A What is the Method of Characteristics in Teaching Analytical Mechanics?

  • A
  • Thread starter Thread starter wrobel
  • Start date Start date
  • Tags Tags
    Method
wrobel
Science Advisor
Insights Author
Messages
1,126
Reaction score
982
This just to share a teaching experience.

Questions about the method of characteristics are raised from time to time in this forum.

Hope the following text will be of some use. This is what we tell to students in courses of
analytical mechanics :)
 

Attachments

Last edited:
Mathematics news on Phys.org
What do you think of adding 2-3 examples and explaining the why's and ideas behind it, and write an insights article about it? The PDE are notoriously under represented.
 
Yes examples are missed I will add them.

UPD: Text is replaced; a discussion about the Hopf equation is added.
 
Last edited:

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

I Gradient descent algorithm and optimizers
Replies
5
Views
2K
On the cusp of fully grasping Method of Characteristics
Replies
1
Views
3K
Math vs. FE Method: Comparing Mechanical Engineering Focus
Replies
2
Views
2K
Lectures on integral invariants and Hamiltonian equations
Replies
16
Views
535
B A Simpler Way to Find the Shaded Area?
Replies
1
Views
2K
Mathematica Solve complex equation analytically
Replies
19
Views
2K
2D vs 3D Method of Characteristics for Rocket Nozzle Design
Replies
4
Views
3K
Question about something that the 1st year university student should know (how hard to study)
Replies
2
Views
1K
A Solving renormalization group equation in QFT
Replies
5
Views
2K
B Characteristics of the parent logarithmic function
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top