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A standard method of evaluating the secant integral presented in various references involves multiplying the numerator and denominator by sec θ + tan θ and then using the substitution u = sec θ + tan θ. This substitution can be obtained from the derivatives of secant and tangent added together, which have secant as a common factor. [6]
The integral of secant cubed is a frequent and challenging [1] indefinite integral of elementary calculus: = + + = ( + | + |) + = ( + ) +, | | < where is the inverse Gudermannian function, the integral of the secant function.
The main idea is to express an integral involving an integer parameter (e.g. power) of a function, represented by I n, in terms of an integral that involves a lower value of the parameter (lower power) of that function, for example I n-1 or I n-2. This makes the reduction formula a type of recurrence relation. In other words, the reduction ...
The formula calculator concept can be applied to all types of calculator, including arithmetic, scientific, statistics, financial and conversion calculators. The calculation can be typed or pasted into an edit box of: A software package that runs on a computer, for example as a dialog box. An on-line formula calculator hosted on a web site.
The field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, [5] as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.
A graphing calculator is a class of hand-held calculator that is capable of plotting graphs and solving complex functions. While there are several companies that manufacture models of graphing calculators, Hewlett-Packard is a major manufacturer.
For , a pseudoinverse of A is defined as a matrix + satisfying all of the following four criteria, known as the Moore–Penrose conditions: [4] [5] A A + {\displaystyle AA^{+}} need not be the general identity matrix, but it maps all column vectors of A to themselves: A A + A = A . {\displaystyle AA^{+}A=\;A.}
The 2 on the top scale is placed over the 5.5 on the bottom scale. The resulting quotient, 2.75 , can then be read below the top scale's 1 : There is more than one method for doing division, and the method presented here has the advantage that the final result cannot be off-scale, because one has a choice of using the 1 at either end.