When a differential equation can be expressed in linear form, it is particularly easy to solve by breaking the equation up into smaller pieces, solving each of those pieces, and summing the solutions.

When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations.

When done well, adhocracy can be very good at problem solving and innovations and thrives in a diverse environment.

When Stetson is captured by his pursuers and marked for elimination, Amanda ends up solving the secret behind the package, finding and rescuing Stetson, and even taking down their opponents, thereby getting introduced to the Agency.

For univariate algebraic equations these are also called roots, even if, properly speaking, one should say the solutions of the algebraic equation P = 0 are the roots of the polynomial P. When solving an equation, it is important to specify in which set the solutions are allowed.

After noting how David set a pattern by setting his son Solomon on the throne before his death, Nadav Na ' man writes, " When taking into account the permanent nature of the co-regency in Judah from the time of Joash, one may dare to conclude that dating the co-regencies accurately is indeed the key for solving the problems of biblical chronology in the eighth century B. C.

When a character is possessed, the player can use their abilities and weapons to find otherwise unreachable areas or levers, kill enemies, or as part of solving puzzles.

When solving dynamic optimization problems by numerical backward induction, the objective function must be computed for each combination of values.

When this is true, solving A cannot be harder than solving B.

When solving longer sums there are additional ways to find clues to locating the correct digits.

When solving sums which have a limited number of solution sets then that can lead to useful clues.

specific problem ( computing outputs for new cases ): " When solving a problem of

When we define upward to be the positive direction, constructing Newton's second law and solving for the normal force on a passenger yields the following equation:

When solving a puzzle, one might notice that if a certain candidate symbol were placed in one square, there would be multiple ways to complete another part of the puzzle, and no extra information could possibly decide between them.

When solving problems involving human-environment interactions, whether global or local, one must have a model of human nature that predicts the environmental conditions under which humans will behave in a decent and creative manner.

When asked why the decision was made only after almost four decades of celebrating Warriors ' Day at the present site, Jamil evaded comment, saying " Alhamdulillah, we are serious in solving this issue ".

When officials revealed in 1995 that the Grace Bridge scored a 4 out of 100 for safety and integrity, retired U. S. Congressman Arthur Ravenel, Jr. ran for the South Carolina Senate with a goal of solving the funding problem.

When solving equations, remember that addition and subtraction are inverse operations-they undo each other ( i. e., 10 + 9-9 =

When Shizuka unknowingly watches the cursed video with Yoko on her lap, they become Asakawa's primary motivation for solving the riddle of the tape.

When he isn't solving crimes, Hoop lives with his elderly mother and participates in dinner theatre.

When these forces are added, the equation of motion has the form:

When calculating the difference in voltage, one must first manipulate the half-cell reactions to obtain a balanced oxidation-reduction equation.

When the flow is everywhere irrotational and inviscid, Bernoulli's equation can be used throughout the flow field.

A number a is a root of P if and only if the polynomial x − a ( of degree one in x ) divides P. It may happen that x − a divides P more than once: if ( x − a )< sup > 2 </ sup > divides P then a is called a multiple root of P, and otherwise a is called a simple root of P. If P is a nonzero polynomial, there is a highest power m such that ( x − a )< sup > m </ sup > divides P, which is called the multiplicity of the root a in P. When P is the zero polynomial, the corresponding polynomial equation is trivial, and this case is usually excluded when considering roots: with the above definitions every number would be a root of the zero polynomial, with undefined ( or infinite ) multiplicity.

When proper units are used for tangential speed v, rotational speed ω, and radial distance r, the direct proportion of v to both r and ω becomes the exact equation:

When v is larger than c, the denominator in the equation for the energy is " imaginary ", as the value inside the square root is negative.

When Dutch physicist J. D. van der Waals received the 1910 Nobel Prize " for his work on the equation of state for gases and liquids " he acknowledged the great influence of Gibbs's work on that subject.

When Λ is zero, this reduces to the original field equation of general relativity.

When T is zero, the field equation describes empty space ( the vacuum ).

When comparing the predicted expansion rate of the universe as given by the tracker solutions with cosmological data, a main feature of tracker solutions is that one needs four parameters to properly describe the behavior of their equation of state, whereas it has been shown that at most a two-parameter model can optimally be constrained by mid-term future data ( horizon 2015-2020 ).

When solved for the diffracted angle maxima, the equation is:

When this condition is expressed in terms of probability densities, the result is called the Chapman – Kolmogorov equation.

When reactive elements such as capacitors, inductors, or transmission lines are involved in a circuit to which AC or time-varying voltage or current is applied, the relationship between voltage and current becomes the solution to a differential equation, so Ohm's law ( as defined above ) does not directly apply since that form contains only resistances having value R, not complex impedances which may contain capacitance (" C ") or inductance (" L ").

# When the balanced equation for a reaction is multiplied by an integer, the corresponding value of ΔH must be multiplied by that integer as well.

When the circles are of equal size, the equation is much simpler, but it still can be solved only approximately.

When this is true the equation is said to obey the superposition principle.

When c is very large and psi is slowly varying so that the lattice can be thought of as a line, this becomes the free Schrödinger equation:

When the domain is the real numbers, this is Cauchy's functional equation.

When the wavelength of a gravity wave is less than twice the depth of the ocean or lake its behavior is governed by the nonlinear Schrodinger equation and its speed is proportional to.

When the pure advection equation, which is free of dissipation, is solved by a numerical approximation method, the energy of the initial wave may be reduced in a way analogous to a diffusional process.

When the color is represented as RGB values, as often is the case in computer graphics, this equation is typically modeled separately for R, G and B intensities, allowing different reflections constants and for the different color channels.