Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
WaveIn physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction, it is said to be a traveling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave.
Long-exposure photographyLong-exposure, time-exposure, or slow-shutter photography involves using a long-duration shutter speed to sharply capture the stationary elements of images while blurring, smearing, or obscuring the moving elements. Long-exposure photography captures one element that conventional photography does not: an extended period of time. The paths of bright moving objects become clearly visible—clouds form broad bands, vehicle lights draw bright streaks, stars leave trails in the sky, and water waves appear smooth.
Star trailA star trail is a type of photograph that uses long exposure times to capture diurnal circles, the apparent motion of stars in the night sky due to Earth's rotation. A star-trail photograph shows individual stars as streaks across the image, with longer exposures yielding longer arcs. The term is used for similar photos captured elsewhere, such as on board the International Space Station and on Mars. Typical shutter speeds for a star trail range from 15 minutes to several hours, requiring a "Bulb" setting on the camera to open the shutter for a period longer than usual.