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August 19th, 2017, 04:51 AM   #1
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Mathematics background for classical mechanics

Hello forum,

I am taking classical mechanics this fall at my university. Is there any math topics anyone would suggest reading up on prior to showing up day 1? Also what math can I expect in your typical classical mechanics class? I feel pretty comfortable with the math learned in your average US college calculus triple sequence. I also know how to handle basic first and second order differential equations from half of my ordinary DE class I am taking currently.

I would greatly appreciate hearing advice from others regarding the mathematics of classical mechanics. I am very nervous.

Thanks!

Jacob
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August 19th, 2017, 05:30 AM   #2
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What physics classes did you take before? Did you take mechanics at university before? At high school?
Also, can you list the contents of the course?
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August 19th, 2017, 06:07 AM   #3
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Review vectors.
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August 19th, 2017, 08:40 AM   #4
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Good advice already given, Americans love vectors, in fact they seem unable to do without them.

So reviewing the course syllabus is also important.

But classical mechanics is more than vectors, at university level you will be stepping beyond force - displacement methods towards Hamiltonian - Lagrangian mechanics, which form the next step up from Newtonian mechanics and lead on to much modern Physics.

Perhaps the best thing to make you aware of are 'Student's Guides'

The Cambridge University guides to
Lagrangians and Hamiltonians
Relativity
Vectors and Tensors

are all ultra modern treatments in small booklet form.

The following older student's guides would make nice late summer reading before the course to give you a head start.

Classical Mechanics : B P Cowan

Principles of Dynamics : M C Glauert

Analytical Mechanics : D F Lawden

Enjoy your course.
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August 19th, 2017, 09:52 AM   #5
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Good advice already given, Americans love vectors, in fact they seem unable to do without them.
We've been trying to keep our love affair with vectors a secret, but with WikiLeaks & all ...

Oh, well ... God save the Queen.

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August 19th, 2017, 10:18 AM   #6
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Good advice already given, Americans love vectors, in fact they seem unable to do without them.
And how do folks across the pond represent the various things vectors are used for?

I suspect anything you can come up with is equivalent to just calling them a "vectour".
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August 19th, 2017, 10:19 AM   #7
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And how do folks across the pond represent the various things vectors are used for?

I suspect anything you can come up with is equivalent to just calling them a "vectour".
We just don't have mosquitos with malaria here.
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August 19th, 2017, 10:40 AM   #8
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We just don't have mosquitos with malaria here.
Maybe not yet!
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August 19th, 2017, 10:48 AM   #9
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And how do folks across the pond represent the various things vectors are used for?

I suspect anything you can come up with is equivalent to just calling them a "vectour".
Your professors Den Hartog, Young, Timoshenko and Sokolnikoff got by without excessive use of vectors as did our professors Pippard, Sir Charles Inglis and Jaeger and Australia's professor Weatherburn. All were leaders in their field.
It should be be noted that they were not shy of vector or tensor methods and used them where appropriate, indeed Jaeger, Sokolnikoff and Weatherburn all produced learned tomes about vectors/tensors.

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Microm@ss
We just don't have mosquitos with malaria here.


I like the Double Entendre of your post involving one of the other scientific meanings of the word vector.
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August 19th, 2017, 01:57 PM   #10
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Quote:
Originally Posted by Micrm@ss View Post
What physics classes did you take before? Did you take mechanics at university before? At high school?
Also, can you list the contents of the course?
Thank you for your response.

I have taken two physics classes at my university. General Physics 1 (mechanics) and General Physics 2 (E&M, optics). I am also a TA for General Physics 1. So I constantly see the Newtonian Physics, just not very deep into it.

The class is divided into two semesters and covers:

Newtonian Mechanics -- Single Particle
Oscillations
Nonlinear Oscillations and Chaos
Gravitation
Calculus of Variations
Hamilton's Principle -- Lagrangian and Hamiltonian Dynamics. <-- (I keep seeing "Hamiltonian" and "Lagrangian" when I try to look up stuff about classical mechanics. I assume it will be an important part.)
Central Force motion
Dynamics of a System of particles
Motion in a noninterial reference frame
Dynamics of rigid bodies
Coupled oscillations
Continuous systems; waves
Special theory of relativity

At some point in this list the class will be broken up between Classical 1 and Classical 2.

I have seen most of these topics in general physics, but only a teaser I am sure.

What are your thoughts? I am just nervous I will be thrown some ugly
nth order differential equation at some point and I will just be clueless . Is Classical Mechanics typically differential equations heavy? Or is that more instructor preference?
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