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2. ### Calculation - Wikipedia

en.wikipedia.org/wiki/Calculation

A calculation is a deliberate process that transforms one or more inputs into one or more results. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm, to the vague heuristics of calculating a strategy in a competition, or calculating the chance of a successful relationship between two people.

3. ### Slide rule - Wikipedia

en.wikipedia.org/wiki/Slide_rule

The pocket-sized Hewlett-Packard HP-35 scientific calculator was the first handheld device of its type, but it cost US\$395 in 1972. This was justifiable for some engineering professionals but too expensive for most students. Around 1974 the handheld electronic scientific calculator made slide rules largely obsolete.

4. ### Differentiation rules - Wikipedia

en.wikipedia.org/wiki/Differentiation_rules

The derivative of () = for any (nonvanishing) function f is: ′ = ′ (()) wherever f is non-zero. In Leibniz's notation, this is written (/) =.The reciprocal rule can be derived either from the quotient rule, or from the combination of power rule and chain rule.

5. ### Integral - Wikipedia

en.wikipedia.org/wiki/Integral

Integrals are also used in thermodynamics, where thermodynamic integration is used to calculate the difference in free energy between two given states. Computation Analytical. The most basic technique for computing definite integrals of one real variable is based on the fundamental theorem of calculus.

6. ### Continued fraction - Wikipedia

en.wikipedia.org/wiki/Continued_fraction

The difference between a given convergent and π is less than the reciprocal of the product of the denominators of that convergent and the next convergent. For example, the fraction 22 / 7 is greater than π , but 22 / 7 − π is less than 1 / 7 × 106 = 1 / 742 (in fact, 22 / 7 − π is just more than 1 / 791 = 1 / 7 × 113 ).

7. ### Acid dissociation constant - Wikipedia

en.wikipedia.org/wiki/Acid_dissociation_constant

Structural effects can also be important. The difference between fumaric acid and maleic acid is a classic example. Fumaric acid is (E)-1,4-but-2-enedioic acid, a trans isomer, whereas maleic acid is the corresponding cis isomer, i.e. (Z)-1,4-but-2-enedioic acid (see cis-trans isomerism).

8. ### Matrix decomposition - Wikipedia

en.wikipedia.org/wiki/Matrix_decomposition

Applicable to: m-by-n matrix A of rank r Decomposition: = where C is an m-by-r full column rank matrix and F is an r-by-n full row rank matrix Comment: The rank factorization can be used to compute the Moore–Penrose pseudoinverse of A, which one can apply to obtain all solutions of the linear system =.

9. ### Newton's method - Wikipedia

en.wikipedia.org/wiki/Newton's_method

Newton's method is a powerful technique—in general the convergence is quadratic: as the method converges on the root, the difference between the root and the approximation is squared (the number of accurate digits roughly doubles) at each step. However, there are some difficulties with the method.