History of Calculus

	Revision 42 . . (edit) December 18, 2001 3:39 pm by Berek
	Revision 41 . . (edit) December 18, 2001 3:24 pm by (logged).132.2.xxx
	Revision 40 . . December 18, 2001 2:43 pm by AxelBoldt
	Revision 39 . . (edit) December 18, 2001 12:27 pm by (logged).252.67.xxx
	Revision 38 . . (edit) December 13, 2001 4:02 am by (logged).77.174.xxx [corrected spelling of immediately]
	Revision 37 . . December 9, 2001 3:56 am by (logged).21.52.xxx
	Revision 36 . . December 9, 2001 3:55 am by (logged).21.52.xxx
	Revision 35 . . November 29, 2001 12:16 am by AxelBoldt
	Revision 34 . . November 28, 2001 11:00 am by (logged).44.206.xxx
	Revision 33 . . November 28, 2001 10:41 am by (logged).44.206.xxx
	Revision 32 . . October 27, 2001 1:35 am by AxelBoldt [Flesh out the story a bit]

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Difference (from prior major revision) (minor diff, author diff)

Changed: 1c1

Calculus, the Latin word for "pebble", refers to several mathematical disciplines. Most commonly, it refers to the detailed analysis of the change in functions and is of utmost importance in all sciences. It is usually divided into two (closely related) branches: differential calculus and integral calculus.

Calculus, the Latin word for "pebble", refers to several mathematical disciplines. Most commonly, it refers to the detailed analysis of the change in functions and is of utmost importance in all sciences. It is usually divided into two (closely related) branches: differential calculus and integral calculus.

Changed: 10c10

Since immediately substituting 0 for h;; would lead to 0/0, or an algebraic hole called a void, which cannot be computed, the numerator must first be simplified until h can be factored out and then canceled against the h of the denominator. The resulting equation is the derivative of the function, or the compilation of the instantaneous slope at each point x''.

Since immediately substituting 0 for h would lead to 0/0, which cannot be computed, the numerator must first be simplified until h can be factored out and then canceled against the h of the denominator. The resulting equation is the derivative of the function, or the compilation of the instantaneous slopes at each point x.

Changed: 12c12

These messy limit calculations can be avoided however because of powerful differentiation rules which allow to find derivatives easily using simple algebraic manipulations. See derivative for the details.

These messy limit calculations can be avoided however because of powerful differentiation rules which allow us to find derivatives easily using simple algebraic manipulations. See derivative for the details.

Changed: 19c19

This allows to recover the total change in a function over some interval from its instantaneous rate of change, by integrating the latter. The fundamental theorem also provides a method to compute many integrals algebraically, without actually performing the limit process, by finding antiderivatives. It also allows to solve some differential equations, equations that relate an unknown function to its derivative. Differential equations are ubiquitous in the sciences.

This allows us to recover the total change in a function over some interval from its instantaneous rate of change, by integrating the latter. The fundamental theorem also provides a method to compute many integrals algebraically, without actually performing the limit process, by finding antiderivatives. It also allows us to solve some differential equations, equations that relate an unknown function to its derivative. Differential equations are ubiquitous in the sciences.

Changed: 21c21

The conceptual foundations of calculus include the function, limit, infinite sequences, infinite series and continuity. Its tools include the [Symbol Manipulation]? techniques associated with [School Algebra]?, and mathematical induction.

The conceptual foundations of calculus include the function, limit, infinite sequences, infinite series and continuity. Its tools include the [Symbol Manipulation]? techniques associated with [School Algebra]?, and mathematical induction.