I think it's a matter of personal preference. I, personally, tend to be more of a "witness stenographer" when taking notes with pen and paper. Because I can type faster than I can write, using a computer allows me more opportunities in class to stop and ponder the material.
I don't think there's any hard and fast rule that says that paper is better than computers or vice versa. Forcing students into using what the professor finds more helpful handicaps students who want to find the method which works best for them.
That study only compared students who doodle to students who daydream in class. They failed to consider that some students actually pay attention and take notes in class -- I think we'd agree that students who pay attention tend to focus better.
I'm replying to this post simply because this one actually intends to answer the original question.
When I took partial differential equations, we used "Advanced Engineering Mathematics" by Erwin Kreyszig.Of course, this is a mathematics book, so about 90% of it is "pure mathematics"... but being a physics student, I felt that it was quite applicable to my taste (physics). It does contain useful physics -- such as the heat equation, wave equation, etc. (Keep in mind that I knew most of the physics already when taking my class in PDEs... so I can't say for sure that someone who doesn't know physics would appreciate the physics discussed in this book).
If you want something that's the opposite of the book I mentioned above -- that is, it assumes you already know differential equations and simply want the physics, I'd recommend "Analytical Mechanics" by Fowles and Cassiday. This book just uses ODEs (not PDEs), but it's filled with examples which use ODEs to solve physics problems.
I'd recommend reading Analytical Mechanics to get yourself acquainted with how physicists use differential equations to solve physics problems, then reading Advanced Engineering Mathematics to see more advanced physics problems. Or maybe Analytical Mechanics would be enough... being that I don't have your PDE textbook;), I'm not sure if Advanced Engineering Mathematics is any better than your math textbook as far as explaining the physics.
I'm an undergraduate physics student assisting a professor in research in quantum mechanics. Although I've only touched quantum computing slightly in my research, I'd like to confirm that much of what mindriot said makes sense according to quantum mechanics as I understand it (I say "as I understand it" because the great Dr. Feynman once said that "no one understands quantum mechanics").
One point I'd like to mention -- the qubit is in both states A and B simultaneously, as far as we can tell. Measuring the qubit to be in state A 30% of the time does not indicate that is actually in that state 30% of the time -- rather, the act of measuring it tends to force it into state A 30% of the time.
Quantum mechanics involves incredibly tiny particles that are easily interrupted because even our most delicate instruments will greatly interrupt the particles we're trying to measure. If this doesn't make sense, imagine that you're sitting in front of a table in a dark room -- there's a marble spinning on the table, and you need to determine which direction it's spinning using a ping-pong ball. You roll the ping-pong ball toward the marble, which diverts the direction of the ping-pong ball, which rolls off and hits a sensor. Now knowing the position of the ping-pong ball, you calculate how its path was diverted by the marble, giving you the direction in which the marble was spinning.
BUT -- the ping-pong ball also hit the marble, which may have pushed the marble off in some direction. This may have made the marble stop spinning altogether, or the marble may now be rolling in some direction instead of spinning.
With qubits, which often assume states "spin up", "spin down", etc., we have the same problem in measuring them. If you don't see the problem in this, imagine if the act of opening a file on your computer altered its contents. Qubits will probably be used more in memory than disk space... but still, if you place a value in memory, you don't want it to change when it comes time to retrieve it.
Quantum computing involves a very delicate balance between how much information we want to "see" in the system and how to leave it alone. Once again, my research is only tangentially related to quantum computing, so I can't answer the question of how they've solved this dilemma (or if it's been solved), but I find it interesting nevertheless.
Recently, Epson lost a lawsuit because their inkjets were causing users to waist an extreme amount of ink. If you own an Epson printer, you may be eligible to receive $50 in free ink -- more information at http://epsonsettlement.com/
The name "Quantum" refers to the discrete nature of our world. Plank first discovered quantum mechanics by noticing that energy was quantized (occurred in discrete quantities). Even today, quantization plays a very large role in the continuing research of quantum mechanics, which is my I believe it to be a fairly good name.
I agree that OpenOffice is still lacking in many features.
Before you all throw dirt on me, let me just state that I am an OpenOffice user -- no, I'm not "betraying" the product -- I prefer not to get religeous about my choices of software.
However, why have I have chosen to live without MS Office? Quite simply, I don't feel that it's worth the price tag. In order for me to pay $400, I expect it have significantly more features that I'll use.
I've been very impressed with some utilities and macros provided by MS Office -- but I don't use these, which is why I decided not to pay the price.
Finally, many of us have been using MS Office for several years. When we first sat down at a computer that used OpenOffice, we noticed a big difference and weren't used to the controls. But wait -- the first time you sat down at a computer using MS Office, did you know how to adjust the line spacing? You had to learn -- in OpenOffice, you need to learn to look in a different place to do the things you're used to.
