Wiki143:WikiProject Mathematics/PlanetMath Exchange/26-XX Real functions

26-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

• PM: Borel lemma, id=6185 -- WP: Borel lemma -- Status: C

Nice article, but some time in the future maybe more can be said about its history and applications. Oleg Alexandrov | talk 01:21, 3 Feb 2005 (UTC)

• PM: derivative notation, id=838 -- WP guess: derivative -- Status: A

PM has a lot of stuff, I doubt we need that. Oleg Alexandrov (talk) 04:48, 15 February 2006 (UTC)

• PM: fundamental theorems of calculus for Lebesgue integration, id=2625 -- WP guess: fundamental theorems of calculus -- Status: A

AdamSmithee 23:04, 18 February 2006 (UTC)

• PM: generalized mean, id=6081 -- WP guess: generalized mean -- Status: NM

But with lots of care. The WP article has lots of stuff which the PM one does not, while PM has just very little stuff which WP does not. Oleg Alexandrov | talk 05:42, 2 Feb 2005 (UTC)

• PM: logarithm, id=2367 -- WP: logarithm -- Status: A

Oleg Alexandrov (talk) 10:46, 28 October 2005 (UTC)

• PM: proof of the fundamental theorem of calculus, id=4463 -- WP guess: fundamental theorem of calculus -- Status: A

AdamSmithee 23:04, 18 February 2006 (UTC)

• PM: root-mean-square, id=3618 -- WP: root-mean-square -- Status: A

Oleg Alexandrov (talk) 10:46, 28 October 2005 (UTC)

• PM: abelian function, id=6354 -- WP guess: abelian function -- Status:

• PM: bibliography for real analysis, id=7599 -- WP: none -- Status: N

AdamSmithee 13:15, 26 April 2006 (UTC)

• PM: mollifier, id=6743 -- WP guess: mollifier -- Status:

• PM: stair function, id=7439 -- WP: stair function -- Status: A

Made redirect to Simple function - AdamSmithee 13:15, 26 April 2006 (UTC)

• PM: alternative proof of the fundamental theorem of calculus, id=7930^new! -- WP guess: alternative proof of the fundamental theorem of calculus -- Status:

• PM: nested interval theorem, id=9835^new! -- WP guess: nested interval theorem -- Status:

• PM: rigorous definition of the logarithm, id=9292^new! -- WP guess: rigorous definition of the logarithm -- Status:

26A03 Foundations: limits and generalizations, elementary topology of the line

• PM: binomial proof of positive integer power rule, id=2721 -- WP guess: binomial proof of positive integer power rule -- Status:

• PM: Cauchy sequence, id=600 -- WP: Cauchy sequence -- Status: A

AdamSmithee 11:21, 26 April 2006 (UTC)

• PM: Dedekind cuts, id=2907 -- WP guess: Dedekind cuts -- Status:

• PM: exponential, id=2730 -- WP: Exponentiation -- Status: A

AdamSmithee 11:21, 26 April 2006 (UTC)

• PM: fraction power, id=7340 -- WP: fraction power -- Status: A

Oleg Alexandrov (talk) 03:10, 4 February 2007 (UTC)

• PM: if d(x_i, x_{i+1})<1/2^i then x_i is a Cauchy sequence, id=6205 -- WP: Cauchy sequence -- Status: N

AdamSmithee 11:21, 26 April 2006 (UTC)

• PM: limit inferior, id=2106 -- WP guess: limit inferior -- Status:

• PM: limit superior, id=2104 -- WP guess: limit superior -- Status:

• PM: power rule, id=2630 -- WP guess: power rule -- Status:

• PM: proof of properties of the exponential, id=6129 -- WP guess: proof of properties of the exponential -- Status: N

Oleg Alexandrov (talk) 03:41, 4 February 2007 (UTC)

• PM: properties of the exponential, id=2731 -- WP: exponential function -- Status: A

Oleg Alexandrov (talk) 03:41, 4 February 2007 (UTC)

• PM: squeeze rule, id=4483 -- WP guess: squeeze rule -- Status: A

Oleg Alexandrov (talk) 03:41, 4 February 2007 (UTC)

• PM: comparison of \sin þeta and þeta near þeta = 0, id=9251^new! -- WP guess: comparison of \sin þeta and þeta near þeta = 0 -- Status:

• PM: derivatives of \sin x and \cos x, id=9257^new! -- WP guess: derivatives of \sin x and \cos x -- Status:

• PM: limit of \displaystyle \frac{1-\cos x}{x} as x approaches 0, id=9256^new! -- WP guess: limit of \displaystyle \frac1-\cos xx as x approaches 0 -- Status:

• PM: limit of \displaystyle \frac{\sin x}{x} as x approaches 0, id=9255^new! -- WP guess: limit of \displaystyle \frac\sin xx as x approaches 0 -- Status:

26A06 One-variable calculus

• PM: Barb\u{a}lat's lemma, id=6552 -- WP guess: Barbalat's lemma, Barbălat's lemma -- Status: NM

The plain latin title needs be the main article, the other one redirectOleg Alexandrov | talk 05:47, 2 Feb 2005 (UTC)

• PM: binomial formula, id=2204 -- WP: binomial theorem -- Status: A

Oleg Alexandrov (talk) 18:55, 20 November 2005 (UTC)

• PM: binomial formula for negative integer powers, id=6654 -- WP: binomial theorem -- Status: A

Oleg Alexandrov (talk) 18:55, 20 November 2005 (UTC)

• PM: Bolzano-Weierstrass theorem, id=2125 -- WP: Bolzano-Weierstrass theorem -- Status: A

AdamSmithee 00:22, 19 February 2006 (UTC)

• PM: boundedness theorem, id=6022 -- WP: boundedness theorem -- Status: M

AdamSmithee 00:22, 19 February 2006 (UTC)

• PM: chain rule, id=2561 -- WP: chain rule -- Status: A

Jeekc 11:13, 10 November 2005 (UTC)

• PM: complex mean-value theorem, id=4543 -- WP guess: complex mean-value theorem -- Status:

• PM: complex Rolle's theorem, id=4542 -- WP guess: complex Rolle's theorem -- Status:

• PM: convergent series, id=2311 -- WP: convergent series -- Status: A

Jeekc 11:13, 10 November 2005 (UTC)

