Functions - Revision history

Admin at 01:12, 26 June 2017

2017-06-26T01:12:56Z

← Older revision		Revision as of 01:12, 26 June 2017
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	Also see: [[Polynomials]]		Also see: [[Polynomials]]

	=~~Mathematics~~=		==Definitions==

			Injective - A function is injective if it is '''one-to-one''' - that is, every element of the domain maps to at most one element of the range. (Note that an injective function may leave items in the range unmapped-to.)

			Bijective - A function is bijective if it is '''BOTH one-to-one AND onto'''. That is, every element of the range is mapped to by exactly one element in the domain. A bijective function is both injective and surjective.

			Surjective - A function is surjective, or '''onto''', if every element of the range is mapped to by at least one element of the domain.

	==Algebra/Precalculus: Topics in Functions==		==Algebra/Precalculus: Topics in Functions==

Admin: /* Algebra/Precalculus: Topics in Functions */

2017-06-26T01:07:23Z

Algebra/Precalculus: Topics in Functions

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 * absolute value
 * inverse functions
+* conic sections - not really function stuff
 ==More About Functions==

Admin: /* Computer Science and Programming */

2017-06-26T01:06:52Z

Computer Science and Programming

← Older revision		Revision as of 01:06, 26 June 2017
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	The study of functions continues in an undergraduate mathematics education with function analysis, split into real analysis and complex analysis. Engineering education focuses on the more practical aspects of functions - computing with software or calculators in the context of solving an applied problem.		The study of functions continues in an undergraduate mathematics education with function analysis, split into real analysis and complex analysis. Engineering education focuses on the more practical aspects of functions - computing with software or calculators in the context of solving an applied problem.

	~~=Computer Science and Programming=~~

	The basic idea of a function is shared in common between the computer science view of functions, the engineering view of functions, and the mathematical view of functions, but beyond that, things diverge pretty quickly.

Admin at 09:05, 10 April 2017

2017-04-10T09:05:08Z

← Older revision		Revision as of 09:05, 10 April 2017
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	** Concavity		** Concavity
	* Quadratic, exponential, log, transformations, trig, trig identities, compositions, inverses, combinations, polynomials, rationals, vectors and matrices, sequences and series		* Quadratic, exponential, log, transformations, trig, trig identities, compositions, inverses, combinations, polynomials, rationals, vectors and matrices, sequences and series

			==More About Functions==

			Like [[Polynomials]], functions start simple enough, but quickly get complicated, and can absorb hours, days, or even lifetimes of research. Functions are a way of mapping inputs to outputs, and they are immensely useful in using mathematics to describe, model, and understand the world.

			Most college-level mathematics courses begin with functions, or arrive at the topic in short order. Functions provide the entire framework for precalculus, and when students hit calculus, it's all about continuous functions - the three conditions of continuity (calculus pop quiz: what are the three conditions of a function <math>f(x)</math> being continuous at a location <math>x=a</math>?) being one of the first topics covered in calculus and one of the principal reasons calculus teachers spend so much time on limits.

			(Answer: the three conditions for a function f(x) to be continuous at x = a are:
			* <math>f(a)</math> must exist
			* <math>\lim_{x \rightarrow a+} f(x) = \lim_{x \rightarrow a-} f(x) = \lim_{x \rightarrow a} f(x)</math>
			* <math>\lim_{x \rightarrow a} f(x) = f(a)</math>

			These three criteria form the criteria for a continuous function. If a function is continuous, the limit of the function as x approaches a can be computed by simply evaluating the function at a.)

			The study of functions continues in an undergraduate mathematics education with function analysis, split into real analysis and complex analysis. Engineering education focuses on the more practical aspects of functions - computing with software or calculators in the context of solving an applied problem.

			=Computer Science and Programming=

			The basic idea of a function is shared in common between the computer science view of functions, the engineering view of functions, and the mathematical view of functions, but beyond that, things diverge pretty quickly.

Admin: /* Mathematics */

2017-04-10T08:37:17Z

Mathematics

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 =Mathematics=
 Intermediate algebra functions outline:
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 * Linear functions
 * (Later chapters cover other kinds of functions)
 Precalculus outline:
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 * absolute value
 * inverse functions

Admin at 08:31, 10 April 2017

2017-04-10T08:31:53Z

← Older revision		Revision as of 08:31, 10 April 2017
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	Also see: [[Polynomials]]		Also see: [[Polynomials]]

			=Mathematics=

	[[Category:~~Mathematics~~]]		Intermediate algebra functions outline:
			* Introduction to functions
			* Function notation
			* Algebra and function composition
			* Slope and rate of change
			* Linear functions
			* (Later chapters cover other kinds of functions)

			College algebra functions outline:
			* <s>Rectangular coordinate system
			* Distance and midpoint
			* 2-variable equations
			* Graphs of lines
			* Properties of functions
			* Graph transformations
			* Inverse variation</s>
			* This was a really weird book...

			Precalculus outline:
			* sets and maps
			* function definitions
			* function notation
			* domain and range
			* rate of change
			* composition
			* transformation
			* absolute value
			* inverse functions






			[[Category:Math]]
			[[Category:Functions]]

Admin: Created page with "Also see: Polynomials Category:Mathematics"

2017-04-10T08:26:30Z

Created page with "Also see: Polynomials Category:Mathematics"

New page

Also see: [[Polynomials]]

[[Category:Mathematics]]