"함수"의 두 판 사이의 차이

2020년 12월 28일 (월) 04:10 기준 최신판

개요

함수와 관련된 기본적인 개념과 수학에서 가장 기본적인 함수 몇가지를 배움.

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기초적인 집합의 개념

중요한 개념 및 정리

일대일대응

초등함수의 예

다항함수 - 상수함수, 일차함수, 이차함수, ...
유리함수
지수함수
로그함수
삼각함수
쌍곡함수

메모

Early attempts to define a function were made by James Gregory (1687), Euler (1748), and, later in the 18th century, by La Croix, Lagrange, and d'Alembert.

All these attempts were intuitive, rough-and-ready affairs and none gained acceptance. Fourier and Cauchy, both around 1820, offered improved versions;

finally Dirichlet in 1837 identified the essential property of uniqueness": y is a function of x when to each value of x in a given interval there correspond as unique value of y". This is not quite the end of the story, of course;in time it became apparentt.

[Atkinson2002]

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 * 함수와 관련된 기본적인 개념과 수학에서 가장 기본적인 함수 몇가지를 배움.
 ==배우기 전에 알고 있어야 하는 것들==
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 * 기초적인 집합의 개념
 ==중요한 개념 및 정리==
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 * [[일대일대응]]
 ==초등함수의 예==
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 * [[쌍곡함수]]
 ==메모==
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 * '''[Atkinson2002]'''
 ==관련논문==
-* '''[Atkinson2002]'''[http://www.jstor.org/stable/1558992 Where Do Functions Come from?] Leigh Atkinson, <cite>The College Mathematics Journal</cite>, Vol. 33, No. 2 (Mar., 2002), pp. 107-112
+* '''[Atkinson2002]'''[http://www.jstor.org/stable/1558992 Where Do Functions Come from?] Leigh Atkinson, <cite>The College Mathematics Journal</cite>, Vol. 33, No. 2 (Mar., 2002), pp. 107-112
-* [http://www.jstor.org/stable/2686848 Evolution of the Function Concept: A Brief Survey] Israel Kleiner, <cite>The College Mathematics Journal</cite>, Vol. 20, No. 4 (Sep., 1989), pp. 282-300
+* [http://www.jstor.org/stable/2686848 Evolution of the Function Concept: A Brief Survey] Israel Kleiner, <cite>The College Mathematics Journal</cite>, Vol. 20, No. 4 (Sep., 1989), pp. 282-300
-* [http://www.jstor.org/stable/3604739 An Introduction to Logarithms] F. G. Brown, <cite>The Mathematical Gazette</cite>, Vol. 11, No. 160 (Oct., 1922), pp. 164-166
+* [http://www.jstor.org/stable/3604739 An Introduction to Logarithms] F. G. Brown, <cite>The Mathematical Gazette</cite>, Vol. 11, No. 160 (Oct., 1922), pp. 164-166
-* [http://www.jstor.org/stable/3026878 A Brief History of Logarithms] R. C. Pierce, Jr., <cite>The Two-Year College Mathematics Journal</cite>, Vol. 8, No. 1 (Jan., 1977), pp. 22-26
+* [http://www.jstor.org/stable/3026878 A Brief History of Logarithms] R. C. Pierce, Jr., <cite>The Two-Year College Mathematics Journal</cite>, Vol. 8, No. 1 (Jan., 1977), pp. 22-26
-* [http://www.jstor.org/stable/2973509 History of the Exponential and Logarithmic Concepts] Florian Cajori, <cite>The American Mathematical Monthly</cite>, Vol. 20, No. 1 (Jan., 1913), pp. 5-14
+* [http://www.jstor.org/stable/2973509 History of the Exponential and Logarithmic Concepts] Florian Cajori, <cite>The American Mathematical Monthly</cite>, Vol. 20, No. 1 (Jan., 1913), pp. 5-14
-== 노트 ==
-* You do not need to do anything special to use subroutines from the Standard C library (libc.a).<ref name="ref_abea">[https://sites.ualberta.ca/dept/chemeng/AIX-43/share/man/info/C/a_doc_lib/aixprggd/genprogc/subr_prgs_libs.htm Chapter 24. Subroutines, Example Programs, and Libraries]</ref>
-* The cc command automatically searches this library for subroutines that a program needs.<ref name="ref_abea" />
-* However, if you use subroutines from another library, you must tell the compiler to search that library.<ref name="ref_abea" />
-* If your program uses subroutines from the library libname.a, compile your program with the flag -lname (lowercase L).<ref name="ref_abea" />
