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Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.
AP Calculus BC is equivalent to a full year regular college course, covering both Calculus I and II. After passing the exam, students may move on to Calculus III (Multivariable Calculus). Purpose. According to the College Board, Calculus BC is a full-year course in the calculus of functions of a single variable.
History of calculus. Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series. Many elements of calculus appeared in ancient Greece, then in China and the Middle East, and still later again in medieval Europe and in India.
Outline of calculus. Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of contemporary mathematics education. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is ...
This is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus. Elementary rules of differentiation [ edit ] Unless otherwise stated, all functions are functions of real numbers ( R ) that return real values; although more generally, the formulae below apply wherever they are well defined [1 ...
Harmonic analysis. Harmonic analysis is a branch of mathematical analysis concerned with the representation of functions and signals as the superposition of basic waves. This includes the study of the notions of Fourier series and Fourier transforms ( Fourier analysis ), and of their generalizations.
v. t. e. In mathematics, a series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity. [1] The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such ...
Trigonometric substitution. Partial fractions in integration. Quadratic integral. Proof that 22/7 exceeds π. Trapezium rule. Integral of the secant function. Integral of secant cubed. Arclength. Solid of revolution.