Here a Field, There a Field, Everywhere a Field Field

Only one day into the past, which doesn’t even call for the time machine, really. Just a time jump. Oh, you don’t know how to do that? Pity. *wahoo!*

This morning started out great with the first half of the chapter on Partial Differentiation. I’ve always liked partial derivatives. They almost feel like cheating, right? Like you have this whole mess of an equation with a million variables but…we’ll just ignore them all and only deal with one! Mwahaha. So it was a genuine pleasure to work through these sections. Even the one on changing variables that took me three pages of looseleaf and numerous cross-outs to work through.

The afternoon was not quite so great. For one, I didn’t get started until pretty late. You wouldn’t think I’d be so busy, being unemployed and all, but the days really do get away from me. By the time I went for a run and made lunch and washed dishes and so on and so on, it was already late afternoon. And my boyfriend and I were planning to go to a baseball game (free tickets since it was Military Appreciation Night, and we got vouchers for free hot dogs), so I had to knuckle down and get to work. And of course I had given myself three chapters that totaled over 90 pages: Magnetic Induction, Alternating-Current Circuits, and Maxwell’s Equations and Electromagnetic Waves. The magnetic induction material was especially long and took me a lot of effort to power through. I get frustrated sometimes trying to think through these problems. One moving charge creates a magnetic field which changes and induces an electric field which causes charges to move and create magnetic fields…okay, I know it’s really not that hard, but it just takes a lot of focus. By the time I got to poor Maxwell I couldn’t even be properly excited about him putting everything together!

But luckily I finished just in time to head out for the baseball game. (The Riverdogs won!)

Today’s fun “new” fact: Flux is quantized, and the small unit of flux is called a fluxon. That just sounds like some mad-scientist shit right there.

I Just Want to Feel Attractive Today

And now we have only a short hop back to Tuesday, June 13. That’s practically today. Tuesday, Thursday, who can keep track of all the T days? *doo-doot doo-doot*

Today I took a break from the mind-bending math but continued with good ol’ Tipler and Mosca. After the lengthy chapters on Monday, I ended up with a short pair of chapters today on The Magnetic Field and Sources of the Magnetic Field. I probably could have balanced this out better when I was making my schedule for the week, but I was just going based off a chapter list. In any case, these were interesting chapters. I especially liked that there was a good section about some practical applications of very basic magnetism concepts—velocity selectors, mass spectrometers, etc. Also I got a chance to look like an idiot at my desk by constantly doing the right-hand rule as I followed along with examples in the text. Good thing I study at home alone!

After the magnetic chapters on magnetism, I picked up with my Codecademy course on Python. Progress has been slower here than I like, but as the lessons are getting a little more complex, they take more time and brainpower, hence slower progress. Still, the end is in sight. I got to play around with creating mathematical functions, which actually felt useful (even though these are actually built in to Python), and got to start on “advanced” topics. Nothing too crazy, but it’s starting to feel a little more natural to get the code down. I also spent five minutes debugging something that turned out to be a single misplaced indent. Oops!

Today’s fun “new” fact: Two straight wires carrying parallel currents will attract each other due to their generated magnetic fields. And in fact, this attractive force is how the SI unit ampere is (currently) defined! The coulomb is then reverse-defined from the ampere.

Photo by Guy vandegrift / CC BY-SA 3.0

Everybody to the Limit

Okay, now we’re only jumping back in time to Monday, June 12. So long ago that was! The main news story was Trump’s bizarre Cabinet meeting. Ah, the good old days. Anyway… *bleep bloop blorp*

After a nice, relaxing weekend, I was ready for Monday morning, even though it brought the remaining sections of the Series and Limits chapter. I was a little worried, but it ended up being not nearly as strenuous as the first part of the chapter. What a relief! I got to practice convergence/divergence tests and practice taking limits. I finished pretty early in the morning and had plenty of time for my lunch break. Which ended up being most of the day, as I decided to make a layer cake for my boyfriend. It was delicious and time consuming! And I didn’t return to my studying until late in the evening. But that’s the joy of setting my own hours!

