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  2. Institutiones calculi integralis - Wikipedia

    en.wikipedia.org/wiki/Institutiones_calculi...

    Institutiones calculi integralis (Foundations of integral calculus) is a three-volume textbook written by Leonhard Euler and published in 1768. It was on the subject of integral calculus and contained many of Euler's discoveries about differential equations .It was written after "Institutiones calculi differentialis" (1755) and "Introductio in ...

  3. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    In Gradshteyn and Ryzhik, integrals originating from the book by Bierens de Haan are denoted by BI. Not all closed-form expressions have closed-form antiderivatives; this study forms the subject of differential Galois theory , which was initially developed by Joseph Liouville in the 1830s and 1840s, leading to Liouville's theorem which ...

  4. List of integration and measure theory topics - Wikipedia

    en.wikipedia.org/wiki/List_of_integration_and...

    List of multivariable calculus topics; List of real analysis topics; List of integrals; List of integrals of exponential functions; List of integrals of hyperbolic functions; List of integrals of irrational functions; List of integrals of logarithmic functions; List of integrals of rational functions; List of integrals of trigonometric functions

  5. Gradshteyn and Ryzhik - Wikipedia

    en.wikipedia.org/wiki/Gradshteyn_and_Ryzhik

    In 1995, Alan Jeffrey published his Handbook of Mathematical Formulas and Integrals. [22] It was partially based on the fifth English edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products and meant as an companion, but written to be more accessible for students and practitioners. [22] It went through four editions up to 2008.

  6. Leibniz integral rule - Wikipedia

    en.wikipedia.org/wiki/Leibniz_integral_rule

    In calculus, the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of the form () (,), where < (), < and the integrands are functions dependent on , the derivative of this integral is expressible as (() (,)) = (, ()) (, ()) + () (,) where the partial derivative indicates that inside the integral, only the ...

  7. Calculus - Wikipedia

    en.wikipedia.org/wiki/Calculus

    Integral calculus is the study of the definitions, properties, and applications of two related concepts, the indefinite integral and the definite integral. The process of finding the value of an integral is called integration. [48]: 508 The indefinite integral, also known as the antiderivative, is the inverse operation to the derivative.

  8. A Course of Pure Mathematics - Wikipedia

    en.wikipedia.org/wiki/A_Course_of_Pure_Mathematics

    the book is organized into the following chapters. i. real variables; ii. functions of real variables; iii. complex numbers; iv. limits of functions of a positive integral variable; v. limits of functions of a continuous variable. continuous and discontinuous functions; vi. derivatives and integrals; vii. additional theorems in the differential ...

  9. Bochner integral - Wikipedia

    en.wikipedia.org/wiki/Bochner_integral

    Such integrals are central to the analysis of distributions in functional spaces and have applications in fields such as stochastic calculus, statistical field theory,and quantum field theory. Let ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},\mathbb {P} )} be a probability space , and consider a random variable X : Ω → B ...

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