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

$${d\over dx} f(x)$$

and Integrals

$$\int f(x)\,dx,$$

respectively.

While ideas related to calculus had been known for some time (Archimedes' Exhaustion Method 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, Extensions Calculus, Fluent, Fluxion, Fractional Calculus, Functional Calculus, Fundamental Theorems of Calculus, Heaviside Calculus, Integral, Integral Calculus, Jacobian, Lambda Calculus, Kirby Calculus, Malliavin Calculus, Predicate Calculus, Propositional Calculus, Slope, Tensor Calculus, Umbral Calculus, Volume

References

Calculus

Anton, H. Calculus with Analytic Geometry, 5th ed. New York: Wiley, 1995.

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.

Brown, K. S. ``Calculus and Differential Equations.'' http://www.seanet.com/~ksbrown/icalculu.htm.

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.

Strang, G. Calculus. Wellesley, MA: Wellesley-Cambridge Press, 1991.