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This is wonderful! Does anyone have any particular recommendations (in any subject)?

baking 7y ago
"The Physics of Energy" by Jaffe & Taylor is definitely on my list. https://www.cambridge.org/core/books/physics-of-energy/7FE67626190E6D164A71B0D61E061E63 https://www.cambridge.org/core/books/physics-of-energy/7FE67...
ironmagma 7y ago
Dynamics of Particles and Rigid Bodies by Anil Rao https://www.amazon.com/Dynamics-Particles-Rigid-Bodies-Systematic/dp/0521187907/ref=nodl_ https://www.amazon.com/Dynamics-Particles-Rigid-Bodies-Syste... Dr. Rao’s systematic approach to solving dynamics problems is consistent and concise. He also has a companion set of lecture notes on YouTube. I remember it as one of the most challenging but rewarding aspects of my engineering school experience. All the principles are described mathematically in a coordinate-free manner. You’ll learn to set up equations of rigid bodies and constraints without all the guesswork and haphazard construction of coordinates typically encountered in a physics textbook.
- b215826 7y ago
  I haven't read the book, but looking at the contents I'm surprised that the author hasn't introduced analytical mechanics anywhere in the book. This might be a good introductory book if you haven't taken a mechanics course before, but using Newton's laws for understanding the dynamics of particles and rigid bodies is a terrible idea. > All the principles are described mathematically in a coordinate-free manner. Newton's laws aren't coordinate free, e.g., Newton's second law written in polar coordinates would look different from Newton's laws in Cartesian coordinates. But, Lagrange's equations are coordinate-system independent.
  - ironmagma 7y ago
    This is definitely not an introductory level book. On the contrary, I wouldn't recommend it unless you've done at least Calc 3 since you'll need a strong grasp of vectors and derivatives. Newton's laws say e.g. the net force on an object (a Euclidean vector) is equal to its mass multiplied by its acceleration (also a Euclidean vector). That in itself is entirely coordinate free, sure it assumes that the vector is not a moment, but that's different from dictating a particular coordinate system. You are right to say that if you wanted to express those laws in different coordinate systems, they would look different, but the key to this system is in essence that you leave any kind of coordinate projections till the very end (lazy evaluation, to put it in a computer science analogy), at which point much of the math is simplified due to term reduction, or various projections cancel each other out. What is tempting to bring in from other materials is the notion that a vector has coordinates, which as far as this philosophy is concerned, they don't. A vector is the direction and magnitude per sé, devoid of the concept of an origin or any particular unit vectors with which you could represent that vector numerically. It's a mindfuck for sure, and it confused all the students in the class for a solid 3 weeks; that's why it's great.
    - b215826 7y ago
      > This is definitely not an introductory level book I disagree. I used Kleppner and Kolenkow as a freshman, and it has pretty much the same content as this book, and I would consider Kleppner and Kolenkow to be an introductory book. Sure, it's more advanced than more common freshmen books like Halliday and Resnick, but it is still very elementary mechanics. Newton's laws is just the tip of the iceberg that is mechanics. Most advanced books, including upper-division undergraduate books, would at least introduce analytical mechanics, whereas this book doesn't. If you want more advanced treatments of mechanics you should look at Landau and Lifshitz, or Arnold, or Marsden, or even Lanczos (the latter three making moderate to extensive use of Riemannian geometry and can be daunting for that reason alone). > but the key to this system is in essence that you leave any kind of coordinate projections till the very end That is not the definition of coordinate invariance, at least as defined in physics. Newton's laws aren't coordinate invariant because the acceleration involves the second derivative of coordinate basis vectors, and that is zero (or constant) only in very few coordinate systems, like Cartesian coordinates for instance. Of course, the statement F = ma still holds true, but becomes very cumbersome to use if, say non-orthogonal coordinate systems are used. As a simple example, try finding the equation of motion of a particle constrained on a smooth surface, say a paraboloid z = x^2 + y^2 in Cartesian coordinates using Newton's laws. Of course, this problem can be solved using Newton's laws by introducing Lagrange multipliers, but that essentially amounts to finding the constraint force. But it would be much better if you could avoid finding the constraint force altogether. > A vector is the direction and magnitude per sé, devoid of the concept of an origin or any particular unit vectors with which you could represent that vector numerically. You're right that it is important to distinguish between the geometrical meaning of polar vectors and their representations in a particular coordinate system. It's even more confusing when axial-/pseudo-vectors, e.g., the cross product of two polar vectors, are introduced since now they do depend on the handedness of the coordinate system used. And why should nature care about handedness? (It actually does, but that's a story for another day.) And this is precisely why analytical mechanics, which is an inherently geometrical subject, was invented in the first place! All equations in analytical mechanics are scalar equations and look the same irrespective of the coordinates you use to describe the system.
mirekrusin 7y ago
Programming in Haskell by Graham Hutton
b215826 7y ago
Uriel Frisch's Turbulence: The Legacy of A. N. Kolmogorov is an accessible introduction to one of the most important and still unsolved problem in classical physics. That book has over 7000 citations on Google Scholar. https://www.cambridge.org/core/books/turbulence/FD8C5E35E5F1CA850E017461942A59AC https://www.cambridge.org/core/books/turbulence/FD8C5E35E5F1...
rodolphoarruda 7y ago
Strategic Decisions is an excellent summary for those looking for starting points in the most well known business strategy models. A good compilation.
wdutch 7y ago
Complex Analysis (The Hitchhiker's Guide to the Plane) by Ian Stewart and David Tall was a particular favorite of mine as an undergrad
- adz_6891 7y ago
  Agreed. Complex analysis was a great course!

