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Chapter 20. Integral Calculus

20. Integral Calculus

Introduction 633

20.1 Integration 634

20.1.1 Indefinite Integration 634 Integrate

20.1.2 More about Indefinite Integration 637

20.1.3 Definite Integration 638 Integrate

20.1.4 Integration over Regions 642 Boole

20.2 Numerical Quadrature 644

20.2.1 Introduction 644 NIntegrate

20.2.2 Strategies and Rules 647

20.2.3 General Adaptive Strategies 648 "GlobalAdaptive", "LocalAdaptive"

20.2.4 Quadrature Rules 652 "GaussKronrodRule", "MultiDimensionalRule", etc.

20.2.5 Singular Integrands 655 IMT, "DoubleExponential", "DuffyCoordinates"

20.2.6 Oscillatory Integrands 658 "ClenshawCurtisRule", "ExtrapolatingOscillatory", etc.

20.2.7 Symbolic Preprocessing 660 "SymbolicPiecewiseSubdivision", "EvenOddSubdivision", etc.

20.2.8 Monte Carlo Methods 662 "MonteCarlo", "AdaptiveMonteCarlo", etc.

20.2.9 More about Quadrature 664 NewtonCotesWeights, GaussianQuadratureWeights, etc.

20.3 Sums and Products 666

20.3.1 Exact Sums 666 Sum

20.3.2 Numerical Sums 667 NSum

20.3.3 Products 670 Product, NProduct

20.4 Transforms 670

20.4.1 Laplace Transforms 670 LaplaceTransform, InverseLaplaceTransform

20.4.2 Z-Transforms 672 ZTransform, InverseZTransform

20.4.3 Fourier Transforms and Series 672 FourierTransform, FourierTrigSeries, etc.

20.4.4 Discrete Fourier Transforms 675 Fourier, InverseFourier, FourierDST, FourierDCT


  

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