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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Message
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| ``Re: essential supremum of a function''
by bci1 on 2009-02-01 15:04:56 |
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| > actually, I'm using sections and not subsections in my
> entries. Dunno which is preferable.
The sections seem to be too large in the Noosphere implementation of Tex. Anyway, here I am sharing with you some of the instructions and examples provided to me by the PMAdmin, CC committee that you might also find useful about the `expected' PM style:
"some of the following entries are what we considered well-written entries:
two examples of a well-written definition:
http://planetmath.org/?op=getobj&from=objects&id=4844
http://planetmath.org/?op=getobj&from=objects&id=448
an example of a well-written theorem:
http://planetmath.org/?op=getobj&from=objects&id=3252
an example of a well-written proof:
http://planetmath.org/?op=getobj&from=objects&id=4463
an example of a well-written biographical/historical entry:
http://planetmath.org/?op=getobj&from=objects&id=4161
an example of a well-written topic entry:
http://planetmath.org/?op=getobj&from=objects&id=7592
http://planetmath.org/?op=getobj&from=objects&id=7007
http://planetmath.org/?op=getobj&from=objects&id=6878 "
http://planetmath.org/?op=getobj&from=objects&id=7592
topics on calculus (Topic)
This entry is an overview of many calculus related entries which can be found here, at PlanetMath.org. By calculus we mean real analysis at the high-school level or college level, and the entries in this page should be at either level. If an entry is written at a higher level, it will be indicated with a âÃÂÃÂGLâÃÂÃÂ? tag.
Expositions
The following are books or notes on calculus:
An Introduction to Calculus.
: The real line
Basic properties of the real numbers:
Decimal expansion
Positive
Inverse number, Opposite number
(GL) Real number
Topic entry on real numbers
Functions of one real variable
Concept of function and real function
Computing limits
Limit of function
Limit of (sin x)/x as x tends to 0
Limit rules of functions
Improper limits
L'HÃÂôpital's rule
Growth of exponential function
Example of computing limits using Taylor expansion
Continuity
Continuous and discontinuous functions
Continuity of natural power
Continuity of sine and cosine
Jump discontinuity example
Intermediate value theorem
Differentiation in one variable
Derivative
Sum rule
Power rule
Product rule
Quotient rule
Chain rule
Derivative of inverse function
Derivatives of sine and cosine
Bolzano's theorem
Least and greatest value of function
Higher order derivatives
Fractional Differentiation
Integration of functions of one real variable
Integral sign
Definition of Riemann integral
A lecture on integration by substitution
A lecture on integration by parts
A lecture on trigonometric integrals and trigonometric substitutions
A lecture on the partial fraction decomposition method
Definite integral
Definite integral
Riemann integral
Fundamental theorem of calculus
Improper integral
List of improper integrals
Approximate integration: Left Hand Rule
Right Hand Rule
Midpoint Rule
Trapezoidal Rule
Simpson's Rule
Integral equation
Fractional Integration
Integral Transforms
Fourier transform
Laplace transform
Fourier-Mellin integral
Mellin's transform
Fourier sine transform
Fourier cosine transform
Multivariable Calculus
Differentiation
Iterated limit
Jacobian matrix
Differentiation under the integral sign
Integration
Stokes' theorem
Differential Equations
Differential equation
(GL) Existence and uniqueness of solution of ordinary differential equations
Index of differential equations
Separation of variables
Method of integrating factors
(GL) Examples of solving a PDE: a) Heat equation, b) Wave equation
Infinite Series
Series of Numbers
Series
Topic entry on series of complex terms
Infinite Series: Tests for Convergence and Examples
(GL?) Non-existence of universal series convergence criterion
Cauchy general condition for convergence
Geometric series, Harmonic series
Sum of series depends on order
Manipulating convergent series
(GL?) Multiplication of series
Leibniz' estimate for alternating series
Function Sequences and Series
Limit of function sequence
The limit of a uniformly convergent sequence of continuous functions is continuous
Sum function of series
Termwise differentiation
Weierstrass' criterion of uniform convergence
(GL) Fourier series
Power Series and Taylor Series
Power series and Taylor series
Taylor's theorem
Newton's binomial series
Example of Taylor polynomials for
Example of Taylor polynomials for the exponential function
Examples on how to find Taylor series from other known series
Getting Taylor series from differential equation "
" This entry is an overview of many calculus related entries which can be found here, at PlanetMath.org. By calculus we \PMlinkescapetext{mean} real analysis at the high-school level or college level, and the entries in this page should be at either level. If an entry is written at a higher level, it will be indicated with a ``GL'' tag.
\section{Expositions}
The following are books or notes on calculus:
\begin{itemize}
\item \PMlinkexternal{An Introduction to Calculus}{http://planetmath.org/?op=getobj&from=lec&id=36}.
