미분방정식 - 편집 역사

2021년 2월 17일 (수) 12:43에 Pythagoras0님의 편집

2021-02-17T12:43:52Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-28T13:36:35Z

메타데이터: 새 문단

2020년 12월 28일 (월) 10:22에 Pythagoras0님의 편집

2020-12-28T10:22:17Z

Pythagoras0: /* 노트 */ 새 문단

2020-12-21T09:51:44Z

노트: 새 문단

2020년 11월 16일 (월) 14:34에 Pythagoras0님의 편집

2020-11-16T14:34:36Z

2015년 8월 18일 (화) 08:36에 Pythagoras0님의 편집

2015-08-18T08:36:35Z

Pythagoras0: 찾아 바꾸기 – “수학사연표” 문자열을 “수학사 연표” 문자열로

2013-01-14T23:37:33Z

찾아 바꾸기 – “수학사연표” 문자열을 “수학사 연표” 문자열로

Pythagoras0: 찾아 바꾸기 – “
$” 문자열을 “: ” 문자열로$

2013-01-12T17:40:02Z

찾아 바꾸기 – “<br><math>” 문자열을 “:<math>” 문자열로

2013년 1월 12일 (토) 15:25에 Pythagoras0님의 편집

2013-01-12T15:25:26Z

Pythagoras0: 찾아 바꾸기 – “네이버(.*)]” 문자열을 “” 문자열로

2012-11-02T20:08:07Z

찾아 바꾸기 – “네이버(.*)]” 문자열을 “” 문자열로

@@ 252번째 줄: / 252번째 줄: @@
   <references />
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q11214 Q11214]

← 이전 판		2020년 12월 28일 (월) 13:36 판
251번째 줄:		251번째 줄:
	===소스===		===소스===
	<references />		<references />
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q11214 Q11214]