• PM: Darboux's theorem (analysis), id=3055 -- WP: Darboux's theorem (analysis) -- Status: C

AdamSmithee 20:42, 19 February 2006 (UTC)

• PM: definite integral, id=1637 -- WP guess: definite integral -- Status:

• PM: derivative of even/odd function (proof), id=4281 -- WP guess: derivative of even/odd function (proof) -- Status:

• PM: Descartes' rule of signs, id=5997 -- WP: Descartes' rule of signs -- Status: M

Jeekc 11:51, 10 November 2005 (UTC)

• PM: direct sum of even/odd functions (example), id=4191 -- WP guess: direct sum of even/odd functions (example) -- Status:

• PM: even/odd function, id=4187 -- WP guess: even/odd function -- Status:

• PM: example of chain rule, id=2843 -- WP: chain rule -- Status: A

AdamSmithee 14:30, 30 December 2005 (UTC)

• PM: example of increasing/decreasing/monotone function, id=4229 -- WP guess: example of increasing/decreasing/monotone function -- Status:

• PM: extended mean-value theorem, id=3478 -- WP: mean-value theorem -- Status: A

AdamSmithee 20:45, 20 February 2006 (UTC)

• PM: extreme value theorem, id=6023 -- WP: extreme value theorem -- Status: A

AdamSmithee 00:22, 19 February 2006 (UTC)

• PM: Fermat's Theorem (stationary points), id=4450 -- WP: Fermat's Theorem (stationary points) -- Status: C

AdamSmithee 20:45, 20 February 2006 (UTC)

• PM: generalized Leibniz rule, id=6042 -- WP guess: generalized Leibniz rule -- Status:

• PM: harmonic number, id=3421 -- WP: harmonic number -- Status: M

Jeekc 11:51, 10 November 2005 (UTC)

• PM: Heaviside step function, id=4476 -- WP guess: Heaviside step function -- Status:

• PM: improper limits, id=6283 -- WP guess: improper limits -- Status:

• PM: increasing/decreasing/monotone function, id=4228 -- WP guess: increasing/decreasing/monotone function -- Status:

• PM: intermediate value theorem, id=423 -- WP: intermediate value theorem -- Status: A

AdamSmithee 14:30, 30 December 2005 (UTC)

• PM: Leibniz' rule, id=4388 -- WP guess: Leibniz' rule -- Status:

• PM: limit, id=2662 -- WP guess: limit -- Status:

• PM: limit rules of functions, id=6528 -- WP guess: limit rules of functions -- Status:

• PM: manipulating convergent series, id=6517 -- WP guess: manipulating convergent series -- Status:

• PM: mean-value theorem, id=1990 -- WP: mean-value theorem -- Status: A

AdamSmithee 20:45, 20 February 2006 (UTC)

• PM: monotonicity criterion, id=4453 -- WP guess: monotonicity criterion -- Status:

• PM: nabla, id=4847 -- WP guess: nabla -- Status:

• PM: one-sided limit, id=2950 -- WP guess: one-sided limit -- Status:

• PM: product rule, id=2628 -- WP guess: product rule -- Status:

• PM: proof of binomial formula, id=2214 -- WP guess: proof of binomial formula -- Status:

• PM: proof of Bolzano-Weierstrass Theorem, id=2129 -- WP guess: Bolzano-Weierstrass Theorem -- Status: N

AdamSmithee 00:22, 19 February 2006 (UTC)

• PM: proof of chain rule, id=2978 -- WP guess: proof of chain rule -- Status:

• PM: proof of complex mean-value theorem, id=6136 -- WP guess: proof of complex mean-value theorem -- Status:

• PM: proof of Darboux's theorem, id=3056 -- WP: Darboux's theorem (analysis) -- Status: M

AdamSmithee 20:42, 19 February 2006 (UTC)

• PM: proof of extended mean-value theorem, id=3589 -- WP: mean-value theorem -- Status: A

AdamSmithee 20:45, 20 February 2006 (UTC)

• PM: proof of Fermat's Theorem (stationary points), id=4452 -- WP: Fermat's Theorem (stationary points) -- Status: M

AdamSmithee 20:45, 20 February 2006 (UTC)

• PM: proof of generalized Leibniz rule, id=6128 -- WP guess: proof of generalized Leibniz rule -- Status:

• PM: proof of intermediate value theorem, id=2813 -- WP: intermediate value theorem -- Status: NM

This proof, going first through the Bolzano theorem special case by interval halving, is more intuitive IMO AdamSmithee 13:27, 26 April 2006 (UTC)

• PM: proof of mean value theorem, id=2960 -- WP: mean value theorem -- Status: A

AdamSmithee 20:45, 20 February 2006 (UTC)

• PM: proof of monotonicity criterion, id=4454 -- WP guess: proof of monotonicity criterion -- Status:

• PM: proof of quotient rule, id=2915 -- WP guess: proof of quotient rule -- Status:

• PM: proof of ratio test, id=2296 -- WP guess: proof of ratio test -- Status:

• PM: proof of Rolle's theorem, id=2947 -- WP: Rolle's theorem -- Status: A

AdamSmithee 11:36, 26 April 2006 (UTC)

• PM: proof of Simpson's rule, id=6509 -- WP guess: proof of Simpson's rule -- Status:

• PM: proof of Taylor's Theorem, id=2814 -- WP: Taylor's theorem -- Status: A

CryptoDerk 07:02, Feb 3, 2005 (UTC)

• PM: quotient rule, id=2913 -- WP guess: quotient rule -- Status:

• PM: ratio test, id=2244 -- WP guess: ratio test -- Status:

• PM: Rolle's theorem, id=422 -- WP: Rolle's theorem -- Status: A

AdamSmithee 11:36, 26 April 2006 (UTC)

• PM: signum function, id=4243 -- WP: signum function -- Status: A

On PM they also talk about signum function for complex argument, but that is reduntant I would think. Oleg Alexandrov (talk) 18:55, 20 November 2005 (UTC)

• PM: Simpson's rule, id=4335 -- WP: Simpson's rule -- Status: A

Oleg Alexandrov (talk) 18:55, 20 November 2005 (UTC)

• PM: sinc function, id=5744 -- WP: sinc function -- Status: A

Oleg Alexandrov (talk) 03:46, 4 February 2007 (UTC)

• PM: sum of series depends on order, id=6520 -- WP guess: sum of series depends on order -- Status:

