August 19th, 2017, 05:51 AM  #1 
Senior Member Joined: Nov 2015 From: United States of America Posts: 162 Thanks: 21 Math Focus: Calculus and Physics  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 
August 19th, 2017, 06:30 AM  #2 
Senior Member Joined: Oct 2009 Posts: 142 Thanks: 60 
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? 
August 19th, 2017, 07:07 AM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 2,656 Thanks: 1327 
Review vectors.

August 19th, 2017, 09:40 AM  #4 
Senior Member Joined: Jun 2015 From: England Posts: 695 Thanks: 199 
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. 
August 19th, 2017, 10:52 AM  #5 
Math Team Joined: Jul 2011 From: Texas Posts: 2,656 Thanks: 1327  
August 19th, 2017, 11:18 AM  #6  
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,602 Thanks: 816  Quote:
I suspect anything you can come up with is equivalent to just calling them a "vectour".  
August 19th, 2017, 11:19 AM  #7 
Senior Member Joined: Oct 2009 Posts: 142 Thanks: 60  
August 19th, 2017, 11:40 AM  #8 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,602 Thanks: 816  
August 19th, 2017, 11:48 AM  #9  
Senior Member Joined: Jun 2015 From: England Posts: 695 Thanks: 199  Quote:
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. Quote:
I like the Double Entendre of your post involving one of the other scientific meanings of the word vector.  
August 19th, 2017, 02:57 PM  #10  
Senior Member Joined: Nov 2015 From: United States of America Posts: 162 Thanks: 21 Math Focus: Calculus and Physics  Quote:
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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