Of course, if I had known how long my physics section would take, perhaps I would have not been so determined to finish. I had assigned myself three more chapters on E&M: Electric Potential, Electrostatic Energy and Capacitance, and Electric Current and Direct-Current Circuits. They weren’t overly difficult, but by 10 PM I was having trouble concentrating. But even if I had to read some of the paragraphs a few times before I really read them, I did get through it!

I got a lot of flashbacks to the first time I went through this material, back in my Electricity and Magnetism I class my sophomore year of college. Our instructor was the most cliched version of a physics professor, with the big gray/white afro and same 2 ties in rotation and so many bad jokes about the subject matter. He always called one the “loneliest number” (a reference I didn’t get until years later) and referred to hippopotami that carried charges between the plates of a capacitor (an analogy that never made sense, but I guess it worked since I still remember it over ten years later!). Ah, Professor Korman. Hope he’s still puzzling the kids and telling bad physics jokes over at USNA.

Today’s fun “new” fact: Another math one today, but I couldn’t resist. I actually exclaimed out loud when I saw “L’Hôpital’s rule!” Because it’s so fun to say, of course, and because I had totally forgotten about it. It’s a simple and wonderful trick that allows you to take a limit of functions that tend to 0/0 or ∞/∞. You just take their derivatives and voila! It’s like magic. Except it’s math.

Photo by Papa November / CC BY-SA 3.0

She is Electric, Can I be Electric Too?

Oh, crap! I realized yesterday that I was getting woefully behind on my blogging. The good news is that it is not because I’m behind on my studying. I thought about just skipping ahead to today, but I’m really trying to document this journey. So let’s play catch-up, shall we? We’ll just hop into my time machine (patent pending) and travel back to last Friday, June 9. *insert appropriate science fiction bleeps and bloops*

Today I got to start on Volume II of Tipler & Mosca! That’s a pretty big milestone. It’s also a much less-used book, as I believe that we didn’t use this as our primary text for some of the topics it includes. In any case, today I got started on E&M with The Electric Field I: Discrete Charge Distributions and The Electric Field II: Continuous Charge Distributions. This is pretty interesting info, getting into some trickier math and less-pretty equations, and setting up the basic concepts that will (spoiler!) later lead to culmination in Maxwell’s equations. Field points have always tripped me up, but this time around I think I have a pretty good feel for it.

I started on the Series and Limits chapter in Mathematical Methods, and it was not a fun journey. I had assigned myself four sections and they took forever to get through. I’ve never been the best with series (I think my pattern recognition is subpar) and working through these examples was frustrating. It didn’t help that I was acutely aware that it was Friday afternoon and my brain was ready for a break after a long week of studies. But I kept with it and did get through every problem, teasing out the correct reasoning and applying it properly. That was good! As frustrating as it was, I feel like I actually made some concrete progress with my mathematics skills.

Another week of books in the books! I’m speeding through basic physics and the calendar is speeding by at an alarming rate, but I’m ready to think about something else for a day or two before diving back in on Monday.

Today’s fun “new” fact: It’s a fun party trick to be able to add a huge amount of numbers together, and I had forgotten the simple formula to do so. But it’s easy! The sum of the first N positive integers is N/2*(N+1). You can check out this site (or Google) for more details on the derivation.

Why’d You Have to Go and Make Things So Complicated?

Phew, what a day! My boyfriend is out of town and I managed to keep myself so busy that I missed dinner and started crying while out on my evening walk. I got a lot done, though!

Today’s studying finished out the chapter on complex numbers in Mathematical Methods. It got into hyperbolic functions, and I had some fun showing some of the hyperbolic function identities and inverses. I also got to practice more manipulation and using de Moivre’s theorem, so it was a good session. Plus the hyperbolic function names are so much fun to say, even if only in my head. Kosh! Cinch! Tanch!