• PM: all derivatives of sinc are bounded by 1, id=7583 -- WP guess: all derivatives of sinc are bounded by 1 -- Status:

• PM: Bolzano's theorem, id=7584 -- WP: Bolzano's theorem -- Status: NM

Could lead to reorganisation and better wording. Otherwise, the info is mostly in there AdamSmithee 11:36, 26 April 2006 (UTC)

• PM: example of computing limits using Taylor expansion, id=7597 -- WP guess: example of computing limits using Taylor expansion -- Status:

• PM: example of ratio test, id=6773 -- WP guess: example of ratio test -- Status:

• PM: intermediate value theorem for extended real numbers, id=7498 -- WP: intermediate value theorem -- Status: NM

AdamSmithee 11:36, 26 April 2006 (UTC)

• PM: proof of Barbalat's lemma, id=6933 -- WP guess: proof of Barbalat's lemma -- Status:

• PM: proof of l'Hôpital's rule for \infty/\infty form, id=7611 -- WP guess: proof of l'Hôpital's rule for \infty/\infty form -- Status:

• PM: proof of quotient rule (using product rule), id=6719 -- WP guess: proof of quotient rule (using product rule) -- Status:

• PM: triangular-wave function, id=7115 -- WP guess: triangular-wave function -- Status:

• PM: alternate statement of Bolzano-Weierstrass theorem, id=8877^new! -- WP guess: alternate statement of Bolzano-Weierstrass theorem -- Status:

• PM: double series, id=8731^new! -- WP guess: double series -- Status:

• PM: fractional differentiation, id=8437^new! -- WP guess: fractional differentiation -- Status:

• PM: integral mean value theorem, id=9604^new! -- WP guess: integral mean value theorem -- Status:

• PM: iterated limit in \mathbb{R}^2, id=9860^new! -- WP guess: iterated limit in \mathbbR^2 -- Status:

• PM: logarithmic proof of product rule, id=8438^new! -- WP guess: logarithmic proof of product rule -- Status:

• PM: logarithmic proof of quotient rule, id=8439^new! -- WP guess: logarithmic proof of quotient rule -- Status:

• PM: Newton's method works for convex real functions, id=7634^new! -- WP guess: Newton's method works for convex real functions -- Status:

• PM: proof of Bolzano's theorem, id=7674^new! -- WP guess: proof of Bolzano's theorem -- Status:

• PM: proof of generalized intermediate value theorem, id=9639^new! -- WP guess: proof of generalized intermediate value theorem -- Status:

• PM: sinc is L^2, id=7697^new! -- WP guess: sinc is L^2 -- Status:

• PM: sinc is not L^1, id=7693^new! -- WP guess: sinc is not L^1 -- Status:

26A09 Elementary functions

• PM: area functions, id=5834 -- WP guess: area functions -- Status:

• PM: complex sine and cosine, id=6398 -- WP guess: complex sine and cosine -- Status:

• PM: cyclometric functions, id=6169 -- WP guess: cyclometric functions -- Status:

• PM: definitions in trigonometry, id=4676 -- WP guess: definitions in trigonometry -- Status:

• PM: derivatives of hyperbolic functions, id=6083 -- WP guess: derivatives of hyperbolic functions -- Status:

• PM: hyperbolic functions, id=2905 -- WP guess: hyperbolic functions -- Status:

• PM: Prosthaphaeresis formulas, id=6121 -- WP guess: Prosthaphaeresis formulas -- Status:

• PM: algebraic function, id=7131 -- WP guess: algebraic function -- Status:

• PM: asymptotes of graph of rational function, id=6908 -- WP guess: asymptotes of graph of rational function -- Status:

• PM: addition and subtraction formulas for tangent, id=9261^new! -- WP guess: addition and subtraction formulas for tangent -- Status:

• PM: angle multiplication and division formulae for tangent, id=9286^new! -- WP guess: angle multiplication and division formulae for tangent -- Status:

• PM: convexity of tangent function, id=9285^new! -- WP guess: convexity of tangent function -- Status:

• PM: cosine at multiples of straight angle, id=7716^new! -- WP guess: cosine at multiples of straight angle -- Status:

• PM: derivation of half-angle formulae for tangent, id=9287^new! -- WP guess: derivation of half-angle formulae for tangent -- Status:

• PM: derivatives of sine and cosine, id=9259^new! -- WP guess: derivatives of sine and cosine -- Status:

• PM: goniometric formulas, id=9293^new! -- WP guess: goniometric formulas -- Status:

• PM: hyperbolic angle, id=9779^new! -- WP guess: hyperbolic angle -- Status:

• PM: rigorous definition of tangent function, id=9254^new! -- WP guess: rigorous definition of tangent function -- Status:

• PM: rigorous definition of trigonometric functions, id=8508^new! -- WP guess: rigorous definition of trigonometric functions -- Status:

• PM: tangent of halved angle, id=9291^new! -- WP guess: tangent of halved angle -- Status:

• PM: Taylor expansion of \sqrt{1+x}, id=7720^new! -- WP guess: Taylor expansion of \sqrt1+x -- Status:

26A12 Rate of growth of functions, orders of infinity, slowly varying functions

• PM: Landau notation, id=90 -- WP guess: Landau notation -- Status:

• PM: quasisymmetric mapping, id=5516 -- WP guess: quasisymmetric mapping -- Status:

• PM: formal definition of Landau notation, id=7049 -- WP guess: formal definition of Landau notation -- Status:

• PM: properties of O and o, id=7048 -- WP: properties of O and o -- Status: A

Oleg Alexandrov (talk) 03:53, 4 February 2007 (UTC)

• PM: \sim is an equivalence relation, id=8319^new! -- WP guess: \sim is an equivalence relation -- Status:

26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)

• PM: continuity of composition of functions, id=5443 -- WP guess: continuity of composition of functions -- Status:

• PM: continuous, id=439 -- WP guess: continuous -- Status:

• PM: Dirichlet's function, id=3639 -- WP: Dirichlet function -- Status: NM

AdamSmithee 14:30, 30 December 2005 (UTC)

• PM: discontinuous, id=4447 -- WP: classification of discontinuities -- Status: A

I created this article, with examples and pictures. Oleg Alexandrov 01:22, 13 September 2005 (UTC)