@@ 10번째 줄: / 10번째 줄: @@
 ** 상미분방정식과 편미분방정식
-−
-−
 ==일계 미분방정식==
 * [[일계 선형미분방정식|일계선형미분방정식]]:<math>\frac{dy}{dt}+a(t)y=b(t)</math>
-* [[완전미분방정식]]:<math>M_y=N_x</math>를 만족시키는 <math>M(x, y)\, dx + N(x, y)\, dy = 0</math>  꼴의 미분방정식
+* [[완전미분방정식]]:<math>M_y=N_x</math>를 만족시키는 <math>M(x, y)\, dx + N(x, y)\, dy = 0</math>  꼴의 미분방정식
-* 다음 미분방정식들은 비선형이다
+* 다음 미분방정식들은 비선형이다
 * [[리카티 미분방정식]]:<math>y' = A(x)+ B(x)y + C(x)y^2, A(x)\neq 0, C(x)\neq 0</math>
 * [[베르누이 미분방정식]]:<math>y'+ P(x)y = Q(x)y^n</math>
-−
-−
 ==이계 선형미분방정식==
@@ 40번째 줄: / 40번째 줄: @@
 * [[리만 미분방정식]]:<math>\frac{d^2w}{dz^2} + \left[ \frac{1-\alpha-\alpha'}{z-a} + \frac{1-\beta-\beta'}{z-b} + \frac{1-\gamma-\gamma'}{z-c} \right] \frac{dw}{dz}+\left[ \frac{\alpha\alpha' (a-b)(a-c)} {z-a} +\frac{\beta\beta' (b-c)(b-a)} {z-b} +\frac{\gamma\gamma' (c-a)(c-b)} {z-c} \right] \frac{w}{(z-a)(z-b)(z-c)}=0</math> 여기서 <math>\alpha+\alpha'+\beta+\beta'+\gamma+\gamma'=1</math>
-* [[호인 미분방정식(Heun's equation)]]:<math>\frac {d^2w}{dz^2} +  \left[\frac{\gamma}{z}+ \frac{\delta}{z-1} + \frac{\epsilon}{z-d} \right]  \frac {dw}{dz}  + \frac {\alpha \beta z -q} {z(z-1)(z-d)} w = 0</math> (여기서 <math>\epsilon=\alpha+\beta-\gamma-\delta+1</math>)
+* [[호인 미분방정식(Heun's equation)]]:<math>\frac {d^2w}{dz^2} +  \left[\frac{\gamma}{z}+ \frac{\delta}{z-1} + \frac{\epsilon}{z-d} \right]  \frac {dw}{dz}  + \frac {\alpha \beta z -q} {z(z-1)(z-d)} w = 0</math> (여기서 <math>\epsilon=\alpha+\beta-\gamma-\delta+1</math>)
-−
-−
 ==비선형 미분방저식==
@@ 51번째 줄: / 51번째 줄: @@
 * [[바이어슈트라스 타원함수 ℘|바이어슈트라스의 타원함수]]:<math>(\frac{dw}{dz})^2=4w^3-g_2w-g_3</math>
-−
-−
 ==스텀-리우빌==
-* [[스텀-리우빌 이론]] 항목에서 자세히 다룸
+* [[스텀-리우빌 이론]] 항목에서 자세히 다룸
 [[스텀-리우빌 이론|스텀-리우빌 이론]]
-−
-−
 ==재미있는 사실==
-−
 * 네이버 지식인 http://kin.search.naver.com/search.naver?where=kin_qna&query=
-−
-−
 ==역사==
-−
 * http://www.google.com/search?hl=en&tbs=tl:1&q=differential+equation
 * [[수학사 연표]]
-−
-−
 ==메모==
@@ 90번째 줄: / 90번째 줄: @@
 * qualitative study
-−
 ==== 하위페이지 ====
@@ 114번째 줄: / 114번째 줄: @@
 ** [[호인 미분방정식(Heun's equation)]]
-−
-−
 ==관련된 항목들==
@@ 126번째 줄: / 126번째 줄: @@
 * [[불가능성의 정리들]]
-−
-−
 ==수학용어번역==
@@ 135번째 줄: / 135번째 줄: @@
 * [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]
 ** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
-* [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판]
+* [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판]
-−
-−
-==사전 형태의 자료==
+==사전 형태의 자료==
 * [http://ko.wikipedia.org/wiki/%EC%83%81%EB%AF%B8%EB%B6%84_%EB%B0%A9%EC%A0%95%EC%8B%9D http://ko.wikipedia.org/wiki/상미분_방정식]
@@ 151번째 줄: / 151번째 줄: @@
 ** http://www.research.att.com/~njas/sequences/?q=
-−
 ==리뷰, 에세이, 강의노트==
 * [http://www.jstor.org/stable/2687502 What It Means to Understand a Differential Equation]
@@ 164번째 줄: / 164번째 줄: @@
 ** T. Craig
-−
-−
-−
 ==관련링크와 웹페이지==
@@ 176번째 줄: / 176번째 줄: @@
 * http://eqworld.ipmnet.ru/en/solutions/ode.htm
-−
 [[분류:미분방정식]]

← 이전 판		2020년 12월 21일 (월) 09:51 판
179번째 줄:		179번째 줄:

	[[분류:미분방정식]]		[[분류:미분방정식]]
		+
		+	== 노트 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q11214 Q11214]
		+	===말뭉치===
		+	# The Differential Equation says it well, but is hard to use.<ref name="ref_7488ce2d">[https://www.mathsisfun.com/calculus/differential-equations.html Differential Equations]</ref>
		+	# Creating a differential equation is the first major step.<ref name="ref_7488ce2d" />
		+	# In Mathematics, a differential equation is an equation that contains one or more functions with its derivatives.<ref name="ref_39f5d84a">[https://byjus.com/maths/differential-equation/ Differential Equations (Definition, Types, Order, Degree, Examples)]</ref>
		+	# The primary purpose of the differential equation is the study of solutions that satisfy the equations and the properties of the solutions.<ref name="ref_39f5d84a" />
		+	# One of the easiest ways to solve the differential equation is by using explicit formulas.<ref name="ref_39f5d84a" />
		+	# A differential equation contains derivatives which are either partial derivatives or ordinary derivatives.<ref name="ref_39f5d84a" />
		+	# In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.<ref name="ref_9e5ce038">[https://en.wikipedia.org/wiki/Differential_equation Differential equation]</ref>
		+	# A partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.<ref name="ref_9e5ce038" />
		+	# Conduction of heat, the theory of which was developed by Joseph Fourier, is governed by another second-order partial differential equation, the heat equation.<ref name="ref_9e5ce038" />
		+	# A differential equation is an equation involving a function and its derivatives.<ref name="ref_746478e9">[https://www.wolframalpha.com/examples/mathematics/differential-equations/ Alpha Examples: Differential Equations]</ref>
		+	# It can be referred to as an ordinary differential equation (ODE) or a partial differential equation (PDE) depending on whether or not partial derivatives are involved.<ref name="ref_746478e9" />
		+	# The first definition that we should cover should be that of differential equation.<ref name="ref_4a3abd97">[https://tutorial.math.lamar.edu/classes/de/definitions.aspx Differential Equations]</ref>
		+	# There is one differential equation that everybody probably knows, that is Newton’s Second Law of Motion.<ref name="ref_4a3abd97" />
		+	# A differential equation is called an ordinary differential equation, abbreviated by ode, if it has ordinary derivatives in it.<ref name="ref_4a3abd97" />
		+	# Likewise, a differential equation is called a partial differential equation, abbreviated by pde, if it has partial derivatives in it.<ref name="ref_4a3abd97" />
		+	# We also investigate how direction fields can be used to determine some information about the solution to a differential equation without actually having the solution.<ref name="ref_8e70e4aa">[https://tutorial.math.lamar.edu/classes/de/de.aspx Differential Equations]</ref>
		+	# Series Solutions – In this section we define ordinary and singular points for a differential equation.<ref name="ref_8e70e4aa" />
		+	# We also show who to construct a series solution for a differential equation about an ordinary point.<ref name="ref_8e70e4aa" />
		+	# rd order differential equation just to say that we looked at one with order higher than 2nd.<ref name="ref_8e70e4aa" />
		+	# A differential equation is an equation involving derivatives.<ref name="ref_bd4e0810">[https://ocw.mit.edu/ans7870/18/18.013a/textbook/HTML/chapter26/section01.html 26.1 Introduction to Differential Equations]</ref>
		+	# You can find the general solution to any separable first order differential equation by integration, (or as it is sometimes referred to, by "quadrature").<ref name="ref_bd4e0810" />
		+	# Suppose we have a first order differential equation that is not separable, so we cannot reduce its solution to quadratures directly.<ref name="ref_bd4e0810" />
		+	# at least look at what a differential equation actually is.<ref name="ref_5b8ac86e">[https://www.khanacademy.org/math/ap-calculus-ab/ab-differential-equations-new/ab-7-1/v/differential-equation-introduction Differential equations introduction (video)]</ref>