In conclusion, everything has a price. OpenOffice requires your time to learn, while Microsoft Office requires $400. If you don't want to pay the price and are willing to take the time, use OpenOffice. If you need the extra features of Microsoft Office, and don't mind the price, use Microsoft.
Neither can claim to be the best for everyone. Use what fits you best. Just don't condemn someone else for using the other one.
Yes. But Microsoft infringes some of Novell's patents (used in SuSE) as well as some of Apple's "flavor" of BSD Unix. IMHO, Microsoft will never file suit because a major backlash of counter-suits will arise.
I've been using Ubuntu Dapper Drake (Ubuntu 6.06) Alpha 5 for about a month or so, and am very impressed with it. Of course, one can't expect the stability of a stabe release from an alpha, but ever since I installed it, I've been very surprised as to how stable it is for an alpha.
This makes me look forward to the stable release even more -- if the alpha's like this... the stable release will be awesome!
The best thing I like about Ubuntu (especially in Dapper) is its hardware support. I have hardware (such as a touchpad, etc.) that never worked correctly in other distros (it even had quirks in Windowze). Ubuntu had great drivers, but Dapper is awesome.
Thanks, Ubuntu Devs!
Suppose some software has been developed that can circumvent the Great Firewall... remember that the Chinese government has the law on their side. The Chinese people can be arrested for using such software -- and they're not "Innocent until proven guilty", either.
Here's Google's dillema: either China blocks Google, or Google complies with China's censorship demands. This is different from Google's refusing to comply with the Justice Department -- because they're not threatening to shut them down. (It they did, Google would most likely comply). Even if Google chooses to "promote democracy" and resist the Chinese government, Google will be blocked and the Chinese people are going to be denied the information anyways. The Chinese government wins either way.
2-dimentional space implies that you can move forward, backward, left, and right. 3-dimentional space adds the motion of up and down.
According to this physicist, the "old" notion of is that with time, we can only move in one direction -- forward. Supposing that he's right, and we have 2 or 3 dimentions in time, we'd be able to move backward, up, down, left, and right in time -- people would be able to switch between several "tracks" in time.
This might work in theory, but I've never observed it.
Sure, we may be able to achieve a "time shift" someday, but that doesn't add a new dimention to time.
This about this -- murder is wrong and no matter what you tell me, and no matter how persuasive you speak, I'm not going to accept murder as OK.
Refusing to accept the opponents' arguments isn't always bad...
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I think it's a matter of personal preference. I, personally, tend to be more of a "witness stenographer" when taking notes with pen and paper. Because I can type faster than I can write, using a computer allows me more opportunities in class to stop and ponder the material.
I don't think there's any hard and fast rule that says that paper is better than computers or vice versa. Forcing students into using what the professor finds more helpful handicaps students who want to find the method which works best for them.
That study only compared students who doodle to students who daydream in class. They failed to consider that some students actually pay attention and take notes in class -- I think we'd agree that students who pay attention tend to focus better.
I'm replying to this post simply because this one actually intends to answer the original question.
When I took partial differential equations, we used "Advanced Engineering Mathematics" by Erwin Kreyszig.Of course, this is a mathematics book, so about 90% of it is "pure mathematics"... but being a physics student, I felt that it was quite applicable to my taste (physics). It does contain useful physics -- such as the heat equation, wave equation, etc. (Keep in mind that I knew most of the physics already when taking my class in PDEs... so I can't say for sure that someone who doesn't know physics would appreciate the physics discussed in this book).
If you want something that's the opposite of the book I mentioned above -- that is, it assumes you already know differential equations and simply want the physics, I'd recommend "Analytical Mechanics" by Fowles and Cassiday. This book just uses ODEs (not PDEs), but it's filled with examples which use ODEs to solve physics problems.
I'd recommend reading Analytical Mechanics to get yourself acquainted with how physicists use differential equations to solve physics problems, then reading Advanced Engineering Mathematics to see more advanced physics problems. Or maybe Analytical Mechanics would be enough... being that I don't have your PDE textbook ;), I'm not sure if Advanced Engineering Mathematics is any better than your math textbook as far as explaining the physics.
Microsoft thrives on copying other ideas, then trying to use their presence to make their product succeed.
Even Windows, their most successful product, did not appear until after Apple presented their new graphical interface.
I'm an undergraduate physics student assisting a professor in research in quantum mechanics. Although I've only touched quantum computing slightly in my research, I'd like to confirm that much of what mindriot said makes sense according to quantum mechanics as I understand it (I say "as I understand it" because the great Dr. Feynman once said that "no one understands quantum mechanics").
One point I'd like to mention -- the qubit is in both states A and B simultaneously, as far as we can tell. Measuring the qubit to be in state A 30% of the time does not indicate that is actually in that state 30% of the time -- rather, the act of measuring it tends to force it into state A 30% of the time.