-* AcknowledgeAllAlarms Subroutine Acknowledges alarms for all tags in the specified Picture.<ref name="ref_160a">[https://www.ge.com/digital/documentation/ifix/version60/Subsystems/FIXVBA/content/acknowledgeallalarms_subroutine.htm AcknowledgeAllAlarms Subroutine]</ref>
-* The subroutine will also acknowledge the alarm associated with this block.<ref name="ref_160a" />
-* The subroutine will acknowledge other alarms, but not the alarm associated with this block.<ref name="ref_160a" />
-* (default) – Allows the subroutines to provide the error messages.<ref name="ref_160a" />
-* PURE Asserts that the procedure has no side effects.<ref name="ref_55c5">[https://www.cita.utoronto.ca/~merz/intel_f10b/main_for/mergedProjects/lref_for/source_files/rfsubr.htm SUBROUTINE]</ref>
-* A subroutine is invoked by a CALL statement or defined assignment.<ref name="ref_55c5" />
-* A subroutine subprogram cannot contain a FUNCTION statement, a BLOCK DATA statement, a PROGRAM statement, or another SUBROUTINE statement.<ref name="ref_55c5" />
-* But, as other languages do, Perl has the ability to make subroutines, which are user-defined functions.<ref name="ref_14fd">[https://www.oreilly.com/library/view/learning-perl-6th/9781449311063/ch04.html Learning Perl, 6th Edition [Book]]</ref>
-* As you may have noticed in the previous example, you may use any global variables within the subroutine body.<ref name="ref_14fd" />
-* Most often, you refer to the invocation as simply calling the subroutine.<ref name="ref_14fd" />
-* You always invoke a subroutine as part of an expression, even if you don’t use the result of the expression.<ref name="ref_14fd" />
-* You can divide up your code into separate subroutines.<ref name="ref_d967">[https://www.tutorialspoint.com/perl/perl_subroutines.htm Tutorialspoint]</ref>
-* In versions of Perl before 5.0, the syntax for calling subroutines was slightly different as shown below.<ref name="ref_d967" />
-* Because the @_ variable is an array, it can be used to supply lists to a subroutine.<ref name="ref_d967" />
-* You can return a value from subroutine like you do in any other programming language.<ref name="ref_d967" />
-* A subroutine is a piece of code that performs a set of actions or calculations, or a combination of the two.<ref name="ref_332d">[https://sourcedaddy.com/ms-access/difference-between-subroutines-and-functions.html Difference Between Subroutines and Functions]</ref>
-* The programmer has to write a subroutine only once, and it can be called from anywhere within the program as many times as needed.<ref name="ref_332d" />
-* You do not have to use the word Call to utilize the subroutine MySub.<ref name="ref_332d" />
-* A function is exactly like a subroutine except that it returns a value.<ref name="ref_332d" />
-* Subroutines are identified in a program by a unique subroutine label.<ref name="ref_efe2">[https://tormach.com/subroutines-reference SUBROUTINES REFERENCE]</ref>
-* The subroutine keyword defines the action associated with the subroutine label.<ref name="ref_efe2" />
-* The sub and endsub keywords are used to define the beginning and end a subroutine.<ref name="ref_efe2" />
-* If the subroutine is defined in the same file as the main program that calls the subroutine, it must be defined before the call statement.<ref name="ref_efe2" />
-* A subroutine is a block of code that performs a task based on some arguments and optionally returns a result.<ref name="ref_c602">[https://www.keil.com/support/man/docs/armasm/armasm_dom1359731145503.htm Assembler User Guide: Register usage in subroutine calls]</ref>
-* By convention, you use registers R0 to R3 to pass arguments to subroutines, and R0 to pass a result back to the callers.<ref name="ref_c602" />
-* To call subroutines, use a branch and link instruction.<ref name="ref_c602" />