		+	# And you might have just caught from how I described it that the solution to a differential equation is a function, or a class of functions.<ref name="ref_5b8ac86e" />
		+	# We'll verify that these indeed are solutions for I guess this is really just one differential equation represented in different ways.<ref name="ref_5b8ac86e" />
		+	# But you'll hopefully appreciate what a solution to a differential equation looks like.<ref name="ref_5b8ac86e" />
		+	# Differential equation, mathematical statement containing one or more derivatives—that is, terms representing the rates of change of continuously varying quantities.<ref name="ref_9bb2783d">[https://www.britannica.com/science/differential-equation Differential equation]</ref>
		+	# When the function involved in the equation depends on only a single variable, its derivatives are ordinary derivatives and the differential equation is classed as an ordinary differential equation.<ref name="ref_9bb2783d" />
		+	# On the other hand, if the function depends on several independent variables, so that its derivatives are partial derivatives, the differential equation is classed as a partial differential equation.<ref name="ref_9bb2783d" />
		+	# Whichever the type may be, a differential equation is said to be of the nth order if it involves a derivative of the nth order but no derivative of an order higher than this.<ref name="ref_9bb2783d" />
		+	# Learning Objectives Calculate the order and degree of a differential equation.<ref name="ref_5f74da62">[https://courses.lumenlearning.com/boundless-calculus/chapter/differential-equations/ Differential Equations]</ref>
		+	# The higher the order of the differential equation, the more arbitrary constants need to be added to the general solution.<ref name="ref_5f74da62" />
		+	# The “order” of a differential equation depends on the derivative of the highest order in the equation.<ref name="ref_5f74da62" />
		+	# The “degree” of a differential equation, similarly, is determined by the highest exponent on any variables involved.<ref name="ref_5f74da62" />
		+	# Also as we have seen so far, a differential equation typically has an infinite number of solutions.<ref name="ref_f6a04ca7">[https://www.whitman.edu/mathematics/calculus_online/section17.01.html 17.1 First Order Differential Equations]</ref>
		+	# Solve a differential equation analytically by using the dsolve function, with or without initial conditions.<ref name="ref_c2ee69ed">[https://www.mathworks.com/help/symbolic/solve-a-single-differential-equation.html Solve Differential Equation]</ref>
		+	# First-Order Linear ODE Solve this differential equation.<ref name="ref_c2ee69ed" />
		+	# Solve this third-order differential equation with three initial conditions.<ref name="ref_c2ee69ed" />
		+	# The last example is the Airy differential equation, whose solution is called the Airy function.<ref name="ref_c2ee69ed" />
		+	# Thus, one of the most common ways to use calculus is to set up an equation containing an unknown function \(y=f(x)\) and its derivative, known as a differential equation.<ref name="ref_d94ff5b0">[https://math.libretexts.org/Courses/Monroe_Community_College/MTH_211_Calculus_II/Chapter_8%3A_Introduction_to_Differential_Equations/8.1%3A_Basics_of_Differential_Equations 8.1: Basics of Differential Equations]</ref>
		+	# Combining like terms leads to the expression \(6x+11\), which is equal to the right-hand side of the differential equation.<ref name="ref_d94ff5b0" />
		+	# A differential equation is an equation involving an unknown function \(y=f(x)\) and one or more of its derivatives.<ref name="ref_d94ff5b0" />
		+	# Consider the equation \(y′=3x^2,\) which is an example of a differential equation because it includes a derivative.<ref name="ref_d94ff5b0" />
		+	# A differential equation is an equation involving terms that are derivatives (or differentials).<ref name="ref_0018c748">[https://ncatlab.org/nlab/show/differential+equation differential equation in nLab]</ref>
		+	# A partial differential equation need not have any solution at all.<ref name="ref_6edac5b5">[https://encyclopediaofmath.org/wiki/Differential_equation,_partial Differential equation, partial]</ref>