Quantum mechanics involves incredibly tiny particles that are easily interrupted because even our most delicate instruments will greatly interrupt the particles we're trying to measure. If this doesn't make sense, imagine that you're sitting in front of a table in a dark room -- there's a marble spinning on the table, and you need to determine which direction it's spinning using a ping-pong ball. You roll the ping-pong ball toward the marble, which diverts the direction of the ping-pong ball, which rolls off and hits a sensor. Now knowing the position of the ping-pong ball, you calculate how its path was diverted by the marble, giving you the direction in which the marble was spinning.
BUT -- the ping-pong ball also hit the marble, which may have pushed the marble off in some direction. This may have made the marble stop spinning altogether, or the marble may now be rolling in some direction instead of spinning.
With qubits, which often assume states "spin up", "spin down", etc., we have the same problem in measuring them. If you don't see the problem in this, imagine if the act of opening a file on your computer altered its contents. Qubits will probably be used more in memory than disk space... but still, if you place a value in memory, you don't want it to change when it comes time to retrieve it.
Quantum computing involves a very delicate balance between how much information we want to "see" in the system and how to leave it alone. Once again, my research is only tangentially related to quantum computing, so I can't answer the question of how they've solved this dilemma (or if it's been solved), but I find it interesting nevertheless.
Recently, Epson lost a lawsuit because their inkjets were causing users to waist an extreme amount of ink. If you own an Epson printer, you may be eligible to receive $50 in free ink -- more information at http://epsonsettlement.com/
The name "Quantum" refers to the discrete nature of our world. Plank first discovered quantum mechanics by noticing that energy was quantized (occurred in discrete quantities). Even today, quantization plays a very large role in the continuing research of quantum mechanics, which is my I believe it to be a fairly good name.
I agree that OpenOffice is still lacking in many features. Before you all throw dirt on me, let me just state that I am an OpenOffice user -- no, I'm not "betraying" the product -- I prefer not to get religeous about my choices of software. However, why have I have chosen to live without MS Office? Quite simply, I don't feel that it's worth the price tag. In order for me to pay $400, I expect it have significantly more features that I'll use. I've been very impressed with some utilities and macros provided by MS Office -- but I don't use these, which is why I decided not to pay the price. Finally, many of us have been using MS Office for several years. When we first sat down at a computer that used OpenOffice, we noticed a big difference and weren't used to the controls. But wait -- the first time you sat down at a computer using MS Office, did you know how to adjust the line spacing? You had to learn -- in OpenOffice, you need to learn to look in a different place to do the things you're used to. In conclusion, everything has a price. OpenOffice requires your time to learn, while Microsoft Office requires $400. If you don't want to pay the price and are willing to take the time, use OpenOffice. If you need the extra features of Microsoft Office, and don't mind the price, use Microsoft. Neither can claim to be the best for everyone. Use what fits you best. Just don't condemn someone else for using the other one.
Yes. But Microsoft infringes some of Novell's patents (used in SuSE) as well as some of Apple's "flavor" of BSD Unix. IMHO, Microsoft will never file suit because a major backlash of counter-suits will arise.
I've been using Ubuntu Dapper Drake (Ubuntu 6.06) Alpha 5 for about a month or so, and am very impressed with it. Of course, one can't expect the stability of a stabe release from an alpha, but ever since I installed it, I've been very surprised as to how stable it is for an alpha. This makes me look forward to the stable release even more -- if the alpha's like this... the stable release will be awesome! The best thing I like about Ubuntu (especially in Dapper) is its hardware support. I have hardware (such as a touchpad, etc.) that never worked correctly in other distros (it even had quirks in Windowze). Ubuntu had great drivers, but Dapper is awesome. Thanks, Ubuntu Devs!
Suppose some software has been developed that can circumvent the Great Firewall... remember that the Chinese government has the law on their side. The Chinese people can be arrested for using such software -- and they're not "Innocent until proven guilty", either.
Here's Google's dillema: either China blocks Google, or Google complies with China's censorship demands. This is different from Google's refusing to comply with the Justice Department -- because they're not threatening to shut them down. (It they did, Google would most likely comply). Even if Google chooses to "promote democracy" and resist the Chinese government, Google will be blocked and the Chinese people are going to be denied the information anyways. The Chinese government wins either way.
2-dimentional space implies that you can move forward, backward, left, and right. 3-dimentional space adds the motion of up and down.
According to this physicist, the "old" notion of is that with time, we can only move in one direction -- forward. Supposing that he's right, and we have 2 or 3 dimentions in time, we'd be able to move backward, up, down, left, and right in time -- people would be able to switch between several "tracks" in time.
This might work in theory, but I've never observed it.
Sure, we may be able to achieve a "time shift" someday, but that doesn't add a new dimention to time.
This about this -- murder is wrong and no matter what you tell me, and no matter how persuasive you speak, I'm not going to accept murder as OK. Refusing to accept the opponents' arguments isn't always bad...
And then, some genious will invent ROUND wheels that have NO humps when rotating!