\end{itemize}
\section{$\Reals$ : The real line}
Basic properties of the real numbers:
\begin{itemize}
\item Decimal expansion
\item Positive
\item Inverse number, Opposite number
\item (GL) \PMlinkid{Real number}{RealNumber}
\item Topic entry on real numbers
\end{itemize}
\section{Functions of one real variable}
\begin{itemize}
\item Concept of function and real function
\end{itemize}
\section{Computing limits}
\begin{itemize}
\item Limit of function
\item \PMlinkname{Limit of (sin {\em x})/{\em x} as {\em x} tends to 0}{LimitOfDisplaystyleFracsinXxAsXApproaches0}
\item Limit rules of functions
\item Improper limits
\item \PMlinkname{L'H\^opital's rule}{LHpitalsRule}
\item Growth of exponential function
\item Example of computing limits using Taylor expansion
\end{itemize}
\section{Continuity}
\begin{itemize}
\item Continuous and discontinuous functions
\item Continuity of natural power
\item Continuity of sine and cosine
\item \PMlinkname{Jump discontinuity example}{ExampleOfJumpDiscontinuity}
\item Intermediate value theorem
\end{itemize}
\section{Differentiation in one variable}
\begin{itemize}
\item Derivative
\item Sum rule
\item Power rule
\item Product rule
\item Quotient rule
\item Chain rule
\item Derivative of inverse function
\item Derivatives of sine and cosine
\item Bolzano's theorem
\item Least and greatest value of function
\item Higher order derivatives
\item Fractional Differentiation
\end{itemize}
\section{Integration of functions of one real variable}
\begin{itemize}
\item Integral sign
\item \PMlinkname{Definition of Riemann integral}{RiemannIntegral}
\item A lecture on integration by substitution
\item A lecture on integration by parts
\item A lecture on trigonometric integrals and trigonometric substitutions
\item A lecture on the partial fraction decomposition method
\end{itemize}
\section{Definite integral}
\begin{itemize}
\item Definite integral
\item Riemann integral
\item Fundamental theorem of calculus
\item Improper integral
\item List of improper integrals
\item Approximate integration: \begin{tabular}{l}
Left Hand Rule \\
Right Hand Rule \\
Midpoint Rule \\
Trapezoidal Rule \\
Simpson's Rule \end{tabular}
\item Integral equation
\item Fractional Integration
\end{itemize}
\section{Integral Transforms}
\begin{itemize}
\item Fourier transform
\item Laplace transform
\item Fourier-Mellin integral
\item Mellin's transform
\item Fourier sine transform
\item Fourier cosine transform
\end{itemize}
\section{Multivariable Calculus}
\subsection{Differentiation}
\begin{itemize}
\item Iterated limit
\item Jacobian matrix
\item Differentiation under the integral sign
\end{itemize}
\subsection{Integration}
\begin{itemize}
\item Stokes' theorem
\end{itemize}
\section{Differential Equations}
\begin{itemize}
\item Differential equation
\item (GL) Existence and uniqueness of solution of ordinary differential equations
\item Index of differential equations
\item Separation of variables
\item Method of integrating factors
\item (GL) Examples of solving a PDE:\,
a) \PMlinkname{Heat equation}{ExampleOfSolvingTheHeatEquation},
b) \PMlinkname{Wave equation}{SolvingTheWaveEquationByDBernoulli}
\end{itemize}
\section{Infinite Series}
\subsection{Series of Numbers}
\begin{itemize}
\item Series
\item Topic entry on series of complex terms
\item \PMlinkexternal{Infinite Series: Tests for Convergence and Examples}{http://planetmath.org/?op=getobj&from=lec&id=37}
\item (GL?) Non-existence of universal series convergence criterion
\item \PMlinkname{Cauchy general condition for convergence}{CauchyCriterionForConvergence}
\item Geometric series, Harmonic series
\item Sum of series depends on order
\item Manipulating convergent series
\item (GL?) Multiplication of series
\item \PMlinkname{Leibniz' estimate for alternating series}{LeibnizEstimateForAlternatingSeries}
\end{itemize}
\subsection{Function Sequences and Series}
\begin{itemize}
\item Limit of function sequence
\item The limit of a uniformly convergent sequence of continuous functions is continuous
\item Sum function of series
\item Termwise differentiation
\item Weierstrass' criterion of uniform convergence
\item (GL) \PMlinkname{Fourier series}{FourierSineAndCosineSeries}
\end{itemize}
\subsection{Power Series and Taylor Series}
\begin{itemize}
\item Power series and Taylor series
\item Taylor's theorem
\item \PMlinkname{Newton's binomial series}{BinomialFormula}
\item \PMlinkid{Example of Taylor polynomials}{ExampleOfTaylorPolynomialsForSinX} for $\sin x$
\item Example of Taylor polynomials for the exponential function
\item Examples on how to find Taylor series from other known series
\item Getting Taylor series from differential equation
\end{itemize}
"
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