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Cancelling 0 from both sides yields =, a false statement. The fallacy here arises from the assumption that it is legitimate to cancel 0 like any other number, whereas, in fact, doing so is a form of division by 0. Using algebra, it is possible to disguise a division by zero [17] to obtain an invalid proof. For example: [18]
Therefore, when one is solving a differential equation and using division one must check what happens if the term is equal to zero, and whether it leads to a singular solution. The Picard–Lindelöf theorem, which gives sufficient conditions for unique solutions to exist, can be used to rule out the existence of singular solutions.
ISBN 0-521-55376-8 (hardback), ISBN 0-521-55655-4 (paperback). (Textbook, targeting advanced undergraduate and postgraduate students in mathematics, which also discusses numerical partial differential equations.) John Denholm Lambert, Numerical Methods for Ordinary Differential Systems, John Wiley & Sons, Chichester, 1991. ISBN 0-471-92990-5.
In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations.
ISBN 0-19-853936-3; A French translation with detailed scholarly addenda and a critical edition of the Chinese text of both the book and its commentary by Karine Chemla and Shuchun Guo is Les neuf chapitres: le classique mathématique de la Chine ancienne et ses commentaires. Paris: Dunod, 2004. ISBN 978-2-10-049589-4.
Suppose further that a 1 /a 2 and a 0 /a 2 are analytic functions. The power series method calls for the construction of a power series solution = =. If a 2 is zero for some z, then the Frobenius method, a variation on this method, is suited to deal with so called "singular points". The method works analogously for higher order equations as ...
Pólya mentions that there are many reasonable ways to solve problems. [3] The skill at choosing an appropriate strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included: Guess and check [9] Make an orderly list [10] Eliminate possibilities [11] Use symmetry [12]
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.