Calculus is the branch of mathematics which deals with the study of rate of change of quantities. This is usually divided into differential calculus and integral calculus which are concerned with derivatives and integrals respectively. DO NOT USE THIS TAG just because your question makes use of calculus.
Questions tagged [calculus]
1102 questions
82
votes
9 answers
How to treat differentials and infinitesimals?
In my Calculus class, my math teacher said that differentials such as $dx$ are not numbers, and should not be treated as such.
In my physics class, it seems like we treat differentials exactly like numbers, and my physics teacher even said that they…
Ovi
- 2,889
4
votes
3 answers
Why do so many laws in physics operate on the second derivative?
Forces affect the second derivative of positions. Waves are described by second derivatives. Etc. Why do much of physics operates on the second derivative?
What physical quantities, if any, operate on the third derivative or higher? Is there a…
user315366
3
votes
4 answers
Based on note, how fast is a stringed instrument's string oscillating?
to be quite honest, I have no idea where to start on this problem mathematically. However, it struck my curiosity and would love to know how it works on a mathematical level.
the problem
You have a guitar. All of the strings start at a resting…
Crow
- 131
2
votes
2 answers
Infinitesimal volume using differentials
I don't understand why in some texts they put that infinitesimal volume $dV = dx dy dz$. If $ V = V(x,y, z)$ infinitesimal volume should be $$dV = \frac{\partial V}{\partial x} dx +\frac{\partial V}{\partial y} dy + \frac{\partial V}{\partial z}…
Girolamo
- 23
1
vote
0 answers
Uniform load applied to a parabolic curve
As I have to design the vertebra bone and its natural boundary conditions I came across a problem.
How can I applied a uniform load if the place where the force is applied is a parabolic curve.
Ok so I get the curve will have this value
$$y(x) =…
Barão António Lopes
- 11
- 2
1
vote
0 answers
Find center of mass and moment applied on beam structure.
I have a simple mathematical problem to solve but it is giving me a slightly difficult time to figure out. The problem:
I have a beam structure with same cross section. It consists of three beam. First in vertical with length 1meter. Second beam…
Nikolas
- 21
0
votes
1 answer
Why center of mass in one dimension is define by $m_1\cdot d_1 = m_2\cdot d_2$?
I know how to calculate centroids in single integrals and double integrals and derive the formula for center of mass, but I don't know why the center of mass is defined by $\text{mass}_1 \times \text{distance}_1 = \text{mass}_2 \times…
Vince
- 101
0
votes
2 answers
When a falling object lands, does the velocity (graph) instantly jump to zero? Or does it "slow down"?
You drop an object. It lands before hitting terminal velocity. What does the velocity graph look like? Jump discontinuity or continuous? (ie: Does it instantly go from moving to not moving? Or does it "gradually" slow down, as molecules…
JackOfAll
- 135
0
votes
1 answer
Flux from cube: Relation between the vector field to that of the opposite side
This is an exerpt from Feynman's lecture:
. . .We wish to find the flux of a vector field $C$ through the surface of the cube. . . First consider the face having edges $\Delta y \quad \& \quad \Delta z$. The flux outward on this face is the…
user36790
-1
votes
1 answer
Acceleration and Velocity Zero at Same Time
Since velocity is the antiderivative of acceleration ∫a(t)dt, how would one take a starting velocity and acceleration and determine what constant change in acceleration would be needed for a and v to be zero at the same time?
Danny
- 11