I also returned to my Python course at Codecademy today. I got into the more advanced part of the course where they just give you a prompt (Define a function that will calculate a Scrabble score, given this dictionary of letter values!) and a blank (or mostly blank) script editor and send you on your way. Definitely frustrating at times but a better way to learn. I had one memorable moment where I spent a good ten minutes trying to figure out why my perfectly set up code wouldn’t work only to finally realize that I had tried to increment with =+ instead of +=. Ahh, coding. I didn’t get quite as far as I had expected—only 10% progress to 71%—but since it was very productive I don’t mind.

I missed getting into the physics today, though, and I am looking forward to cracking open Volume II of Tipler and Mosca tomorrow!

Today’s fun “new” fact: The main hyperbolic function identity is just slightly different than that of the main trigonometric identity! On the one hand: , and on the other: !

We’ve Got a Big Big Mess on Our Hands Tonight

Good morning! I should have written this post yesterday, but my laptop battery ran out and I was too lazy to go charge it (the charging cord is upstairs, very very far from my couch!). But here we are now, time for a quick recap of yesterday’s work. It was a good day of studying. I actually finished quite early and had enough time on my hands to start consuming A Series of Unfortunate Events, which has been sitting in my to-watch list forever.

I got through another two chapters in Tipler and Mosca: The Second Law of Thermodynamics and Thermal Properties and Processes. This was a pretty big milestone, because not only did it complete Part III (Thermodynamics), but it also completed Volume I! That’s right, tomorrow I am on to Volume II where more of the fun resides. That made me feel pretty good, especially because after Tipler and Mosca I am going to dive into BoB and I am super excited for that!

One of the things I really enjoyed about this section was the various statements of the second law of thermodynamics. This text included five—the Kelvin statement, the heat-engine statement, the Clausius statement, the refrigerator statement, and the entropy statement. Here we have this fundamental law of nature, and we have all these different ways of trying to express and get at the underlying truth. To me, this kind of goes back to the debate of whether mathematics (and physics) are created or discovered. Not something I propose to answer (I’m not the philosopher in the family!), but something I find interesting to think about.

After the physics, I got to dive into some math. As I’m getting a little farther in the Mathematical Methods text, I’ve broken down my studying into sections (not trying to do a whole chapter at once) and I’ve started actually working through the in-line examples. It was fun to break out pencil and paper and get to work! I even got to bang my head against the wall of trigonometric identities and simplifying functions. I’m on the third chapter, focused on complex numbers, and did the sections on introducing complex numbers, manipulation of complex numbers, polar representation, and de Moivre’s theorem. Complex numbers are amazing. I remember being blown away the first time I learned that we could just assign an imaginary component to deal with a thorny issue (in this case, the square root of -1), and that it opened up a whole new world of math. It’s still pretty amazing to me today.

Today’s fun “new” fact: The entropy of the universe is constantly increasing ahhhh! Okay, so I didn’t actually forget this one, but for some reason reading about it always sounds vaguely ominous. Energy becomes unavailable to do work! It’s irreversible! Disorder is inevitable! Panic!

Just kidding! As the late great Douglas Adams would say, don’t panic. 🙂

It’s Getting Hot in Here

I had a busy day today! I spent the morning working on my Python course over at Codecademy. I finished going through the “review” material from when I previously completed the first few lessons and got into new stuff–which meant actually writing code! That was exciting. I made a (very rudimentary) Battleship game, and it worked with only a few issues to be debugged, so good for me. I’m at 61% through the course now, so a couple more sessions should finish it up.

After a busy interlude of running errands and finally getting to the gym for the first time in weeks, I dove back into Tipler and Mosca. I’m on to Part III now, and I covered the first two chapters: Temperature and the Kinetic Theory of Gases and Heat and the First Law of Thermodynamics. This is pretty familiar territory for me, since thermodynamics composed a large part of my Navy nuclear studies, but it’s also a somewhat tricky topic. Will I ever understand the equipartition theorem on a deep level? Ah, well, I shall have to be content with being semi-able to apply it for now.

