This entry is an overview of many calculus related entries which can be found here, at PlanetMath.org. By calculus we 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.
1 Expositions
The following are books or notes on calculus:
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http://planetmath.org/?op=getobj&from=lec&id=36An Introduction to Calculus.
2 : The real line
Basic properties of the real numbers:
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Decimal expansion
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Positive
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Inverse number, Opposite number
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(GL) http://planetmath.org/node/RealNumberReal number
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3 Functions of one real variable
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4 Computing limits
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Limit of function
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Limit of (sin x)/x as x tends to 0 (http://planetmath.org/LimitOfDisplaystyleFracsinXxAsXApproaches0)
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L’Hôpital’s rule (http://planetmath.org/LHpitalsRule)
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5 Continuity
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Jump discontinuity example (http://planetmath.org/ExampleOfJumpDiscontinuity)
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6 Differentiation in one variable
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Bolzano’s theorem
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Least and greatest value of function
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7 Integration of functions of one real variable
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Integral sign
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Definition of Riemann integral (http://planetmath.org/RiemannIntegral)
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A lecture on the partial fraction decomposition method
8 Definite integral
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Riemann integral
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Integral equation
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9 Integral Transforms
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10 Multivariable Calculus
10.1 Differentiation
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10.2 Integration
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Stokes’ theorem
11 Differential Equations
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(GL) Examples of solving a PDE: a) Heat equation (http://planetmath.org/ExampleOfSolvingTheHeatEquation), b) Wave equation (http://planetmath.org/SolvingTheWaveEquationByDBernoulli)
12 Infinite Series
12.1 Series of Numbers
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Series
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Cauchy general condition for convergence (http://planetmath.org/CauchyCriterionForConvergence)
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Leibniz’ estimate for alternating series (http://planetmath.org/LeibnizEstimateForAlternatingSeries)
12.2 Function Sequences and Series
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Sum function of series
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(GL) Fourier series (http://planetmath.org/FourierSineAndCosineSeries)
12.3 Power Series and Taylor Series
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Taylor’s theorem
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Newton’s binomial series (http://planetmath.org/BinomialFormula)
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http://planetmath.org/node/ExampleOfTaylorPolynomialsForSinXExample of Taylor polynomials for
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Getting Taylor series from differential equation
13 Additional Topic
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Non-Newtonian calculus