		+	# If the partial differential equation being considered is the Euler equation for a problem of variational calculus in more dimensions, a variational method is often employed.<ref name="ref_6edac5b5" />
		+	# The order of a partial differential equation is the order of the highest derivative involved.<ref name="ref_b3c4e8be">[http://www.scholarpedia.org/article/Partial_differential_equation Partial differential equation]</ref>
		+	# A solution (or a particular solution) to a partial differential equation is a function that solves the equation or, in other words, turns it into an identity when substituted into the equation.<ref name="ref_b3c4e8be" />
		+	# A differential equation can look pretty intimidating, with lots of fancy math symbols.<ref name="ref_50027daa">[https://www.myphysicslab.com/explain/what-is-a-diff-eq-en.html myPhysicsLab What Is A Differential Equation?]</ref>
		+	# Each of those variables has a differential equation saying how that variable evolves over time.<ref name="ref_50027daa" />
		+	# The task is to find a function whose various derivatives fit the differential equation over a long span of time.<ref name="ref_50027daa" />
		+	# It is easy to confirm that you have a solution: just plug the solution in to the differential equation!<ref name="ref_50027daa" />
		+	# The final few pages of this class will be devoted to an introduction to differential equation.<ref name="ref_b53ac4e5">[https://ltcconline.net/greenl/courses/117/DiffEQ/diffEQDefs.htm Differential Equations]</ref>
		+	# A differential equation is an equation (you will see an " = " sign) that has derivatives.<ref name="ref_b53ac4e5" />
		+	# If y = f(x) is a solution to a differential equation, then if we plug " y " into the equation, we get a true statement.<ref name="ref_b53ac4e5" />
		+	# We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov's accelerated gradient method.<ref name="ref_85bea581">[https://jmlr.org/papers/v17/15-084.html A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights]</ref>
		+	# The aim of this paper is to study a boundary value problem of the hybrid differential equation with linear and nonlinear perturbations.<ref name="ref_baf4902d">[https://www.hindawi.com/journals/ijde/ International Journal of Differential Equations]</ref>
		+	# The example of a cooling coffee cup is used to find the differential equation and solve it using differentiation.<ref name="ref_2f5e7f28">[https://www.tudelft.nl/en/eemcs/study/online-education/math-explained/ordinary-differential-equations/ Ordinary Differential Equations]</ref>
		+	# If we solve a first order differential equation by variables separable method, we necessarily have to introduce an arbitrary constant as soon as the integration is performed.<ref name="ref_4f329b28">[https://www.toppr.com/guides/maths/differential-equations/general-and-particular-solutions-of-a-differential-equation/ General and Particular Differential Equations Solutions: Videos, Examples]</ref>
		+	# Similarly, the general solution of a second order differential equation will contain 2 necessary arbitrary constants and so on.<ref name="ref_4f329b28" />
		+	# A Particular Solution of a differential equation is a solution obtained from the General Solution by assigning specific values to the arbitrary constants.<ref name="ref_4f329b28" />
		+	# The function f(t) must satisfy the differential equation in order to be a solution.<ref name="ref_4f329b28" />
		+	# In this tutorial we will show you how to define an ordinary differential equation (ODE) in the Fitting function Builder dialog and perform a fit of the data using this fitting function.<ref name="ref_a84801df">[https://www.originlab.com/doc/Tutorials/Fitting-Ordinary-Differential-Equation Fitting with an Ordinary Differential Equation]</ref>
		+	# In this tutorial, we will use a first order ordinary differential equation as an example: where a is a parameter in the ordinary differential equation and y0 is the initial value for the ODE.<ref name="ref_a84801df" />
		+	===소스===
		+	<references />

