High School What are the general calculus concepts used in classical physics?

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SUMMARY

The discussion centers on the essential calculus concepts utilized in classical physics, specifically focusing on differential equations and integrals. Key topics include functions of multiple variables, partial derivatives, and the integral of functions over various dimensions. Notably, physical laws, such as Maxwell's Equations, are often represented as differential or integral equations, highlighting their fundamental role in physics. Understanding these concepts is crucial for grasping the mathematical framework underlying classical physics.

PREREQUISITES
  • Understanding of functions of multiple variables
  • Knowledge of partial derivatives
  • Familiarity with integrals over lines, surfaces, and volumes
  • Basic comprehension of differential equations
NEXT STEPS
  • Study Maxwell's Equations in detail
  • Learn about the application of partial differential equations in physics
  • Explore integral equations and their significance in classical mechanics
  • Investigate the role of calculus in electromagnetism and fluid dynamics
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in the mathematical foundations of classical physics, particularly those focusing on calculus applications in physical laws.

DeltaForce
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What are the key calculus concepts used in classical physics mechanics?
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Differential equations and integrals.
Ask a generic question and you'll get a generic answer.
 
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The concept of a function of one or many variables (up to 4 independent variables , three for the spatial coordinates x,y,z (or ρ,θ,φ in spherical coordinates) and one for the time coordinate),

The concept of derivative of the function (partial derivatives in the case the function has many variables or simple derivative in the case our function has only one independent variable)

The concept of integral of a function (integral over a line or a curve, over a surface, or over a volume)

Almost all physical laws come in the form of differential equations (equations that contain functions and partial or simple derivatives of functions) or integral equations (equations that contain functions and integrals of the functions). The most typical example are Maxwell's Equations in classical electromagnetism which can be expressed both as partial differential equations and as integral equations.
 
Anachronist said:
Differential equations and integrals.
Ask a generic question and you'll get a generic answer.
Thanks, that's what I was looking for.
 
In sci-fi when an author is talking about space travellers or describing the movement of galaxies they will say something like “movement in space only means anything in relation to another object”. Examples of this would be, a space ship moving away from earth at 100 km/s, or 2 galaxies moving towards each other at one light year per century. I think it would make it easier to describe movement in space if we had three axis that we all agree on and we used 0 km/s relative to the speed of...

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