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  2. Integral of the secant function - Wikipedia

    en.wikipedia.org/wiki/Integral_of_the_secant...

    The integral of the secant function was historically one of the first integrals of its type ever evaluated, before most of the development of integral calculus. It is important because it is the vertical coordinate of the Mercator projection , used for marine navigation with constant compass bearing .

  3. Integral of secant cubed - Wikipedia

    en.wikipedia.org/wiki/Integral_of_secant_cubed

    This is one of several integrals usually done in a first-year calculus course in which the most natural way to proceed involves integrating by parts and returning to the same integral one started with (another is the integral of the product of an exponential function with a sine or cosine function; yet another the integral of a power of the ...

  4. 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.

  5. Matrix calculus - Wikipedia

    en.wikipedia.org/wiki/Matrix_calculus

    In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.

  6. List of integrals of exponential functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    Toyesh Prakash Sharma, Etisha Sharma, "Putting Forward Another Generalization Of The Class Of Exponential Integrals And Their Applications.," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.1-8, 2023.

  7. Magnus expansion - Wikipedia

    en.wikipedia.org/wiki/Magnus_expansion

    When n = 1, the solution is given as a product integral = ⁡ (()). This is still valid for n > 1 if the matrix A(t) satisfies A(t 1) A(t 2) = A(t 2) A(t 1) for any pair of values of t, t 1 and t 2. In particular, this is the case if the matrix A is independent of t. In the general case, however, the expression above is no longer the solution ...

  8. Matrix exponential - Wikipedia

    en.wikipedia.org/wiki/Matrix_exponential

    For matrix-matrix exponentials, there is a distinction between the left exponential Y X and the right exponential X Y, because the multiplication operator for matrix-to-matrix is not commutative. Moreover, If X is normal and non-singular, then X Y and Y X have the same set of eigenvalues. If X is normal and non-singular, Y is normal, and XY ...

  9. Multiple integral - Wikipedia

    en.wikipedia.org/wiki/Multiple_integral

    A double integral, on the other hand, is defined with respect to area in the xy-plane. If the double integral exists, then it is equal to each of the two iterated integrals (either "dy dx" or "dx dy") and one often computes it by computing either of the iterated integrals. But sometimes the two iterated integrals exist when the double integral ...