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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 .

  3. 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 ...

  4. Calculus Made Easy - Wikipedia

    en.wikipedia.org/wiki/Calculus_Made_Easy

    Calculus Made Easy ignores the use of limits with its epsilon-delta definition, replacing it with a method of approximating (to arbitrary precision) directly to the correct answer in the infinitesimal spirit of Leibniz, now formally justified in modern nonstandard analysis and smooth infinitesimal analysis.

  5. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful.

  6. Integral - Wikipedia

    en.wikipedia.org/wiki/Integral

    A line integral (sometimes called a path integral) is an integral where the function to be integrated is evaluated along a curve. [42] Various different line integrals are in use. In the case of a closed curve it is also called a contour integral. The function to be integrated may be a scalar field or a vector field.

  7. Integration by reduction formulae - Wikipedia

    en.wikipedia.org/wiki/Integration_by_reduction...

    In integral calculus, integration by reduction formulae is a method relying on recurrence relations. It is used when an expression containing an integer parameter , usually in the form of powers of elementary functions, or products of transcendental functions and polynomials of arbitrary degree , can't be integrated directly.

  8. Feynman parametrization - Wikipedia

    en.wikipedia.org/wiki/Feynman_parametrization

    Vladimir A. Smirnov: Feynman Integral Calculus, Springer, ISBN 978-3-54030610-8 (Aug.,2006). Vladimir A. Smirnov: Analytic Tools for Feynman Integrals , Springer, ISBN 978-3-64234885-3 (Jan.,2013). Johannes Blümlein and Carsten Schneider (Eds.): Anti-Differentiation and the Calculation of Feynman Amplitudes , Springer, ISBN 978-3-030-80218-9 ...

  9. Riemann integral - Wikipedia

    en.wikipedia.org/wiki/Riemann_integral

    The Darboux integral is defined whenever the Riemann integral is, and always gives the same result. Conversely, the gauge integral is a simple but more powerful generalization of the Riemann integral and has led some educators to advocate that it should replace the Riemann integral in introductory calculus courses. [12]

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