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Page "Examples of differential equations" ¶ 24
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method and for
Though he is also concerned with freeing dance from pedestrian modes of activity, Merce Cunningham has selected a very different method for achieving his aim.
The very fact that they came so near to winning by the wrong method, war, led directly to their losing both the war and the wrong thing they fought for, since it forced Lincoln to free their slaves as a military measure.
In method as well as in theme this little anecdote with its details selected as much for expressiveness and allegory as for `` realism '', anticipates a kind of musical composition, as well as a kind of fictional composition, in which, as Leverkuhn says, `` there shall be nothing unthematic ''.
Comprehensive examination of any policy question calls for the performance of the intellectual tasks inseparable from any problem-solving method.
Let us not confuse the issue by labeling the objective or the method `` psychoanalytic '', for this is a well established term of art for the specific ideas and procedures initiated by Sigmund Freud and his followers for the study and treatment of disordered personalities.
A credulousness, a distaste for documentation, an uncritical reliance on contemporary accounts, and a proneness to assume a theory as true before adequate proof was provided were all evidences of his failure to comprehend the use of the scientific method or to evaluate the responsibilities of the historian to his reading public.
It was going to be hard going all the way because he hadn't written seriously for a while, except for a few stories, was tired of the old method of realismo he had so successfully used in The Sky Is Red.
It is the only method left for a man to escape from a woman's world.
This condition will undoubtedly continue until such time as a state uniform system of evaluation is established, or through mutual agreement of the local assessing officials for a method of standard assessment practice to be adopted.
Beginning with the October 1959 issue of the Journal, the method of production of copy for photo-offset reproduction was changed from varityping to hot typesetting.
Another recent achievement was the successful development of a method for the complete combustion in a bomb calorimeter of a metal in fluorine when the product is relatively non-volatile.
The method used for computing the respective Federal and State shares in total program costs is specifically set forth in the Act.
We are initiating research on the use of solid state materials for infrared detection using a method which will not require cooling of materials to attain high sensitivity.
This method of computing compression ratio cannot be used accurately for engines that have pistons with either domed or irregularly shaped heads.
It is generally an inaccurate method of rating, for the horsepower is that of the compressor motor, and many other components beside it determine how much cooling you'll get.
The longer I work, the more I am sure that for me, at least, a workmanlike method is important.
One of the advantages of this method is that the `` pill '' can remain in the patient for several days, permitting observation under natural conditions.
The final choice of material depends upon such factors as costs, method of fabrication, degree of complexity, number of units required, time available for tooling, and projected life expectancy of the unit.
More unitized lumber is being shipped on flat cars, and NLRDA studies show that flat cars loaded with the new Type 6-B floating-load method can be unloaded for as little as $.054/mbf.
The third method was, to our knowledge, successfully applied for the first time by C. Sheer and co-workers ( Ref. 2 ).
Although the Af calculation is obvious by analogy with that for gravitational field and osmotic pressure, it is interesting to confirm it by a method which can be generalized to include related effects.

method and solving
In these cases, statistical mechanics is a more valid method of solving the problem than continuous aerodynamics.
A method for solving a decision problem given in the form of an algorithm is called a decision procedure for that problem.
* Dynamic programming, a method of solving complex problems by breaking them down into simpler steps
Dialectical materialism is not, and never has been, a programmatic method for solving particular physical problems.
1520 – 1591 ), father of Galileo and the inventor of monody, made use of the method in successfully solving musical problems, firstly, of tuning such as the relationship of pitch to string tension and mass in stringed instruments, and to volume of air in wind instruments ; and secondly to composition, by his various suggestions to composers in his Dialogo della musica antica e moderna ( Florence, 1581 ).
In this method the research participant is asked to think aloud while performing a task, such as solving a math problem.
This is also a method for solving mazes.
In 1969 Heinrich Heesch published a method for solving the problem using computers.
GPS was possibly the first method of separating problem solving strategy from information about particular problems.
Laplace also recognised that Joseph Fourier's method of Fourier series for solving the diffusion equation could only apply to a limited region of space as the solutions were periodic.
The usual method for solving logistical problems for smaller armies was foraging or " living off the land ".
A general procedure ( the chakravala, or " cyclic method ") for solving Pell's equation was finally found by Jayadeva ( cited in the eleventh century ; his work is otherwise lost ); the earliest surviving exposition appears in Bhāskara II's Bīja-gaṇita ( twelfth century ).
Between 1880 and 1887, Heaviside developed the operational calculus ( involving the D notation for the differential operator, which he is credited with creating ), a method of solving differential equations by transforming them into ordinary algebraic equations which caused a great deal of controversy when first introduced, owing to the lack of rigour in his derivation of it.
He invented the operator method for solving linear differential equations, which resembles current Laplace transform methods ( see inverse Laplace transform, also known as the " Bromwich integral ").
The first general method for solving the Pell equation ( for all N ) was given by Bhaskara II in 1150, extending the methods of Brahmagupta.
An alternative method to solving, once finding the first non-trivial solution, one could take the original equation and factor the left hand side as a difference of squares, yielding Once in this form, one can simply raise each side of the equation to the kth power, and recombining the factored form to a single difference statement.
The resulting algorithm for solving Pell's equation is more efficient than the continued fraction method, though it still does not take polynomial time.
Radiosity is an application of the finite element method to solving the rendering equation for scenes with purely diffuse surfaces.
Another common method for solving the radiosity equation is " shooting radiosity ," which iteratively solves the radiosity equation by " shooting " light from the patch with the most error at each step.
Shen Lin and Brian Kernighan first published their method in 1972, and it was the most reliable heuristic for solving travelling salesman problems for nearly two decades.
* Hadamard's method of descent, a technique for solving partial differential equations
The " ladder operator " method, due to Paul Dirac, allows us to extract the energy eigenvalues without directly solving the differential equation.
It is widely conjectured that there is no computationally inexpensive method to solve chess even in the very weak sense of determining with certainty the value of the initial position, and hence the idea of solving chess in the stronger sense of obtaining a practically usable description of a strategy for perfect play for either side seems unrealistic today.
A third method, developed by Funk and Buchman, and refined by others, classifies electronic games into six categories: general entertainment ( no fighting or destruction ), educational ( learning or problem solving ), fantasy violence ( cartoon characters that must fight or destroy things, and risk being killed, in order to achieve a goal ), human violence ( like fantasy violence, but with human rather than cartoon characters ), nonviolent sports ( no fighting or destruction ), and sports violence ( fighting or destruction involved ).

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