-* Subroutines - In computer programming, a subroutine is a sequence of program instructions that performs a specific task, packaged as a unit.<ref name="ref_afb0">[https://bournetocode.com/projects/GCSE_Computing_Fundamentals/pages/3-2-7-subroutines.html 3.2.7 Subroutines (Procedures and Functions)]</ref>
-* In different programming languages, a subroutine may be called a procedure, a function, a routine, a method, or a subprogram.<ref name="ref_afb0" />
-* The generic term 'callable unit' is sometimes used.<ref name="ref_afb0" />
-* In this example: def displayTotal(total): 'total' is a parameter that will be passed to the 'displayTotal' subroutine.<ref name="ref_afb0" />
-* E very subroutine in Java must be defined inside some class.<ref name="ref_3294">[http://math.hws.edu/javanotes/c4/s2.html Javanotes 8.1, Section 4.2 -- Static Subroutines and Static Variables]</ref>
-* This makes Java rather unusual among programming languages, since most languages allow free-floating, independent subroutines.<ref name="ref_3294" />
-* One purpose of a class is to group together related subroutines and variables.<ref name="ref_3294" />
-* Static subroutines are easier to understand: In a running program, a static subroutine is a member of the class itself.<ref name="ref_3294" />
-* NAME is the name given to the subroutine and must follow the same rules as variables.<ref name="ref_ff3c">[https://www.oc.nps.edu/~bird/oc3030_online/fortran/subs/subs.html Subroutines and Functions]</ref>
-* In a subroutine, values are returned via the arguments.<ref name="ref_ff3c" />
-* The number and type of the arguments in the CALLing statement must agree with the number and type of the arguments in the SUBROUTINE.<ref name="ref_ff3c" />
-* The subroutine on the left has no arguments and simply prints out a message when it is called.<ref name="ref_ff3c" />
-* The code for a subroutine can be written to the same file as the calling program.<ref name="ref_3647">[https://infosys.beckhoff.com/content/1033/tcnci/9007199725851019.html Subroutine techniques]</ref>
-* In this case the subroutine is linked directly: it is automatically also loaded as the file is read.<ref name="ref_3647" />
-* A procedure is a subroutine that performs a specific task.<ref name="ref_7347">[https://www.bbc.co.uk/bitesize/guides/zb33rwx/revision/4 Procedures and functions of subroutines]</ref>
-* When the task is complete, the subroutine ends and the main program continues from where it left off.<ref name="ref_7347" />
-* , followed by that subroutine's name.<ref name="ref_b750">[https://pages.mtu.edu/~shene/COURSES/cs201/NOTES/chap07/subroutine.html Designing Subroutines]</ref>
-* Here are a examples: The following is a subroutine called Factorial .<ref name="ref_b750" />
-* Subroutines can be internal to a program or a module.<ref name="ref_b750" />
-* In Fortran and other programming languages, this corresponds to creating a set of subprograms.<ref name="ref_ab63">[https://www.ichec.ie/academic/national-hpc/documentation/fortran-tutorial/subprograms Subprograms, functions and subroutines]</ref>
-* Fortran subroutines are similar to functions, except that they can return more than one variable or array to the calling program.<ref name="ref_ab63" />
-* Another difference is that the output values are returned via the arguments to the subroutine.<ref name="ref_ab63" />
-* A subroutine subprogram must have a SUBROUTINE statement as the first statement.<ref name="ref_9bde">[https://docs.oracle.com/cd/E19957-01/805-4939/6j4m0vnbg/index.html SUBROUTINE (FORTRAN 77 Language Reference)]</ref>
-* Like many languages, Perl provides for user-defined subroutines.<ref name="ref_2388">[https://www.cs.ait.ac.th/~on/O/oreilly/perl/prog/ch02_07.htm [Chapter 2] 2.7 Subroutines]</ref>
-* You can generate anonymous subroutines, accessible only through references.<ref name="ref_2388" />
-* The return value of the subroutine (or of any other block, for that matter) is the value of the last expression evaluated.<ref name="ref_2388" />