"The Physics of Energy" by Jaffe & Taylor is definitely on my list. https://www.cambridge.org/core/books/physics-of-energy/7FE67626190E6D164A71B0D61E061E63 https://www.cambridge.org/core/books/physics-of-energy/7FE67...

ironmagma 7y ago

Dynamics of Particles and Rigid Bodies by Anil Rao https://www.amazon.com/Dynamics-Particles-Rigid-Bodies-Systematic/dp/0521187907/ref=nodl_ https://www.amazon.com/Dynamics-Particles-Rigid-Bodies-Syste... Dr. Rao’s systematic approach to solving dynamics problems is consistent and concise. He also has a companion set of lecture notes on YouTube. I remember it as one of the most challenging but rewarding aspects of my engineering school experience. All the principles are described mathematically in a coordinate-free manner. You’ll learn to set up equations of rigid bodies and constraints without all the guesswork and haphazard construction of coordinates typically encountered in a physics textbook.

b215826 7y ago
I haven't read the book, but looking at the contents I'm surprised that the author hasn't introduced analytical mechanics anywhere in the book. This might be a good introductory book if you haven't taken a mechanics course before, but using Newton's laws for understanding the dynamics of particles and rigid bodies is a terrible idea. > All the principles are described mathematically in a coordinate-free manner. Newton's laws aren't coordinate free, e.g., Newton's second law written in polar coordinates would look different from Newton's laws in Cartesian coordinates. But, Lagrange's equations are coordinate-system independent.
- ironmagma 7y ago
  This is definitely not an introductory level book. On the contrary, I wouldn't recommend it unless you've done at least Calc 3 since you'll need a strong grasp of vectors and derivatives. Newton's laws say e.g. the net force on an object (a Euclidean vector) is equal to its mass multiplied by its acceleration (also a Euclidean vector). That in itself is entirely coordinate free, sure it assumes that the vector is not a moment, but that's different from dictating a particular coordinate system. You are right to say that if you wanted to express those laws in different coordinate systems, they would look different, but the key to this system is in essence that you leave any kind of coordinate projections till the very end (lazy evaluation, to put it in a computer science analogy), at which point much of the math is simplified due to term reduction, or various projections cancel each other out. What is tempting to bring in from other materials is the notion that a vector has coordinates, which as far as this philosophy is concerned, they don't. A vector is the direction and magnitude per sé, devoid of the concept of an origin or any particular unit vectors with which you could represent that vector numerically. It's a mindfuck for sure, and it confused all the students in the class for a solid 3 weeks; that's why it's great.
  - b215826 7y ago
    > This is definitely not an introductory level book I disagree. I used Kleppner and Kolenkow as a freshman, and it has pretty much the same content as this book, and I would consider Kleppner and Kolenkow to be an introductory book. Sure, it's more advanced than more common freshmen books like Halliday and Resnick, but it is still very elementary mechanics. Newton's laws is just the tip of the iceberg that is mechanics. Most advanced books, including upper-division undergraduate books, would at least introduce analytical mechanics, whereas this book doesn't. If you want more advanced treatments of mechanics you should look at Landau and Lifshitz, or Arnold, or Marsden, or even Lanczos (the latter three making moderate to extensive use of Riemannian geometry and can be daunting for that reason alone). > but the key to this system is in essence that you leave any kind of coordinate projections till the very end That is not the definition of coordinate invariance, at least as defined in physics. Newton's laws aren't coordinate invariant because the acceleration involves the second derivative of coordinate basis vectors, and that is zero (or constant) only in very few coordinate systems, like Cartesian coordinates for instance. Of course, the statement F = ma still holds true, but becomes very cumbersome to use if, say non-orthogonal coordinate systems are used. As a simple example, try finding the equation of motion of a particle constrained on a smooth surface, say a paraboloid z = x^2 + y^2 in Cartesian coordinates using Newton's laws. Of course, this problem can be solved using Newton's laws by introducing Lagrange multipliers, but that essentially amounts to finding the constraint force. But it would be much better if you could avoid finding the constraint force altogether. > A vector is the direction and magnitude per sé, devoid of the concept of an origin or any particular unit vectors with which you could represent that vector numerically. You're right that it is important to distinguish between the geometrical meaning of polar vectors and their representations in a particular coordinate system. It's even more confusing when axial-/pseudo-vectors, e.g., the cross product of two polar vectors, are introduced since now they do depend on the handedness of the coordinate system used. And why should nature care about handedness? (It actually does, but that's a story for another day.) And this is precisely why analytical mechanics, which is an inherently geometrical subject, was invented in the first place! All equations in analytical mechanics are scalar equations and look the same irrespective of the coordinates you use to describe the system.

mirekrusin 7y ago

Programming in Haskell by Graham Hutton

b215826 7y ago

Uriel Frisch's Turbulence: The Legacy of A. N. Kolmogorov is an accessible introduction to one of the most important and still unsolved problem in classical physics. That book has over 7000 citations on Google Scholar. https://www.cambridge.org/core/books/turbulence/FD8C5E35E5F1CA850E017461942A59AC https://www.cambridge.org/core/books/turbulence/FD8C5E35E5F1...

rodolphoarruda 7y ago

Strategic Decisions is an excellent summary for those looking for starting points in the most well known business strategy models. A good compilation.

wdutch 7y ago

Complex Analysis (The Hitchhiker's Guide to the Plane) by Ian Stewart and David Tall was a particular favorite of mine as an undergrad

adz_6891 7y ago
Agreed. Complex analysis was a great course!