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Calculus
In general, "a" calculus is an abstract theory developed in a purely formal way.
"The" calculus, more properly called analysis (or real analysis or, in older literature, infinitesimal
analysis), is the branch of mathematics studying the rate of change of quantities
(which can be interpreted as slopes of curves) and the
length, area, and volume of objects.
The calculus is sometimes divided into differential
and integral calculus, concerned with derivatives
and integrals
respectively.
While ideas related to calculus had been known for some time (Archimedes' method of exhaustion was a form of calculus), it was not until the independent work
of Newton and Leibniz that the modern elegant tools and ideas of calculus were developed.
Even so, many years elapsed until the subject was put on a mathematically rigorous
footing by mathematicians such as Weierstrass.
SEE ALSO: Arc Length, Area, Calculus of Variations, Change
of Variables Theorem, Derivative, Differential
Calculus, Ellipsoidal Calculus, Exterior
Algebra, Fluent, Fluxion,
Fractional Calculus, Functional
Calculus, Fundamental Theorems
of Calculus, Heaviside Calculus, Integral,
Integral Calculus, Jacobian,
Lambda Calculus, Kirby
Calculus, Malliavin Calculus, Multivariable
Calculus, Partial Derivative, Predicate
Calculus, Propositional Calculus, Slope, Stochastic Calculus,
Tensor Calculus, Umbral
Calculus, Volume
REFERENCES:
Anton, H. Calculus:
A New Horizon, 6th ed. New York: Wiley, 1999.
Apostol, T. M. Calculus, 2nd ed., Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra.
Waltham, MA: Blaisdell, 1967.
Apostol, T. M. Calculus, 2nd ed., Vol. 2: Multi-Variable Calculus and Linear Algebra, with Applications
to Differential Equations and Probability. Waltham, MA: Blaisdell, 1969.
Apostol, T. M.; Chrestenson, H. E.; Ogilvy, C. S.; Richmond, D. E.; and Schoonmaker, N. J. A
Century of Calculus, Part I: 1894-1968. Washington, DC: Math. Assoc. Amer.,
1992.
Apostol, T. M.; Mugler, D. H.; Scott, D. R.; Sterrett, A. Jr.; and Watkins, A. E. A
Century of Calculus, Part II: 1969-1991. Washington, DC: Math. Assoc. Amer.,
1992.
Ayres, F. Jr. and Mendelson, E. Schaum's Outline of Theory and Problems of Differential and Integral Calculus, 3rd ed.
New York: McGraw-Hill, 1990.
Borden, R. S. A
Course in Advanced Calculus. New York: Dover, 1998.
Boyer, C. B. A History of the Calculus and Its Conceptual Development. New York: Dover,
1989.
Courant, R. and John, F. Introduction
to Calculus and Analysis, Vol. 1. New York: Springer-Verlag, 1999.
Courant, R. and John, F. Introduction
to Calculus and Analysis, Vol. 2. New York: Springer-Verlag, 1990.
Hahn, A. Basic Calculus: From Archimedes to Newton to Its Role in Science. New York: Springer-Verlag,
1998.
Kaplan, W. Advanced
Calculus, 4th ed. Reading, MA: Addison-Wesley, 1992.
Marsden, J. E. and Tromba, A. J. Vector
Calculus, 4th ed. New York: W. H. Freeman, 1996.
MathPages. "Calculus and Differential Equations." http://www.mathpages.com/home/icalculu.htm.
Mendelson, E. 3000 Solved Problems in Calculus. New York: McGraw-Hill, 1988. Strang, G. Calculus.
Wellesley, MA: Wellesley-Cambridge Press, 1991.
Weisstein, E. W. "Books about Calculus." http://www.ericweisstein.com/encyclopedias/books/Calculus.html.
Referenced on Wolfram|Alpha: Calculus
CITE THIS AS:
Weisstein, Eric W. "Calculus." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Calculus.html
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