Do Physics Problems Utilize Calculus Continuity Graphs?

[science_rules]

This is not a homework question--I am just curious to know if there are any connections between calculus graphs involving continuity (say, a hole in a graph, which we are studying in my first under-graduate Calculus course), and the types of limit problems used in physics. i understand that in physics, algebraic limits? are used (to find the derivative of things, such as for acceleration, i think), but i wonder if the cartesian continuity graphs are used in any type of physics problems. i hope this question doesn't sound stupid, and i hope that it's not too incoherent! my calc prof. mentioned that she once studied some statistics and said that she had to solve a (thermodynamics?) problem that involved "continuity", which i guess would be using a sort of physics problem using the continuity concept. it's just that i fail to see a connection between the kind of algebraic limits that physics uses to find acceleration and such, and the kinds of cartesian graphs that we are analyzing in calculus (such as, there is a line going through the graph, but the limit does not equal the function, etc.). is this just a purely mathematical thing, or what??

 

[Valerie Park]

It is possible to use calculus graphs involving continuity in certain physics problems, such as thermodynamics. For example, when a system is in thermal equilibrium, the temperature of the system must remain constant throughout. This requires the system to be in a state of thermal equilibrium, which can be represented by a graph that shows the system's temperature as a function of time. In order to determine the temperature at any given time, it is necessary to find the limits of the graph at that time point, which is where the concept of continuity comes into play. The same concept can also be applied to other physical systems, such as wave motion, where the wave's amplitude must remain constant over time.

 

[sir-pinski]

There is definitely a connection between calculus graphs involving continuity and the types of limit problems used in physics. In fact, the concept of continuity is essential in many physics problems that involve motion, such as finding the position, velocity, and acceleration of an object at a given time.

In physics, algebraic limits are used to find the derivative of a function, which represents the rate of change of a physical quantity. This is especially important in problems involving motion, where the acceleration of an object can be determined by taking the derivative of its velocity function.

On the other hand, the concept of continuity is also used in physics to ensure that a physical quantity remains constant over a given interval of time. For example, in thermodynamics, the continuity equation is used to describe the conservation of mass and energy in a system. This concept is similar to the idea of continuity in calculus, where a function is considered continuous if there are no breaks or holes in its graph.

Furthermore, the idea of a limit in calculus can also be applied in physics to model physical phenomena. For instance, in the study of black holes, the concept of a limit is used to describe the point at which the gravitational pull becomes infinite and the laws of physics break down.

In conclusion, calculus graphs involving continuity and the types of limit problems used in physics are closely connected. Both concepts are essential in understanding and solving various physical problems, and their use in both fields highlights the interconnectedness of mathematics and science.