-* Or you may use an explicit return statement to specify the return value and exit the subroutine from any point in the subroutine.<ref name="ref_2388" />
-* FlashBASIC or BASIC provides the ability to call subroutines.<ref name="ref_8236">[https://www3.rocketsoftware.com/rocketd3/support/documentation/d3nt/91/refman/pickbasic-flashbasic/subroutine_statement.htm subroutine Statement]</ref>
-* You can write a subroutine in any language that supports subroutines.<ref name="ref_e538">[https://infocenter.informationbuilders.com/wf80/topic/pubdocs/reporting/UsingFunctions/source/topic208.htm Writing a Subroutine]</ref>
-* When you write a subroutine you need to consider the requirements and limits that affect it.<ref name="ref_e538" />
-* Call subroutine SIMPLE (PRINCPAL, DATE_PUT, YRRATE, TOTAL).<ref name="ref_e538" />
-* If you move the SIMPLE subroutine into a file separate from the main program and compile it, you can call the subroutine.<ref name="ref_e538" />
-* A subroutine is a user-defined command that can be called to perform a block of logic and optionally return a value.<ref name="ref_f035">[https://www.promodel.com/onlinehelp/promodel/80/C-06%20-%20Subroutines.htm Subroutines]</ref>
-* ProModel handles subroutines in three ways.<ref name="ref_f035" />
-* First, a subroutine may be processed by the calling logic as though the subroutine is part of the calling logic.<ref name="ref_f035" />
-* This way is the most commonly used, and is done by simply referencing the subroutine by name in some logic or expression.<ref name="ref_f035" />
-* All of these terms refer to a single conceptual object, which, when first invented, was called a subroutine.<ref name="ref_c56b">[https://www.mtholyoke.edu/courses/dstrahma/cs221/olr/olr9.htm Subroutines]</ref>
-* In others, such as C/C++, both types (functions and procedures) are called functions.<ref name="ref_c56b" />
-* A subroutine is a sequence of instructions that can be called (branched to), causing the sequence of instructions to execute.<ref name="ref_c56b" />
-* A procedure can have both input and output parameters.<ref name="ref_c56b" />
-* A subroutine begins with the keyword subroutine followed by the name of the routine and any arguments, and ends with the keyword endsub .<ref name="ref_64d8">[http://www.eviews.com/help/content/cprogram-Subroutines.html EViews Help: Subroutines]</ref>
-* This subroutine has no arguments so that it will behave identically every time it is used.<ref name="ref_64d8" />
-* You may use the return command to force EViews to exit from the subroutine at any time.<ref name="ref_64d8" />
-* A common use of return is to exit from the subroutine if an unanticipated error is detected.<ref name="ref_64d8" />
-* Subroutines are similar to functions, yet differ from them in several ways.<ref name="ref_5a4c">[https://www.lrsm.upenn.edu/~vitek/courses/f77intro/node27.html Structure of subroutine subprograms]</ref>
-* Subroutine is invoked using a call statement from anywhere else in your F77 code.<ref name="ref_5a4c" />
-* Keywords subroutine and end are used to define the beginning and end of a subroutine.<ref name="ref_5a4c" />
-* This is very convenient once you want to leave a subroutine in the middle and forget the remaining commands.<ref name="ref_5a4c" />
-* Using subprograms allows you to tackle bite size pieces of a problem individually.<ref name="ref_01e1">[http://www.chem.ox.ac.uk/fortran/subprograms.html Functions and Subroutines]</ref>
-* Subroutines, on the other hand, can return several results.<ref name="ref_01e1" />
-* As with functions, there are some rules for using subroutines.<ref name="ref_01e1" />
-* All variables used by the subroutine, including the arguments, must be declared in the subroutine.<ref name="ref_01e1" />
