Recent content by EternusVia

  1. EternusVia

    Proving that the Harmonic Series is divergent

    Hello everyone, I too had to solve this problem, and I think I found a nice way to write the solution. I'd like to share it here. We can regroup the harmonic series as follows: \sum_{n=1}^{\infty} \frac{1}{n} =...
  2. EternusVia

    I Interpretation of the Reynolds Transport Theorem?

    Background: I am taking an undergraduate fluid mechanics class. I seem to have a misunderstanding with my interpretation of Reynolds Transport theorem (RTT), which I have written below: $$\frac{DB_{sys}}{Dt} = \frac{\partial}{\partial t}\int_{CV}\rho bd V +\int_{CS}\rho b \vec{V}\cdot...
  3. EternusVia

    How to prove -(-x)=x

    JasonMorand, I think that stupidmath's proof is valid. He proves it essentially the same way you do -- by claiming 0 = 0.
  4. EternusVia

    Binding energy / mass deficit of Earth-moon system?

    I reviewed the definition of binding energy. Effectively, binding energy is the energy you need to put in to separate the objects of the system infinitely and at rest. Sense they have to be at rest, I should have calculated the kinetic energy of the moon and added it to the potential energy...
  5. EternusVia

    Binding energy / mass deficit of Earth-moon system?

    Homework Statement Consider the earth-moon system (whose constituent pats we take to be the earth and the moon separately). a) Compute this system's gravitational potential energy (in joules) and the mass deficit (in kilograms). The radius of the moon's orbit is 384,000 km, and its period is...
  6. EternusVia

    Induction Problem (Polya)

    That worked! I would post the process, but it follows almost immediately from applying the formula for the sum of an arithmetic progression. Thank you
  7. EternusVia

    Induction Problem (Polya)

    Homework Statement Consider the table: 1 = 0 + 1 2 + 3 + 4 = 1 + 8 5 + 6 + 7 + 8 + 9 = 8 + 27 10 + 11 + 12 + 13 + 14 + 15 + 16 = 27 + 64 Guess the general law suggested by these examples, express it in suitable mathematical notation, and prove it. Homework Equations [/B] It's clear that if...
  8. EternusVia

    Programs Intersection of Physics and Applied Math?

    Hello all, I am interested in both physics and applied math. One of my professors is willing to work with me to get into a great applied math school, but I don't want to abandon my passion for physics. Is there work being done at the intersection of applied math and physics? Is it reasonable...
  9. EternusVia

    Solving Simultaneous Inequalities

    Hi Ray, That is a clever idea. I used it to find part of the solution but couldn't get the rest. Not sure what I'm doing wrong. ##3cos(\theta) + 4sin(\theta) = Asin(\theta + \phi)## ##Asin(\theta + \phi) = Asin(\theta)cos(\phi) + Acos(\theta)sin(\phi)## ##Acos(\phi) = 4## and ##Asin(\phi) =...
  10. EternusVia

    Solving Simultaneous Inequalities

    Homework Statement [/B] I am trying to solve the simultaneous inequalities (1) and (2) shown in the following image. The solution is provided, but I'm not sure how they solved for it. [PLAIN]http:// Homework Equations N/A The Attempt at a Solution [/B] I tried to solve this set of...
  11. EternusVia

    What is a free body diagram

    Perfect, thank you!
  12. EternusVia

    What is a free body diagram

    Do people normally draw torque in a free body diagram as a curved arrow?
  13. EternusVia

    What is a free body diagram

    Hello, thank you for your post. Where do moments fit into this? Is a moment the same as a torque? Should they be shown in a free body diagram?
  14. EternusVia

    Linear Algebra, Determine the Volume of the Parallelepiped

    Thank you all for your insightful replies and questions. Am I interpreting this correctly... If I start with a vertex and create three vectors from the given points, no matter which three vectors, I will get the volume of the parallelepiped? Even if the vectors are, say, the diagonals of the...
  15. EternusVia

    Linear Algebra, Determine the Volume of the Parallelepiped

    That's really helpful; thank you. Do you know of a way to label the points in Wolfram?
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