@@ 5번째 줄: / 5번째 줄: @@
 * 학부과정에서는 [[상미분방정식]] 과목과 [[편미분방정식]]이 있음
 * 미분방정식의 해를 적당한 클래스의 함수(가령 초등함수, 초등함수의 적분) 들을 이용하여 표현하는 문제(solvability, integrability, quadrature)
-*  분류법<br>
+*  분류법
 ** 미분방정식의 계(order)
 ** 선형미분방정식과 비선형미분방정식
@@ 16번째 줄: / 16번째 줄: @@
 ==일계 미분방정식==
-* [[일계 선형미분방정식|일계선형미분방정식]]:<math>\frac{dy}{dt}+a(t)y=b(t)</math><br>
+* [[일계 선형미분방정식|일계선형미분방정식]]:<math>\frac{dy}{dt}+a(t)y=b(t)</math>
-* [[완전미분방정식]]:<math>M_y=N_x</math>를 만족시키는 <math>M(x, y)\, dx + N(x, y)\, dy = 0</math>  꼴의 미분방정식<br>
+* [[완전미분방정식]]:<math>M_y=N_x</math>를 만족시키는 <math>M(x, y)\, dx + N(x, y)\, dy = 0</math>  꼴의 미분방정식
 * 다음 미분방정식들은 비선형이다
-* [[리카티 미분방정식]]:<math>y' = A(x)+ B(x)y + C(x)y^2, A(x)\neq 0, C(x)\neq 0</math><br>
+* [[리카티 미분방정식]]:<math>y' = A(x)+ B(x)y + C(x)y^2, A(x)\neq 0, C(x)\neq 0</math>
-* [[베르누이 미분방정식]]:<math>y'+ P(x)y = Q(x)y^n</math><br>
+* [[베르누이 미분방정식]]:<math>y'+ P(x)y = Q(x)y^n</math>
@@ 28번째 줄: / 28번째 줄: @@
 ==이계 선형미분방정식==
-*  다음 형태로 주어지는 미분방정식을 [[이계 선형 미분방정식|이계선형미분방정식]]이라 함:<math>\frac{d^2y}{dx^2}+p(x)\frac{dy}{dx}+q(x)y=g(x)</math><br>
+*  다음 형태로 주어지는 미분방정식을 [[이계 선형 미분방정식|이계선형미분방정식]]이라 함:<math>\frac{d^2y}{dx^2}+p(x)\frac{dy}{dx}+q(x)y=g(x)</math>
-* [[상수계수 이계 선형미분방정식]]:<math>ay''+by'+cy=0</math><br>
+* [[상수계수 이계 선형미분방정식]]:<math>ay''+by'+cy=0</math>
-* [[에어리 (Airy) 함수와 미분방정식|Airy 미분방정식]]:<math>y'' - xy = 0</math><br>
+* [[에어리 (Airy) 함수와 미분방정식|Airy 미분방정식]]:<math>y'' - xy = 0</math>
-* [[베셀 미분방정식]]:<math>x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + (x^2 - \alpha^2)y = 0</math><br>
+* [[베셀 미분방정식]]:<math>x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + (x^2 - \alpha^2)y = 0</math>
-* [[에르미트 다항식(Hermite polynomials)]]:<math>y''-2xy'+\lambda y=0</math><br>
+* [[에르미트 다항식(Hermite polynomials)]]:<math>y''-2xy'+\lambda y=0</math>
-* [[르장드르 다항식]]:<math>(1-x^2)y''-2xy'+\lambda(\lambda+1) y=0</math><br>
+* [[르장드르 다항식]]:<math>(1-x^2)y''-2xy'+\lambda(\lambda+1) y=0</math>
-* [[체비셰프 다항식]]:<math>(1-x^2)y''-xy'+\lambda^2 y=0</math><br>
+* [[체비셰프 다항식]]:<math>(1-x^2)y''-xy'+\lambda^2 y=0</math>
-*  라게르 미분방정식:<math>xy''+(1-x)y'+\lambda y=0</math><br>
+*  라게르 미분방정식:<math>xy''+(1-x)y'+\lambda y=0</math>
-* [[오일러 미분방정식]]:<math>x^2\frac{d^2y}{dx^2}+\alpha x\frac{dy}{dx}+\beta y=0</math><br>
+* [[오일러 미분방정식]]:<math>x^2\frac{d^2y}{dx^2}+\alpha x\frac{dy}{dx}+\beta y=0</math>
-* [[초기하 미분방정식(Hypergeometric differential equations)]]:<math>z(1-z)\frac{d^2w}{dz^2}+(c-(a+b+1)z)\frac{dw}{dz}-abw = 0</math><br>
+* [[초기하 미분방정식(Hypergeometric differential equations)]]:<math>z(1-z)\frac{d^2w}{dz^2}+(c-(a+b+1)z)\frac{dw}{dz}-abw = 0</math>
