By George Elmer Forsythe, Michael A. Malcolm, Cleve B. Moler

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**Example text**

Notice that both dblquad and triplequad assume that ƒ accepts as input a vector x and scalars y and z and returns a vector of results, so that the preceding functions spam2 and spam3 have to be modified in order to satisfy these requirements. Notice that the class includes a method for integration (it assumes finite values for all the elements of F). 7197. 4861. 4856. 1944. Due to discontinuity, finer partitions are requested for a good precision. 3716. The exact result is . – In some situations, the available data is not on a grid, but just on sparse points.

Triplequad adapts to the same use as integral3 by considering a box containing the region of integration and extending the integrand by zero outside the region of integration. Notice that both dblquad and triplequad assume that ƒ accepts as input a vector x and scalars y and z and returns a vector of results, so that the preceding functions spam2 and spam3 have to be modified in order to satisfy these requirements. Notice that the class includes a method for integration (it assumes finite values for all the elements of F).

7197. 4861. 4856. 1944. Due to discontinuity, finer partitions are requested for a good precision. 3716. The exact result is . – In some situations, the available data is not on a grid, but just on sparse points. This situation is considered in Chapter 3. 2 Variational Methods for Algebraic Equations Let us begin our exploration of variational methods by a situation which may appear as simple, but contains the fundamental elements necessary to the implementation of variational methods in complex situations: the variational formulation of algebraic equations and its consequences.