Had a talk with my boyfriend this afternoon about whether I’m overdoing it or worrying too much about being prepared for school. I know he is a bit surprised I’m not relaxing more during my time off, but I think this is important. My fellow incoming students are all bright people (will admit I initially typed “kids” there), coming right out of undergrad, from prestigious universities. I was pretty good at physics back in my day, but the rust from the intervening years is very, very real. I want to be able to do quality research as soon as possible, and that means having the basics down, not struggling to remember the zeroth law of thermodynamics. I don’t think I will regret any of my self-study. Besides, I enjoy it!

Today’s fun “new” fact: The rms speed of hydrogen molecules is about 17% of the earth’s escape speed (11.2 km/s), which is (simplistically) why the atmosphere doesn’t retain hydrogen. The molecules eventually all just rocket off into space! This is a sort of duh fact, but one I hadn’t thought about in a while, and I think it is very cool. It’s also hugely relevant for me, as planetary atmospheres is a big component of the exoplanet field right now!

Photo by Cmglee / CC BY-SA 3.0

The Hills Are Alive (With the Sound of Music)

Happy Monday! I must say, it is wonderfully pleasant to have a busy Monday doing things that I actually care about to look forward to. Also apparently, when left to my natural rhythm, I need about 9 hours of sleep. Zzzz. Perhaps this will decrease as I become fully rested, but perhaps not.

Today I set for myself three chapters to study: Oscillations, Traveling Waves, and Superposition and Standing Waves. This was pretty ambitious, honestly. It’s the entire Part II of this book! But I got through it all, and it makes sense. I hit this pretty hard when studying for the pGRE, so I feel relatively comfortable with the material presented. There are a lot of interesting practical examples regarding music and musical instruments that are very interesting. Amazing how people came up with this stuff intuitively/through trial and error long before we could show the principles behind what is happening in even a relatively simple instrument!

I returned to Mathematical Methods today, and luckily this chapter went more smoothly than the last one. This was a re-introduction to calculus, covering derivatives and integrals. Weird that I find this easier to follow than the algebra chapter, but this is (as stated in the book) the kind of math most frequently found in physical sciences, so perhaps that is not surprising.

And I even had time to take a long midday break to go see Wonder Woman and buy exorbitant amounts of junk food at Sam’s Club with my boyfriend! What a nice Monday. =)

Today’s fun “new” fact: Okay, so this has mostly been about physics so far, but today I’m giving the honors to math. While I’ve always known in the back of my mind what a derivative is and how to derive one (hehe), if yesterday you’d asked me to do it, I might have flailed a little. But it’s really actually simple to show, for example, the derivative of a simple power function. For f(x)=x2, take the limit as ∆x approaches zero of [f(x+∆x)-f(x)]/∆x.

((x+∆x)2-x2)/∆x

(x2+2x∆x+∆2-x2)/∆x

(2x∆x+∆x2)/∆x

2x+∆x

And as ∆x goes to zero: f'(x)=2x.

Fun!

Your Fingertips, Well They Know the Code*

Oops, a bit tardy getting this post up! Been having a little trouble self-motivating the past couple days, in fact, because I didn’t get my Friday chapters done until Saturday night. I have properly chastised myself, but I’m not too worried. I’ve given myself weekends off, so there is some flexibility in my schedule, and I did get it done eventually!

So Friday AM I scheduled myself to work on coding. I learned to code in Basic a long time ago, and I loved making little text games and mazes and such. While my skills are a little (a lot) outdated, it gives me a decent grounding in the mindset of coding. I also started doing a Codecademy course in Python about 2 years ago, although I only made it about halfway through. However, the general consensus on the best language to know for physics seems to be Python, so I’m revisiting the course. I spent Friday going back through the lessons I had already done to remind myself of the syntax and such. It was pretty simple, but it felt good to go through some basic lines of code.

Once I finish the Python course (I anticipate that being in the next week or so), I plan to check out a resource I found specifically for physics called Computational Physics by Dr. Mark Newman. Some of it is available for free on his site, so I will start with that. If it is a useful resource, I’ll purchase the full book and try to work through it. I think this will place me in excellent footing for the fall.