-* A routine or subroutine, also referred to as a function, procedure, and subprogram, is code called and executed anywhere in a program.<ref name="ref_3856">[https://www.computerhope.com/jargon/r/routine.htm What is a Routine and Subroutine?]</ref>
-* For example, a routine may be used to save a file or display the time.<ref name="ref_3856" />
-* In cases like this, you can create a subroutine.<ref name="ref_4827">[https://www.neurobs.com/pres_docs/html/06_introduction_to_programming/07_chapter_7_-_subroutines.htm Chapter 7 - Subroutines]</ref>
-* A subroutine can save a lot of time not only in writing your scenarios, but also in making your code more flexible and easier to re-use.<ref name="ref_4827" />
-* However, if you have put those lines of code into a subroutine, you will only need to update the subroutine.<ref name="ref_4827" />
-* In some ways, creating a subroutine is like defining your own method.<ref name="ref_4827" />
-* As in the case of modules, import lists serve to document the interface between a subroutine and the rest of the program.<ref name="ref_1a60">[https://www.sciencedirect.com/topics/computer-science/subroutines Subroutines - an overview]</ref>
-* The only problem is a decision problem: when should a function be implemented as a subroutine and when should it become a coroutine?<ref name="ref_d312">[https://www.sciencedirect.com/topics/engineering/subroutine Subroutine - an overview]</ref>
-* Is one or more internal subprograms (defining internal procedures).<ref name="ref_d53c">[https://scc.ustc.edu.cn/zlsc/sugon/intel/compiler_f/main_for/lref_for/source_files/rfsubr.htm SUBROUTINE]</ref>
-* A subroutine subprogram cannot contain a BLOCK DATA statement, a PROGRAM statement, or a MODULE statement.<ref name="ref_d53c" />
-* A subroutine can contain SUBROUTINE and FUNCTION statements to define internal procedures.<ref name="ref_d53c" />
-* A set of Instructions which are used repeatedly in a program can be referred to as Subroutine.<ref name="ref_68bc">[https://www.geeksforgeeks.org/subroutine-subroutine-nesting-and-stack-memory/ Subroutine, Subroutine nesting and Stack memory]</ref>
-* When a Subroutine is required it can be called many times during the Execution of a Particular program.<ref name="ref_68bc" />
-* A call Subroutine Instruction calls the Subroutine.<ref name="ref_68bc" />
-* Subroutine linkage method is a way in which computer call and return the Subroutine.<ref name="ref_68bc" />
-* In computer programming, a subroutine is a sequence of program instructions that performs a specific task, packaged as a unit.<ref name="ref_18cb">[https://en.wikipedia.org/wiki/Subroutine Subroutine]</ref>
-* Subroutines may be defined within programs, or separately in libraries that can be used by many programs.<ref name="ref_18cb" />
-* In different programming languages, a subroutine may be called a routine, subprogram, function, method, or procedure.<ref name="ref_18cb" />
-* The subroutine may return a computed value to its caller (its return value), or provide various result values or output parameters.<ref name="ref_18cb" />
-* A procedure returns no values and is called in a statement, not an expression.<ref name="ref_c7c4">[https://cs.lmu.edu/~ray/notes/subroutines/ subroutines]</ref>
-* The languages use some mechanism like "void context" or employ a special return value like or to make functions look like procedures.<ref name="ref_c7c4" />
-* A subroutine's signature specifies the number, order, names, modes and types of its parameters and return values.<ref name="ref_c7c4" />
-* Should we search in outer scopes, even when subroutines of the same name are "closer" to the call?<ref name="ref_c7c4" />
-===소스===
- <references />

"함수"의 두 판 사이의 차이

2020년 12월 28일 (월) 04:10 기준 최신판

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개요

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중요한 개념 및 정리

초등함수의 예

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