Memorization for Physics/Engineering

[phrontist]

So, I've just begun my second quarter of IBH Physics I, a class I've wanted to take since my age could be expressed with my fingers. I've also just picked up The Amazing "Pocket Ref", and while it will probably be able to supply me with all the constants and misc. figures I'll ever need, I'm thinking about tidbits worth memorizing. What does the CD community think worthy of memorization? Real Engineers: What have you actually bothered to memorize? Things that I've thought of flashcard-ing right now are:

• The IBH Physics Equation sheet (Duh)
• Gravitational Constant
• Avogadro's Constant
• Greek Alphabet
• Inches-Centimeters Conversion factor
• Trig Identities - Ah, but which should I really commit to memory? Which will really be useful in calculus? Which will be helpful in calculus?

I'm not just talking about things I need to memorize, but things that are handy to know.

Stock your mind, stock your mind. It is your house of treasure, and no one in the world can interfere with it... You might be poor, your shoes might be broken, but your mind is a palace! - Angela's Ashes

[Karthik]

Originally Posted by phrontist

Trig Identities - Ah, but which should I really commit to memory? Which will really be useful in calculus? Which will be helpful in calculus?

I've been a TA for first year Calculus for four years now. When in comes to Trig, there's very little that you actually have to memorize. Here's the musts.

• Your friendly triangles -- (1,1, root 2) & (1, root 3, 2)
• Your basic trigonometric ratios -- SOH-CAH-TOA, and the reciprocals
  • From these first two, you know calculate the values of any basic angles
• (Sin x)^2 + (Cos x)^2 =1

With a working knowledge of elementary geometry, you can derive everything else you'll ever need. But if you don't want to be doing that during a test, here's the next level of stuff you'll want to committ to memory.

• The double angle formulae for Sin and Cos
  • With the double angle formulae, you can now get radical expressions for things as complicated as Sin 1

I'm a firm believer that when it comes to math, you really don't need to memorize. I tend to derive pretty much everything on the fly. I've found that this style of learning and doing, allows for a much more fluent application of the knowledge. Math means so much more, when you know where all you formulas are coming from.


There are hundreds of trig identities you could memorize, but you'll save yourself a lot of time if you just learn how to derive them.

[phrontist]

Originally Posted by Karthik

I've been a TA for first year Calculus for four years now. When in comes to Trig, there's very little that you actually have to memorize. Here's the musts.

• Your friendly triangles -- (1,1, root 2) & (1, root 3, 2)
• Your basic trigonometric ratios -- SOH-CAH-TOA, and the reciprocals
  • From these first two, you know calculate the values of any basic angles
• (Sin x)^2 + (Cos x)^2 =1

With a working knowledge of elementary geometry, you can derive everything else you'll ever need. But if you don't want to be doing that during a test, here's the next level of stuff you'll want to committ to memory.

• The double angle formulae for Sin and Cos
  • With the double angle formulae, you can now get radical expressions for things as complicated as Sin 1

I'm a firm believer that when it comes to math, you really don't need to memorize. I tend to derive pretty much everything on the fly. I've found that this style of learning and doing, allows for a much more fluent application of the knowledge. Math means so much more, when you know where all you formulas are coming from.


There are hundreds of trig identities you could memorize, but you'll save yourself a lot of time if you just learn how to derive them.

Thanks Karthik! Exactly the kind of info I was looking for. I agree though that trig identities shouldn't be memorized instead of knowing how to derive them, rather that they should be memorized to increase speed.

[Dave Flowerday]

Originally Posted by phrontist

Real Engineers: What have you actually bothered to memorize?

I'm not sure if this is the answer you really want to hear, but...

I personally think intentionally memorizing anything is a waste of time. Everything that I need to know on a regular basis on my job gets implicitly memorized by repetitive use, and for everything else it's much more useful to just know where to look to find the answer. If I don't use something often enough to remember it automatically and I do spend the time to actually memorize it, what are the odds that I'm still going to remember it 6 months from now? Not very good (for me anyway), and even if I do remember it I'd still feel the need to look it up to double-check myself anyway.

I always thought that the memorizing thing was a big change from high-school to college. Seems like a lot of time was spent in high-school memorizing things for tests. Once I got to college, I didn't need to spend time memorizing because most (if not all) engineering classes let us bring in textbooks, notes, and calculators. I think the logic there is that it's much more important to spend study time understanding how to work the problem (even if you have to look up the formula) than to spend it memorizing the formulas and then have no idea what the formulas really do 5 years from now.

[Yan Wang]

Originally Posted by phrontist

• The IBH Physics Equation sheet (Duh)
• Gravitational Constant
• Avogadro's Constant
• Greek Alphabet
• Inches-Centimeters Conversion factor
• Trig Identities - Ah, but which should I really commit to memory? Which will really be useful in calculus? Which will be helpful in calculus?

From taking AP Chem and AP Physics last year, the Gravitational Constant and Avogadro's number just became second nature. Don't bother memorizing them if you're taking the course... repetitive use, as Mr. Flowerday said, will result in memorization. Plus, if you don't use it often, why bother memorizing it?

I wouldn't know why you'd want to memorize the greek alphabet... I guess many letters are used as physical constants and in formulas, but again, you'll know them by heart after doing problem sets (ugh).

I highly recommend memorizing certain trig identities for Calculus. It makes things go much faster. I agree with Karthik that knowing where everything comes from is important, but after you learn that, memorize it so you don't need to spend that extra 30 seconds deriving it. In Calc, the ones worth memorizing are the Trig derivatives:

(sinx)' = cosx
(tanx)' = (secx)^2
(secx)' = secxtanx

Use the co-rule for the derivatives of the co-functions.

[Mike Betts]

I tend to agree with the venerable Mr. Flowerday. Don't memorize. Train yourself to look it up. It eliminates problems which creep in from a faulty memory.

As one of my old college professors put it, "You don't get partial credit if the bridge falls down".

Having said that, I do tend to know a lot of constants "approximately". It's nice to estimate what your answer should be and know that it's a good ballpark number.

Mike

[GeorgeTheEng]

I agree, memorization isn't neccessary. Visit an Engineer and look at his desk, most will have a least 6 or 7 reference books on thier desk.

What you use, you'll remember... If you don't use it regularly, what's the point of having it memorized? And at least in my College experience, Eng good profs recognize this and let you bring references to exams. It's knowing how to apply an equation, not where it's sin^2 or sin^3

[AmyPrib]

Yep, I think if you just know where to look, that's the best way to do it. When you get in college, many classes end up letting you have "cheat" sheets for tests. But by the time you write down all the examples, and forumlas, and numbers on that sheet, you realize during the test that you just know it... because you spent the time to write it down....For some, it's a pretty good way to study, because it's a form of repetition. Half the time I made these huge elaborate cheat sheets, and then not need to use them during a test.. (but, for me putting examples of different equation applications came in handy). Those that dont' let you have cheat sheets, make one anyways and use it to study... It can be a last minute glance thing, but very useful in the future.

You'll also find that, even if you don't memorize something, you know exactly where to find it.... "umm.. i remember that it was in the upper right corner of the right side page, roughly in this chapter, and it was highlighted green"... it's kinda strange that you can remember what the page looks like but you can't remember the exact equation. But, at least you know where to find it... that's the key...

And, college classes, you'll find that after second year, all the courses seem to relate to each other, and you'll end up using numbers and equations in more places than you care to... so you'll unknowingly start memorzing some things...Many equations are derivations of each other, so if you can start somewhere, you can probably get elsewhere.

Some of the things you listed will eventually become second nature, but they are all useful. But if you want to make these types of things a quick lookup, then make yourself a page of what you think will be important items. Then you know exactly where to look, and enough usage will blast it into memory.

I never did understand why schools spend so much time forcing you to memorize things for a test, just so you can forget it the next day. You spend too much time memorizing it that you forget to learn how to use it. It's the application that needs to be understood.

[Venkatesh]

I have found it very useful to know the sines and cosines of a few angles (30, 60, 45) in decimal form. They got stuck in memory after doing so many problems with them.

Also, for Physics, the value of g on earth is very useful (32 ft/(sec*sec)). It will stick in your mind after the first two or three weeks of problems, if its not already there.

[abeD]

Originally Posted by phrontist

[*] The IBH Physics Equation sheet (Duh)

From taking two years of AP physics, you really don't need to memorize the equations on the sheet since they will always be there for you....but there are other equations not on these formula sheets that apply to certain situations that are used in lots of problems that you should commit to memory as you will have little time on the actual exam to derive them (obivously being able to also derive them helps too). Many engineers that I know don't memorize much but instead have reference books that they just look to whenever they need some constant or something of that nature.