS ORIGINATE
From video resources page in e-learning -- https://elearning.wmich.edu/d2l/le/content/253075/Home


WHAT IS A FUNCTION (part one)?





WHAT IS A FUNCTION (part two)?




Determining the Domain and Range of a Function




click for video - embedding disabled
HOW TO GRAPH A PIECE WISE DEFINED FUNCTION

❖ A Way to remember the Entire Unit Circle for Trigonometry ❖



Finding All Asymptotes of a Rational Function (Vertical, Horizontal, Oblique / Slant)




EQUATIONS OF LINES

Algebra 22 - Point-Slope Form



Click link for video - embedding disabled.

USING THE LIMIT DEFINITION TO FIND THE DERIVATIVE

FIND THE EQUATION OF A TANGENT LINE (part one)




FIND THE EQUATION OF A TANGENT LINE (part two)




Grit: the power of passion and perseverance | Angela Lee Duckworth





PLAYLIST OF VIDEOS FOR THE RULES OF DIFFERENTIATION - 14 VIDEOS TOTAL





Calculus - Finding the Derivative by the Definition 2



TRIGONMETRIC DERIVATIVES




VISUALIZATION OF PRODUCT RULE FOR DERIVATIVES




CHAIN RULE



PRODUCT RULE WITH CHAIN RULE AND FACTORING




Derivatives - Quotient and Chain Rule and Simplifying



DERIVATIVE OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS PART ONE




DERIVATIVE OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS PART TWO




DERIVATIVE OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS PART THREE





DERIVATIVE OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS PART FOUR




IMPLICIT DIFFERENTIATION



LOGARITHMIC DIFFERENTIATION - 1



LOGARITHMIC DIFFERENTIATION - 2



RELATED RATES -1




RELATED RATES -2



RELATED RATES -3



OPTIMIZATION-1



OPTIMIZATION-2



OPTIMIZATION-3

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+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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Reflect and connect.

Have someone give you a kiss, and tell you that I love you.

I miss you so very much, Mom.

Talk to you tomorrow, Mom.

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- Days ago = 606 days ago

- Bloggery committed by chris tower - 1703.02 - 10:10

NOTE on time: When I post late, I had been posting at 7:10 a.m. because Google is on Pacific Time, and so this is really 10:10 EDT. However, it still shows up on the blog in Pacific time. So, I am going to start posting at 10:10 a.m. Pacific time, intending this to be 10:10 Eastern time. I know this only matters to me, and to you, Mom. But I am not going back and changing all the 7:10 a.m. times. But I will run this note for a while. Mom, you know that I am posting at 10:10 a.m. often because this is the time of your death.