-* [[리만 미분방정식]]:<math>\frac{d^2w}{dz^2} + \left[ \frac{1-\alpha-\alpha'}{z-a} + \frac{1-\beta-\beta'}{z-b} + \frac{1-\gamma-\gamma'}{z-c} \right] \frac{dw}{dz}+\left[ \frac{\alpha\alpha' (a-b)(a-c)} {z-a} +\frac{\beta\beta' (b-c)(b-a)} {z-b} +\frac{\gamma\gamma' (c-a)(c-b)} {z-c} \right] \frac{w}{(z-a)(z-b)(z-c)}=0</math><br> 여기서 <math>\alpha+\alpha'+\beta+\beta'+\gamma+\gamma'=1</math><br>
+* [[리만 미분방정식]]:<math>\frac{d^2w}{dz^2} + \left[ \frac{1-\alpha-\alpha'}{z-a} + \frac{1-\beta-\beta'}{z-b} + \frac{1-\gamma-\gamma'}{z-c} \right] \frac{dw}{dz}+\left[ \frac{\alpha\alpha' (a-b)(a-c)} {z-a} +\frac{\beta\beta' (b-c)(b-a)} {z-b} +\frac{\gamma\gamma' (c-a)(c-b)} {z-c} \right] \frac{w}{(z-a)(z-b)(z-c)}=0</math> 여기서 <math>\alpha+\alpha'+\beta+\beta'+\gamma+\gamma'=1</math>
-* [[호인 미분방정식(Heun's equation)]]:<math>\frac {d^2w}{dz^2} +  \left[\frac{\gamma}{z}+ \frac{\delta}{z-1} + \frac{\epsilon}{z-d} \right]  \frac {dw}{dz}  + \frac {\alpha \beta z -q} {z(z-1)(z-d)} w = 0</math> (여기서 <math>\epsilon=\alpha+\beta-\gamma-\delta+1</math>)<br>
+* [[호인 미분방정식(Heun's equation)]]:<math>\frac {d^2w}{dz^2} +  \left[\frac{\gamma}{z}+ \frac{\delta}{z-1} + \frac{\epsilon}{z-d} \right]  \frac {dw}{dz}  + \frac {\alpha \beta z -q} {z(z-1)(z-d)} w = 0</math> (여기서 <math>\epsilon=\alpha+\beta-\gamma-\delta+1</math>)
@@ 48번째 줄: / 48번째 줄: @@
 ==비선형 미분방저식==
-* [[팽르베 미분방정식(Painlevé Equations)|팽르베 미분방정식]]<br>
+* [[팽르베 미분방정식(Painlevé Equations)|팽르베 미분방정식]]
-* [[바이어슈트라스 타원함수 ℘|바이어슈트라스의 타원함수]]:<math>(\frac{dw}{dz})^2=4w^3-g_2w-g_3</math><br>
+* [[바이어슈트라스 타원함수 ℘|바이어슈트라스의 타원함수]]:<math>(\frac{dw}{dz})^2=4w^3-g_2w-g_3</math>
@@ 94번째 줄: / 94번째 줄: @@
 ==== 하위페이지 ====
-* [[미분방정식]]<br>
+* [[미분방정식]]
-** [[Fuchsian 미분방정식(Fuchsian differential equation)]]<br>
+** [[Fuchsian 미분방정식(Fuchsian differential equation)]]
-** [[그린 함수(Green's function)]]<br>
+** [[그린 함수(Green's function)]]
-** [[리만 미분방정식]]<br>
+** [[리만 미분방정식]]
-** [[리카티 미분방정식]]<br>
+** [[리카티 미분방정식]]
-** [[맴돌이군과 미분방정식]]<br>
+** [[맴돌이군과 미분방정식]]
-** [[베르누이 미분방정식]]<br>
+** [[베르누이 미분방정식]]
-** [[베셀 미분방정식]]<br>
+** [[베셀 미분방정식]]
-** [[스텀-리우빌 이론]]<br>
+** [[스텀-리우빌 이론]]
-** [[오일러 미분방정식]]<br>
+** [[오일러 미분방정식]]
-** [[완전미분방정식]]<br>
+** [[완전미분방정식]]
-** [[이계 미분방정식]]<br>
+** [[이계 미분방정식]]
-*** [[상수계수 이계 선형미분방정식]]<br>
+*** [[상수계수 이계 선형미분방정식]]
-*** [[이계 선형 미분방정식]]<br>
+*** [[이계 선형 미분방정식]]
-** [[일계 선형미분방정식]]<br>
+** [[일계 선형미분방정식]]
-** [[정규특이점(regular singular points)]]<br>
+** [[정규특이점(regular singular points)]]
-** [[치환적분과 변수분리형 미분방정식]]<br>
+** [[치환적분과 변수분리형 미분방정식]]
-** [[팽르베 미분방정식(Painlevé Equations)]]<br>
+** [[팽르베 미분방정식(Painlevé Equations)]]
-** [[호인 미분방정식(Heun's equation)]]<br>
+** [[호인 미분방정식(Heun's equation)]]
@@ 133번째 줄: / 133번째 줄: @@
 * http://www.google.com/dictionary?langpair=en|ko&q=
-* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]<br>
+* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]
 ** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
 * [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판]
@@ 148번째 줄: / 148번째 줄: @@
 * http://www.wolframalpha.com/input/?i=
 * [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions]
-* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]<br>
+* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
 ** http://www.research.att.com/~njas/sequences/?q=
 ==리뷰, 에세이, 강의노트==
-* [http://www.jstor.org/stable/2687502 What It Means to Understand a Differential Equation]<br>
+* [http://www.jstor.org/stable/2687502 What It Means to Understand a Differential Equation]
 ** John H. Hubbard, <cite>The College Mathematics Journal</cite>, Vol. 25, No. 5 (Nov., 1994), pp. 372-384
-* [http://www.jstor.org/stable/2320204 Elementary Quadratures of Ordinary Differential Equations]<br>
+* [http://www.jstor.org/stable/2320204 Elementary Quadratures of Ordinary Differential Equations]
 ** Li Hong-Xiang, <cite>[http://www.jstor.org/action/showPublication?journalCode=amermathmont The American Mathematical Monthly]</cite>, Vol. 89, No. 3 (Mar., 1982), pp. 198-208
-* [http://www.jstor.org/stable/3617402 Symmetry and Differential Equations]<br>
+* [http://www.jstor.org/stable/3617402 Symmetry and Differential Equations]
 ** J. V. Greenman, <cite>[http://www.jstor.org/action/showPublication?journalCode=mathgaze The Mathematical Gazette]</cite>, Vol. 61, No. 418 (Dec., 1977), pp. 279-283
-* [http://www.jstor.org/stable/2318252 Anatomy of the Ordinary Differential Equation]<br>
+* [http://www.jstor.org/stable/2318252 Anatomy of the Ordinary Differential Equation]
 ** W. T. Reid, <cite>[http://www.jstor.org/action/showPublication?journalCode=amermathmont The American Mathematical Monthly]</cite>, Vol. 82, No. 10 (Dec., 1975), pp. 971-984
-* <br>
 ** T. Craig

← 이전 판		2013년 1월 14일 (월) 23:37 판
88번째 줄:		88번째 줄:

	* http://www.google.com/search?hl=en&tbs=tl:1&q=differential+equation		* http://www.google.com/search?hl=en&tbs=tl:1&q=differential+equation
−	* [[~~수학사연표 (역사)\|수학사연표~~]]	+	* [[수학사 연표]]

← 이전 판		2013년 1월 12일 (토) 15:25 판
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	==블로그==		==블로그==
		+	[[분류:미분방정식]]

← 이전 판		2012년 11월 2일 (금) 20:08 판
206번째 줄:		206번째 줄:

	==블로그==		==블로그==
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−	~~네이버 ]~~