Pierre-Simon Laplace (1749-1827)
Laplace was a French mathematician, astronomer, and physicist who applied the Newtonian theory of gravitation to the solar system (an important problem of his day). He played a leading role in the development of the metric system.
The Laplace Transform is widely used in engineering applications (mechanical and electronic), especially where the driving force is discontinuous. It is also used in process control.
If x=t and y= t^3 find the integral of xydx from 0 to 3.
Solution:
x = t
dx = dt
y = t^3
∫ ( t^4) dt = 1/5 t^5 + C
evaluated from 0 to 3
= 1/5 [(3)^5 - 0]
= 3^5/5
= 243/5
∫ (t^4)dt evaluated (0-3) = 243/5
Solution:
int (cot x) dx
let cot x = cosx/sinx
int (cosx/sinx) dx = int (1/sinx) cosx dx
let u = sin x ; du = cos x
Recall: Dx (ln u) = du/u
int (1/sinx)(cosx) dx = ln (sinx) + C
Answer:
int (cot x) = ln (sin x) + C
Answer:
Dx [ ln(secx) ]let u = secx
Du (secx) = tanx secx
Dx (lnu) = du/u
= secxtanx/sec xDx [ ln(secx)] = tanx
LIDAR (Light Detection And Ranging, also LADAR) is an optical remote sensing technology that can measure the distance to, or other properties of a target by illuminating the target with light, often using pulses from a laser.
- A FASOR used at the Starfire Optical Range for LIDAR and laser guide star experiments is tuned to the sodium D2a line and used to excite sodium atoms in the upper atmosphere.
Further information about LADAR can be found here.