For my slightly delayed Tipler and Mosca studying, I had 2 chapters: Static Equilibrium and Elasticity and Fluids. I’m not going to lie, the fluids stuff was tedious. I am not sure why. Perhaps it reminds me too much of my Navy science experiences, or maybe it is just a weak spot for me. In any case, these two chapters brought me to the end of Part I! That was an exciting little milestone for me.

It was the first time that I found something I had written in my textbook. In general, I am not a big fan of writing in my books, but here I had made a small pencil note rewriting the equation for buoyancy to show the relation between apparent weight and weight. It was a small thing, but I was really struck by it. For one thing, it shows that this must have been something I kept getting mixed up for no good reason (hello, weak spot…), but for another it was a blast out of my past. I used this textbook for my first semester of physics, which was way back in the fall of 2006 (!). Could my past self have imagined that, over 10 years later, I would be poring over this book again, preparing myself to go back into physics? It’s a strange thought. It reminded me that I once wrote a vision statement–later, after graduating from college, after deciding I wouldn’t stay in the Navy–that placed me at MIT studying planetary science. And then I ended up turning that chance down! But for another awesome opportunity!

Anyway, it’s been an intro/retrospective couple days. I look forward to knuckling back down tomorrow and tackling some more math, physics, and blasts from my past.

Today’s fun “new” fact: The hydrostatic paradox. I understand why the pressure in a fluid is the same at any horizontal point, and water level is independent of container shape, but it’s still weird to see it play out.

*Today’s lyric title is a bit more obscure, but it comes from a song by one of my favorite bands (Jack’s Mannequin), so you should check it out!

Welcome to the Jungle

Well, I am back from Peru and ready to dive back in to some physics! Trekking the Andes was definitely not a rest for my body, but it was a nice mental break. Plus I got to do some practical application of the angle of repose while trying to decide if I could stand on a particular muddy slope! If you are interested in my Peru adventures, I will have a more detailed post over on my writing/lifestyle blog, The Write Side of Life. But for now, back to business!

The fall and school feel a lot closer now that the calendar has ticked over to June. I promised myself I would kick into high gear in June, and I got off to a good start today. I wrote myself a study schedule through next week, continuing with my Tipler and Mosca adventures while adding in some Python courses and Mathematical Methods for Physics and Engineering, 2nd Edition, by Riley, Hobson, and Bence. Ah, yes. This brick of a book. I thought that I would be able to sail blithely through the first couple chapters, which deal with introductory mathematics.

Silly me.

I forgot that this book is dense and difficult to read. This is not Tipler and Mosca, with bright colorful pages and fun facts and pictures. This is math. There are words, equations, proofs, diagrams, and so much knowledge in every paragraph. I don’t mean to slam on the authors, but this is not an easy book to follow. And I like math! I took an unnecessary semester of summer school just so I could take a Differential Equations class in college! But my brain wants to scream when getting hit with sentences like this in the very first section:

To take the most obvious example, comparison of the constant terms (formally the coefficient of x0) in the first and third expression shows that , or, using the product notation, .

It’s not even that it’s terribly difficult, it’s just hard to focus on and lots of panic begins to set in that I am hopelessly behind and will never be able to hack it in graduate school. I am a smart person, but eight years is a long time to have been out of school. No one has been asking me to factor polynomials in a very long time!

But math panic aside, it feels good to be getting right back into it with my studying. And on the physics side, today I did chapters on Relativity and Gravity, which are both interesting and mind-blowing topics. I love reading about things like time dilation. They seem so crazy and out there, but they follow implacably from a base set of tenets.

Today’s fun “new” fact: Clocks that are moving in parallel don’t show the same time! The clock that is in the lead lags by xc/v2. Synchronization goes out the window. For some reason, this boggles my mind way more than time dilation or length contraction on their own, although of course this is merely an extension of the same principles.