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The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations .
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. [1] The terms path integral , curve integral , and curvilinear integral are also used; contour integral is used as well, although that is typically reserved for line integrals in the complex plane .
The term differential is used in calculus to refer to an infinitesimal (infinitely small) change in some varying quantity. For example, if x is a variable, then a change in the value of x is often denoted Δx (pronounced delta x). The differential dx represents an infinitely small change in the variable x. The idea of an infinitely small or ...
Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.
The mass of an object of known density, the moment of inertia of objects, and the potential energies due to gravitational and electromagnetic forces can all be found by the use of calculus. An example of the use of calculus in mechanics is Newton's second law of motion, which states that the derivative of an object's momentum concerning time ...
The calculus of variations began with the work of Isaac Newton, such as with Newton's minimal resistance problem, which he formulated and solved in 1685, and later published in his Principia in 1687, [2] which was the first problem in the field to be formulated and correctly solved, [2] and was also one of the most difficult problems tackled by variational methods prior to the twentieth century.
Development of a formulation of arc length suitable for applications to mathematics and the sciences is a focus of calculus. In the most basic formulation of arc length for a parametric curve (thought of as the trajectory of a particle), the arc length is obtained by integrating the speed of the particle over the path.
: distance from the origin of the line u {\displaystyle \mathbf {u} } : direction of line (a non-zero vector) Searching for points that are on the line and on the sphere means combining the equations and solving for d {\displaystyle d} , involving the dot product of vectors:
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