Download Algebraic and transcendental functions

Transcendental Function
A transcendental function is a function that does not satisfy a polynomial equation whose
coefficients are themselves polynomials, in contrast to an algebraic function, which does satisfy
such an equation. In other words a transcendental function is a function which "transcends"
algebra in the sense that it cannot be expressed in terms of a finite sequence of the algebraic
operations of addition, multiplication, and root extraction.
Examples of transcendental functions include the exponential function, the logarithm, and the
trigonometric functions.
Formally, an analytic function ƒ(z) of one real or complex variable z is transcendental if it is
algebraically independent of that variable.
Algebraic and transcendental functions
The logarithm and the exponential function are examples of transcendental functions.
Transcendental function is a term often used to describe the trigonometric functions, i.e., sine,
cosine, tangent, cotangent, secant, and cosecant, also.
A function that is not transcendental is said to be algebraic. Examples of algebraic functions are
rational functions and the square root function.
The operation of taking the indefinite integral of an algebraic function is a source of
transcendental functions. For example, the logarithm function arose from the reciprocal function
in an effort to find the area of a hyperbolic sector. Thus the hyperbolic angle and the hyperbolic
functions sinh, cosh, and tanh are all transcendental.
In differential algebra one studies how integration frequently creates functions algebraically
independent of some class taken as 'standard', such as when one takes polynomials with
trigonometric functions as variables.
Dimensional analysis
In dimensional analysis, transcendental functions are notable because they make sense only when
their argument is dimensionless (possibly after algebraic reduction). Because of this,
transcendental functions can be an easy-to-spot source of dimensional errors. For example, log(10
m) is a nonsensical expression, unlike log(5 meters / 3 meters) or log(3) meters . One could
attempt to apply a logarithmic identity to get log(10) + log(m), which highlights the problem:
applying a non-algebraic operation to a dimension creates meaningless results.
Some Examples
All of the following functions are transcendental: except for a few rare cases, it is generally not
possible to relate the value, f(x), of any of these functions to its input x by a finite number of
algebraic operations.
A function which is not an algebraic function. In other words, a function which
"transcends," i.e., cannot be expressed in terms of, algebra. Examples of transcendental
functions include the exponential function, the trigonometric functions, and the inverse
functions of both.
In mathematics, a function not expressible as a finite combination of the algebraic
operations of addition, subtraction, multiplication, division, raising to a power, and
extracting a root. Examples include the functions log , sin , cos , and any functions
containing them. Such functions are expressible in algebraic terms only as infinite series.
In general, the term transcendental means nonalgebraic. transcendental number.
The operation of taking the indefinite integral of a function is a prolific source of transcendental
functions, in the way that the logarithm function arises from the reciprocal function. In
differential algebra it is studied how integration frequently creates functions algebraically
independent of some class taken as 'standard', such as it created by taking polynomials with
trigonometric functions
Alternative Orthography: TRANSCENDENTAL FUNCTION
Hexadecimal (or equivalents, 770AD-1900s)
54 52 41 4E 53 43 45 4E 44 45 4E 54 41 4C
46 55 4E 43 54 49 4F 4E
Leonardo da Vinci (1452-1519; backwards)
Binary Code (1918-1938, probably earlier)
01010100 01010010 01000001 01001110 01010011 01000011 01000101 01001110 01000100
01000101 01001110 01010100 01000001 01001100 00100000 01000110 01010101 01001110
01000011 01010100 01001001 01001111 01001110
HTML Code (1990)
&#84 &#82 &#65 &#78 &#83 &#67 &#69 &#78 &#68 &#69 &#78 &#84 &#65 &#76
&#32 &#70 &#85 &#78 &#67 &#84 &#73 &#79 &#78
ISO 10646 (1991-1993)
0054 0052 0041 004E 0053 0043 0045 004E 0044 0045 004E 0054 0041 004C
004E 0043 0054 0049 004F 004E
0046 0055
Encryption (beginner's substitution cypher):
545235485337394838394854354624055483754434948
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Kanwal - faryal
BCS (HONS)
Roll No: 9002
Semester: 2
SUBMITTED TO: Mr. ATIF