• PM: function continuous at only one point, id=6629 -- WP guess: function continuous at only one point -- Status:

• PM: limit function of sequence, id=6209 -- WP guess: limit function of sequence -- Status:

• PM: proof of Weierstrass' criterion of uniform convergence, id=6394 -- WP guess: proof of Weierstrass' criterion of uniform convergence -- Status: N

Oleg Alexandrov (talk) 04:15, 4 February 2007 (UTC)

• PM: restriction of a continuous mapping is continuous, id=4690 -- WP guess: restriction of a continuous mapping is continuous -- Status:

• PM: semi-continuous, id=3069 -- WP guess: semi-continuous -- Status:

• PM: semicontinuous, id=4844 -- WP guess: semicontinuous -- Status:

• PM: sum function of series, id=6223 -- WP guess: sum function of series -- Status:

• PM: termwise differentiation, id=6231 -- WP guess: termwise differentiation -- Status:

• PM: uniformly continuous, id=3068 -- WP guess: uniformly continuous -- Status:

• PM: Weierstrass function, id=1181 -- WP: Weierstrass function -- Status: NM

AdamSmithee 14:30, 30 December 2005 (UTC)

• PM: Weierstrass' criterion of uniform convergence, id=6225 -- WP: Weierstrass' criterion of uniform convergence -- Status: A

Oleg Alexandrov (talk) 04:15, 4 February 2007 (UTC)

• PM: C^n, id=6701 -- WP guess: C^n -- Status:

• PM: C^n norm, id=6702 -- WP guess: C^n norm -- Status:

• PM: composition of continuous mappings is continuous, id=7070 -- WP guess: composition of continuous mappings is continuous -- Status:

• PM: continuity of natural power, id=7590 -- WP guess: continuity of natural power -- Status:

• PM: equivalent formulations for continuity, id=7106 -- WP guess: equivalent formulations for continuity -- Status:

• PM: If f\colon X\to Y is continuous then f\colon X\to f(X) is continuous, id=7062 -- WP guess: If f\colon X\to Y is continuous then f\colon X\to f(X) is continuous -- Status:

• PM: Sets where sequence of continuous functions diverge, id=7226 -- WP guess: Sets where sequence of continuous functions diverge -- Status:

• PM: uniformly continuous on \mathbb{R} is roughly linear, id=6910 -- WP guess: uniformly continuous on \mathbbR is roughly linear -- Status:

• PM: condition for uniform convergence of sequence of functions, id=9435^new! -- WP guess: condition for uniform convergence of sequence of functions -- Status:

• PM: continuity of sine and cosine, id=9263^new! -- WP guess: continuity of sine and cosine -- Status:

• PM: example of jump discontinuity, id=8567^new! -- WP guess: example of jump discontinuity -- Status:

• PM: least and greatest zero, id=8742^new! -- WP guess: least and greatest zero -- Status:

• PM: proof of Weierstrass' criterion of uniform convergence, id=8596^new! -- WP guess: proof of Weierstrass' criterion of uniform convergence -- Status:

26A16 Lipschitz (Hölder) classes

• PM: Lipschitz condition, id=765 -- WP guess: Lipschitz continuity -- Status: A

Oleg Alexandrov 22:27, 13 September 2005 (UTC)

• PM: Lipschitz condition and differentiability, id=776 -- WP guess: Lipschitz condition and differentiability -- Status:

• PM: Lipschitz condition and differentiability result, id=4145 -- WP guess: Lipschitz condition and differentiability result -- Status:

• PM: Lipschitz function, id=5054 -- WP: Lipschitz continuity -- Status: A

Oleg Alexandrov 22:27, 13 September 2005 (UTC)

• PM: uniform continuity of Lipschitz functions, id=6834 -- WP guess: uniform continuity of Lipschitz functions -- Status:

• PM: example of Lipschitz condition, id=9567^new! -- WP guess: example of Lipschitz condition -- Status:

26A18 Iteration

• PM: iteration, id=3027 -- WP: iterated function -- Status: A

linas 00:08, 8 June 2006 (UTC)

• PM: periodic point, id=3026 -- WP: periodic point -- Status: A

linas 23:59, 7 June 2006 (UTC)

26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems

• PM: derivative of Riemann integral, id=6155 -- WP: derivative of Riemann integral -- Status: A

AdamSmithee 11:50, 26 April 2006 (UTC)

• PM: differentiable function, id=2919 -- WP guess: differentiable function -- Status:

• PM: differentiable functions are continuous, id=6154 -- WP guess: differentiable functions are continuous -- Status:

• PM: example of differentiable function which is not continuously differentiable, id=5597 -- WP guess: example of differentiable function which is not continuously differentiable -- Status:

• PM: l'Hôpital's rule, id=2657 -- WP guess: l'Hôpital's rule -- Status:

• PM: Leibniz notation, id=2750 -- WP guess: Leibniz notation -- Status:

• PM: proof of De l'Hôpital's rule, id=3930 -- WP guess: proof of De l'Hôpital's rule -- Status:

• PM: proof of power rule, id=2631 -- WP guess: proof of power rule -- Status:

• PM: proof of product rule, id=2629 -- WP guess: proof of product rule -- Status:

• PM: proof of sum rule, id=2638 -- WP guess: proof of sum rule -- Status:

• PM: related rates, id=3054 -- WP guess: related rates -- Status:

• PM: sum rule, id=2637 -- WP guess: sum rule -- Status:

• PM: tangent line, id=6511 -- WP guess: tangent line -- Status:

• PM: one-sided derivatives, id=7582 -- WP guess: one-sided derivatives -- Status:

• PM: tangent plane (elementary), id=6679 -- WP guess: tangent plane (elementary) -- Status:

• PM: alternative proof of derivative of x^n, id=8013^new! -- WP guess: alternative proof of derivative of x^n -- Status:

• PM: derivative of x^n, id=7811^new! -- WP guess: derivative of x^n -- Status:

• PM: derivative of inverse function, id=9359^new! -- WP guess: derivative of inverse function -- Status:

• PM: derivatives by pure algebra, id=8018^new! -- WP guess: derivatives by pure algebra -- Status:

• PM: determining envelope, id=9494^new! -- WP guess: determining envelope -- Status:

• PM: differentiation under the integral sign, id=8599^new! -- WP guess: differentiation under the integral sign -- Status:

• PM: example of Cauchy multiplication rule, id=9876^new! -- WP guess: example of Cauchy multiplication rule -- Status:

• PM: example of differentiation under integral sign, id=9318^new! -- WP guess: example of differentiation under integral sign -- Status:

• PM: function differentiable at only one point, id=7767^new! -- WP guess: function differentiable at only one point -- Status:

• PM: higher order derivatives, id=9004^new! -- WP guess: higher order derivatives -- Status:

• PM: logarithmic derivative, id=9015^new! -- WP guess: logarithmic derivative -- Status:

• PM: mean curvature at surface point, id=9830^new! -- WP guess: mean curvature at surface point -- Status:

• PM: Meusnier's theorem, id=9863^new! -- WP guess: Meusnier's theorem -- Status:

• PM: normal curvatures, id=9821^new! -- WP guess: normal curvatures -- Status:

• PM: normal line, id=9476^new! -- WP guess: normal line -- Status:

• PM: normal section, id=9820^new! -- WP guess: normal section -- Status:

• PM: proof of properties of derivatives by pure algebra, id=8028^new! -- WP guess: proof of properties of derivatives by pure algebra -- Status:

• PM: surface normal, id=9753^new! -- WP guess: surface normal -- Status:

• PM: Taylor series of arcus tangent, id=8748^new! -- WP guess: Taylor series of arcus tangent -- Status:

26A30 Singular functions, Cantor functions, functions with other special properties

• PM: Cantor function, id=5554 -- WP: Cantor function -- Status: A

linas 00:00, 8 June 2006 (UTC)

• PM: Dirac sequence, id=5623 -- WP guess: Dirac sequence -- Status:

• PM: Dirichlet kernel, id=5629 -- WP: Dirichlet kernel -- Status: A

linas 00:01, 8 June 2006 (UTC)

• PM: example of a strictly increasing quasisymmetric singular function, id=5603 -- WP guess: example of a strictly increasing quasisymmetric singular function -- Status:

• PM: Fejer kernel, id=5630 -- WP: Fejer kernel -- Status: A

linas 00:03, 8 June 2006 (UTC)

• PM: Landau kernel, id=5624 -- WP guess: Landau kernel -- Status:

• PM: singular function, id=5548 -- WP guess: singular function -- Status:

• PM: another example of Dirac sequence, id=9683^new! -- WP guess: another example of Dirac sequence -- Status:

26A33 Fractional derivatives and integrals

• PM: fractional integration, id=8416^new! -- WP guess: fractional integration -- Status:

26A36 Antidifferentiation

• PM: antiderivative, id=1631 -- WP guess: antiderivative -- Status:

• PM: integration by parts, id=2683 -- WP guess: integration by parts -- Status:

• PM: integration of differential binomial, id=6408 -- WP guess: integration of differential binomial -- Status:

• PM: integrations by parts for the Lebesgue integral, id=4449 -- WP guess: integrations by parts for the Lebesgue integral -- Status:

• PM: substitution for integration, id=6114 -- WP guess: substitution for integration -- Status:

• PM: a lecture on integration by parts, id=7574 -- WP guess: a lecture on integration by parts -- Status:

• PM: a lecture on integration by substitution, id=7573 -- WP guess: a lecture on integration by substitution -- Status:

• PM: A lecture on trigonometric integrals and trigonometric substitution, id=7576 -- WP guess: A lecture on trigonometric integrals and trigonometric substitution -- Status:

• PM: area under Gaussian curve, id=7065 -- WP guess: area under Gaussian curve -- Status:

• PM: Euler's substitutions for integration, id=9681^new! -- WP guess: Euler's substitutions for integration -- Status:

• PM: integration of rational function of sine and cosine, id=9380^new! -- WP guess: integration of rational function of sine and cosine -- Status:

• PM: logarithmic integral, id=9341^new! -- WP guess: logarithmic integral -- Status:

• PM: Torricelli's trumpet, id=9643^new! -- WP guess: Torricelli's trumpet -- Status:

• PM: Weierstrass substitution formulas, id=9383^new! -- WP guess: Weierstrass substitution -- Status:

26A42 Integrals of Riemann, Stieltjes and Lebesgue type

• PM: continuous functions are Riemann integrable, id=4461 -- WP guess: continuous functions are Riemann integrable -- Status:

• PM: fundamental theorem of calculus, id=5660 -- WP guess: fundamental theorem of calculus -- Status:

• PM: generalized Riemann integral, id=4328 -- WP guess: generalized Riemann integral -- Status:

• PM: Lebesgue integral, id=1920 -- WP: Lebesgue integral -- Status: A

AdamSmithee 13:39, 26 April 2006 (UTC)

• PM: Lebesgue measure, id=348 -- WP guess: Lebesgue measure -- Status:

• PM: monotone convergence theorem, id=3106 -- WP guess: monotone convergence theorem -- Status:

• PM: proof of continuous functions are Riemann integrable, id=4462 -- WP guess: proof of continuous functions are Riemann integrable -- Status:

• PM: proof of monotone convergence theorem, id=4075 -- WP guess: proof of monotone convergence theorem -- Status:

• PM: quadrature, id=1286 -- WP guess: quadrature -- Status:

• PM: Riemann sum, id=368 -- WP: Riemann sum -- Status: A

AdamSmithee 13:39, 26 April 2006 (UTC)

• PM: Riemann-Stieltjes integral, id=3187 -- WP guess: Riemann-Stieltjes integral -- Status:

• PM: uniform convergence of integral, id=6277 -- WP guess: uniform convergence of integral -- Status:

• PM: a lecture on the partial fraction decomposition method, id=7586 -- WP guess: a lecture on the partial fraction decomposition method -- Status:

• PM: area of plane region, id=7094 -- WP guess: area of plane region -- Status:

• PM: Continuous functions of several variables are Riemann summable, id=6875 -- WP guess: Continuous functions of several variables are Riemann summable -- Status:

• PM: polyrectangle, id=6777 -- WP: polyrectangle -- Status: A

Oleg Alexandrov (talk) 03:40, 18 February 2007 (UTC)

• PM: Riemann integral, id=370 -- WP guess: Riemann integral -- Status:

• PM: Riemann multiple integral, id=6778 -- WP guess: Riemann multiple integral -- Status:

• PM: substitution notation, id=6880 -- WP guess: substitution notation -- Status:

• PM: an integrable function which does not tend to zero, id=9233^new! -- WP guess: an integrable function which does not tend to zero -- Status:

• PM: Dirac measure, id=9680^new! -- WP guess: Dirac measure -- Status:

• PM: example of estimating a Riemann integral, id=9236^new! -- WP guess: example of estimating a Riemann integral -- Status:

• PM: fundamental theorem of calculus for Kurzweil-Henstock integral, id=8964^new! -- WP guess: fundamental theorem of calculus for Kurzweil-Henstock integral -- Status:

• PM: integrating \tan x over [0,\frac{\pi}{2}], id=7977^new! -- WP guess: [[integrating \tan x over [0,\frac\pi2]]] -- Status:

• PM: integration of polynomial, id=7971^new! -- WP guess: integration of polynomial -- Status:

• PM: Lebesgue integral over a subset of the measure space, id=8332^new! -- WP guess: Lebesgue integral over a subset of the measure space -- Status:

• PM: left hand rule, id=7974^new! -- WP guess: left hand rule -- Status:

• PM: midpoint rule, id=7976^new! -- WP guess: midpoint rule -- Status:

• PM: partition, id=7978^new! -- WP guess: partition -- Status:

• PM: properties of the Lebesgue integral of Lebesgue integrable functions, id=8334^new! -- WP guess: properties of the Lebesgue integral of Lebesgue integrable functions -- Status:

• PM: properties of the Lebesgue integral of nonnegative measurable functions, id=8331^new! -- WP guess: properties of the Lebesgue integral of nonnegative measurable functions -- Status:

• PM: right hand rule, id=7975^new! -- WP guess: right hand rule -- Status:

26A46 Absolutely continuous functions

• PM: absolutely continuous on [0,1 versus absolutely continuous on [\varepsilon, 1] for every \varepsilon >0], id=8300^new! -- WP guess: [[absolutely continuous on [0,1] versus absolutely continuous on [\varepsilon, 1] for every \varepsilon >0]] -- Status:

26A51 Convexity, generalizations

• PM: convex function, id=231 -- WP : convex function -- Status: A

Mikkalai 05:02, 14 Feb 2005 (UTC)

• PM: logarithmically convex function, id=5664 -- WP guess: logarithmically convex function -- Status: M

Merged into convex function. Mikkalai 05:02, 14 Feb 2005 (UTC)

• PM: almost convex, id=7169 -- WP guess: almost convex -- Status:

• PM: characterization of almost convex functions, id=7173 -- WP guess: characterization of almost convex functions -- Status:

• PM: continuity of convex functions, id=7319 -- WP guess: continuity of convex functions -- Status:

26A99 Miscellaneous

• PM: addition formula, id=6374 -- WP guess: addition formula -- Status:

• PM: analytic, id=1147 -- WP: analytic function -- Status: A

Oleg Alexandrov 20:38, 12 Feb 2005 (UTC)

• PM: elementary function, id=6420 -- WP guess: elementary function -- Status:

• PM: infinitely-differentiable function that is not analytic, id=3081 -- WP: an infinitely differentiable function that is not analytic -- Status: A

They have quite some similarities. Oleg Alexandrov 19:14, 15 Feb 2005 (UTC)

• PM: power function, id=6421 -- WP guess: power function -- Status:

• PM: real function, id=6218 -- WP guess: real function -- Status:

26B05 Continuity and differentiation questions

• PM: C^\infty_0(U) is not empty, id=4422 -- WP guess: C^\infty_0(U) is not empty -- Status:

• PM: Rademacher's theorem, id=4128 -- WP guess: Rademacher's theorem -- Status:

• PM: sense-preserving mapping, id=5546 -- WP guess: sense-preserving mapping -- Status:

• PM: smooth functions with compact support, id=4423 -- WP guess: smooth functions with compact support -- Status:

26B10 Implicit function theorems, Jacobians, transformations with several variables

• PM: directional derivative, id=847 -- WP guess: directional derivative -- Status:

• PM: gradient, id=892 -- WP guess: gradient -- Status:

• PM: implicit differentiation, id=2660 -- WP guess: implicit differentiation -- Status:

• PM: implicit function theorem, id=3347 -- WP guess: implicit function theorem -- Status:

• PM: Jacobian matrix, id=842 -- WP guess: Jacobian matrix -- Status:

• PM: proof of implicit function theorem, id=4113 -- WP guess: proof of implicit function theorem -- Status:

• PM: change of variables in integral on \mathbb{R}^n, id=7349 -- WP guess: change of variables in integral on \mathbbR^n -- Status:

• PM: derivation of directional derivative, id=7267 -- WP guess: derivation of directional derivative -- Status:

• PM: gradient in curvilinear coordinates, id=7309 -- WP guess: gradient in curvilinear coordinates -- Status:

• PM: nabla acting on products, id=7300 -- WP guess: nabla acting on products -- Status:

• PM: potential of hollow ball, id=9619^new! -- WP guess: potential of hollow ball -- Status:

26B12 Calculus of vector functions

• PM: chain rule (several variables), id=2798 -- WP guess: chain rule (several variables) -- Status:

• PM: Clairaut's theorem, id=4642 -- WP guess: Clairaut's theorem -- Status:

• PM: divergence, id=3271 -- WP guess: divergence -- Status:

• PM: extremum, id=3373 -- WP guess: extremum -- Status:

• PM: Fubini's theorem, id=4307 -- WP guess: Fubini's theorem -- Status:

• PM: Generalised N-dimensional Riemann Sum, id=4270 -- WP guess: Generalised N-dimensional Riemann Sum -- Status:

• PM: Generalized N-dimensional Riemann Integral, id=4271 -- WP guess: Generalized N-dimensional Riemann Integral -- Status:

• PM: Helmholtz equation, id=3592 -- WP guess: Helmholtz equation -- Status:

• PM: Hessian matrix, id=3370 -- WP guess: Hessian matrix -- Status:

• PM: irrotational field, id=3591 -- WP guess: irrotational field -- Status:

• PM: Jordan Content of an N-cell, id=4269 -- WP guess: Jordan Content of an N-cell -- Status:

• PM: laminar field, id=6360 -- WP guess: laminar field -- Status:

• PM: Laplace equation, id=3593 -- WP guess: Laplace equation -- Status:

• PM: partial derivative, id=841 -- WP guess: partial derivative -- Status:

• PM: plateau, id=3374 -- WP: plateau (mathematics) -- Status: C

Mikkalai 05:11, 4 Feb 2005 (UTC)

• PM: proof of Green's theorem, id=2690 -- WP guess: proof of Green's theorem -- Status:

• PM: regularity theorem for the Laplace equation, id=6655 -- WP guess: regularity theorem for the Laplace equation -- Status:

• PM: relations between Hessian matrix and local extrema, id=3375 -- WP guess: relations between Hessian matrix and local extrema -- Status:

• PM: solenoidal field, id=3590 -- WP guess: solenoidal field -- Status:

• PM: Hessian form, id=6708 -- WP guess: Hessian form -- Status:

• PM: least and greatest value of function, id=7581 -- WP guess: least and greatest value of function -- Status:

• PM: methods to find extremum, id=7580 -- WP guess: methods to find extremum -- Status:

• PM: proof of arithmetic-geometric means inequality using Lagrange multipliers, id=7278 -- WP guess: proof of arithmetic-geometric means inequality using Lagrange multipliers -- Status:

• PM: Taylor's formula in Banach spaces, id=7328 -- WP guess: Taylor's formula in Banach spaces -- Status:

• PM: tests for local extrema in Lagrange multiplier method, id=7336 -- WP guess: tests for local extrema in Lagrange multiplier method -- Status:

• PM: cuboid with least surface, id=9770^new! -- WP guess: cuboid with least surface -- Status:

• PM: example of vector potential, id=7663^new! -- WP guess: example of vector potential -- Status:

• PM: extremum points of function of several variables, id=9769^new! -- WP guess: extremum points of function of several variables -- Status:

• PM: proof of chain rule (several variables), id=8145^new! -- WP guess: proof of chain rule (several variables) -- Status:

• PM: proof of least and greatest value of function, id=7865^new! -- WP guess: proof of least and greatest value of function -- Status:

• PM: vector potential, id=7662^new! -- WP guess: vector potential -- Status:

26B15 Integration: length, area, volume

• PM: arc length, id=1090 -- WP guess: arc length -- Status:

• PM: centre of mass, id=7322 -- WP guess: centre of mass -- Status:

• PM: derivation of a definite integral formula using the method of exhaustion, id=6634 -- WP guess: derivation of a definite integral formula using the method of exhaustion -- Status:

• PM: proof of Ruffa's formula for continuous functions, id=6636 -- WP guess: proof of Ruffa's formula for continuous functions -- Status:

• PM: centre of mass of half-disc, id=9706^new! -- WP guess: centre of mass of half-disc -- Status:

• PM: length of curve in a metric space, id=9085^new! -- WP guess: length of curve in a metric space -- Status:

• PM: perimeter of astroid, id=9564^new! -- WP guess: perimeter of astroid -- Status:

26B20 Integral formulas (Stokes, Gauss, Green, etc.)

• PM: Green's theorem, id=1678 -- WP guess: Green's theorem -- Status:

• PM: classical Stokes' theorem, id=7316 -- WP guess: classical Stokes' theorem -- Status:

• PM: Gauss Green theorem, id=6741 -- WP guess: Gauss Green theorem -- Status:

26B25 Convexity, generalizations

• PM: extremal value of convex/concave functions, id=4165 -- WP guess: extremal value of convex/concave functions -- Status:

• PM: convex functions lie above their supporting lines, id=9268^new! -- WP guess: convex functions lie above their supporting lines -- Status:

• PM: proof of criterion for convexity, id=9288^new! -- WP guess: proof of criterion for convexity -- Status:

26B30 Absolutely continuous functions, functions of bounded variation

• PM: absolutely continuous function, id=4448 -- WP guess: absolutely continuous function -- Status:

• PM: total variation, id=3996 -- WP guess: total variation -- Status:

• PM: absolutely continuous function, id=7116 -- WP guess: absolutely continuous function -- Status:

• PM: BV function, id=6969 -- WP: BV function -- Status: M

by User:Daniele.tampieri. 03:53, 18 February 2007 (UTC)

• PM: example of a BV function which is not W^{1,1}, id=6979 -- WP guess: example of a BV function which is not W^1,1 -- Status:

26B99 Miscellaneous

• PM: derivation of zeroth weighted power mean, id=3620 -- WP guess: derivation of zeroth weighted power mean -- Status:

• PM: weighted power mean, id=267 -- WP guess: weighted power mean -- Status:

26C15 Rational functions

• PM: partial fractions of expressions, id=5812 -- WP guess: partial fractions of expressions -- Status:

• PM: partial fractions of expressions and partition problems (recreational), id=6645 -- WP guess: partial fractions of expressions and partition problems (recreational) -- Status:

• PM: rational function, id=4300 -- WP guess: rational function -- Status:

26C99 Miscellaneous

• PM: Laguerre polynomial, id=2753 -- WP: Laguerre polynomial -- Status: M

linas 17:13, 26 Mar 2005 (UTC)

26D05 Inequalities for trigonometric functions and polynomials

• PM: Jordan's inequality, id=13 -- WP guess: Jordan's inequality -- Status:

• PM: proof of Jordan's Inequality, id=3585 -- WP guess: proof of Jordan's Inequality -- Status:

• PM: Shapiro inequality, id=4404 -- WP guess: Shapiro inequality -- Status:

• PM: Weierstrass product inequality, id=4744 -- WP guess: Weierstrass product inequality -- Status:

26D10 Inequalities involving derivatives and differential and integral operators

• PM: Gronwall's lemma, id=3901 -- WP : Gronwall's lemma -- Status: C

(not by me). Oleg Alexandrov 22:43, 13 September 2005 (UTC)

• PM: proof of Gronwall's lemma, id=3902 -- WP guess: proof of Gronwall's lemma -- Status: N

It's a proof. Oleg Alexandrov 22:43, 13 September 2005 (UTC)

• PM: Hermite-Hadamard integral inequality, id=9209^new! -- WP guess: Hermite-Hadamard integral inequality -- Status:

• PM: proof of Hermite-Hadamard integral inequality, id=9269^new! -- WP guess: proof of Hermite-Hadamard integral inequality -- Status:

• PM: relation between positive function and its gradient when its Hessian matrix is bounded, id=7887^new! -- WP guess: relation between positive function and its gradient when its Hessian matrix is bounded -- Status:

26D15 Inequalities for sums, series and integrals

• PM: arithmetic-geometric-harmonic means inequality, id=25 -- WP guess: arithmetic-geometric-harmonic means inequality -- Status:

• PM: Carleman's inequality, id=4405 -- WP: Carleman's inequality -- Status: C

Oleg Alexandrov (talk) 04:08, 5 February 2007 (UTC)

• PM: Chebyshev's inequality, id=277 -- WP guess: Chebyshev's inequality -- Status:

• PM: derivation of geometric mean as the limit of the power mean, id=5741 -- WP guess: derivation of geometric mean as the limit of the power mean -- Status:

• PM: general means inequality, id=2934 -- WP guess: general means inequality -- Status:

• PM: Jensen's inequality, id=234 -- WP guess: Jensen's inequality -- Status:

• PM: MacLaurin's Inequality, id=3835 -- WP: MacLaurin's Inequality -- Status: C

Oleg Alexandrov (talk) 04:03, 18 February 2007 (UTC)

• PM: Minkowski inequality, id=230 -- WP: Minkowski inequality -- Status:

• PM: Muirhead's theorem, id=3736 -- WP guess: Muirhead's theorem -- Status: A

Oleg Alexandrov (talk) 04:03, 18 February 2007 (UTC)

• PM: power mean, id=266 -- WP guess: power mean -- Status:

• PM: proof of arithmetic-geometric means inequality, id=6482 -- WP guess: proof of arithmetic-geometric means inequality -- Status:

• PM: proof of arithmetic-geometric-harmonic means inequality, id=2970 -- WP guess: proof of arithmetic-geometric-harmonic means inequality -- Status:

• PM: proof of arithmetic-geometric-harmonic means inequality, id=3013 -- WP guess: proof of arithmetic-geometric-harmonic means inequality -- Status:

• PM: proof of Chebyshev's inequality, id=3582 -- WP guess: proof of Chebyshev's inequality -- Status:

• PM: proof of general means inequality, id=3619 -- WP guess: proof of general means inequality -- Status:

• PM: proof of Jensen's inequality, id=3060 -- WP guess: proof of Jensen's inequality -- Status:

• PM: proof of Minkowski inequality, id=2987 -- WP guess: proof of Minkowski inequality -- Status:

• PM: proof of rearrangement inequality, id=3583 -- WP guess: proof of rearrangement inequality -- Status:

• PM: proof of Young's inequality by picture, id=5575 -- WP guess: proof of Young's inequality by picture -- Status:

• PM: rearrangement inequality, id=276 -- WP guess: rearrangement inequality -- Status:

• PM: Schur's inequality, id=3836 -- WP guess: Schur's inequality -- Status:

• PM: Young's inequality, id=3834 -- WP guess: Young's inequality -- Status:

• PM: proof of arithmetic-geometric-harmonic means inequality, id=6909 -- WP guess: proof of arithmetic-geometric-harmonic means inequality -- Status:

• PM: another proof of Jensen's inequality, id=7881^new! -- WP guess: another proof of Jensen's inequality -- Status:

• PM: another proof of Young inequality, id=7715^new! -- WP guess: another proof of Young inequality -- Status:

• PM: Hardy's inequality, id=9368^new! -- WP guess: Hardy's inequality -- Status:

• PM: proof of PTAH inequality, id=9178^new! -- WP guess: proof of PTAH inequality -- Status:

• PM: PTAH inequality, id=9169^new! -- WP guess: PTAH inequality -- Status:

26D99 Miscellaneous

• PM: Bernoulli's inequality, id=275 -- WP guess: Bernoulli's inequality -- Status:

• PM: majorization, id=6043 -- WP guess: majorization -- Status:

• PM: proof of Bernoulli's inequality, id=2900 -- WP guess: proof of Bernoulli's inequality -- Status:

• PM: characterizations of majorization, id=7291 -- WP guess: characterizations of majorization -- Status:

• PM: another proof of Bernoulli's inequality, id=7717^new! -- WP guess: another proof of Bernoulli's inequality -- Status:

• PM: inequalities for differences of powers, id=7776^new! -- WP guess: inequalities for differences of powers -- Status:

• PM: limit of (1 + s_n)^n is one when limit of n s_n is zero, id=7780^new! -- WP guess: limit of (1 + s_n)^n is one when limit of n s_n is zero -- Status:

• PM: Proof of Bernoulli's Inequality employing the Mean Value Theorem, id=7803^new! -- WP guess: Proof of Bernoulli's Inequality employing the Mean Value Theorem -- Status:

• PM: proof of inequalities for difference of powers, id=7777^new! -- WP guess: proof of inequalities for difference of powers -- Status:

26E35 Nonstandard analysis

• PM: construction of Dirac delta function, id=2848 -- WP guess: construction of Dirac delta function -- Status:

• PM: hyperreal, id=2847 -- WP guess: hyperreal -- Status:

• PM: example of infinite hyperreal number, id=9809^new! -- WP guess: example of infinite hyperreal number -- Status:

• PM: example of infinitesimal hyperreal number, id=9808^new! -- WP guess: example of infinitesimal hyperreal number -- Status:

• PM: functional analysis, id=8636^new! -- WP guess: functional analysis -- Status:

• PM: properties of hyperreals under field operations, id=9818^new! -- WP guess: properties of hyperreals under field operations -- Status:

• PM: structure of finite hyperreal numbers, id=9810^new! -- WP guess: structure of finite hyperreal numbers -- Status:

26E60 Means

• PM: arithmetic-geometric mean, id=5893 -- WP guess: arithmetic-geometric mean -- Status:

• PM: spherical mean, id=5568 -- WP: spherical mean -- Status: A

Oleg Alexandrov (talk) 04:09, 2 April 2007 (UTC)

• PM: arithmetic-geometric mean as a product, id=9478^new! -- WP guess: arithmetic-geometric mean as a product -- Status:

• PM: complex arithmetic-geometric mean, id=9480^new! -- WP guess: complex arithmetic-geometric mean -- Status:

• PM: convergence of arithmetic-geometric mean, id=9474^new! -- WP guess: convergence of arithmetic-geometric mean -- Status:

26E99 Miscellaneous

• PM: zero of a function, id=4921 -- WP guess: zero of a function -- Status: