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Why are so many of the important equations of physics first or second order differential equations (schrodinger etc).Why are there few third or fourth order differential equations that describe the physical world?
vanesch said:I can only second that !
But as the question *why* does spacetime have these symmetries, the answer is then that these leave the laws of nature invariant, which are... second order diff. equations...
GT1 said:Why do the laws of nature have to be second order diff. equations in order to be invariant ?
dst said:But if there is a non-zero jerk over time then surely there has to be a non-zero d^4x/dt^4 and a d^5x/dt^5, etc. Why are these not considered?
A differential equation is a mathematical equation that relates a function to its derivatives. In physics, they are used to describe the relationship between a physical quantity and its rate of change over time.
Differential equations are important in physics because they allow us to model and understand the behavior of physical systems. Many laws and principles in physics, such as Newton's laws of motion and the laws of thermodynamics, can be expressed as differential equations.
Ordinary differential equations involve a single independent variable, such as time, and its derivatives. Partial differential equations involve multiple independent variables and their derivatives. In physics, ordinary differential equations are often used to describe the motion of a single particle, while partial differential equations are used to describe the behavior of continuous systems, such as fluids and electromagnetic fields.
There are various methods for solving differential equations in physics, including analytical and numerical methods. Analytical methods involve finding an exact solution to the equation using mathematical techniques, while numerical methods involve approximating the solution through iterative calculations.
Differential equations are used in many areas of physics, including mechanics, electromagnetism, thermodynamics, and quantum mechanics. They are used to describe the motion of objects, the behavior of fluids and gases, the propagation of electromagnetic waves, and the behavior of quantum systems, among others.