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VU MTH603 VU Current GDB Solution Spring 2013

VU MTH603 VU Current GDB Solution Spring 2013

Numerical integration aims at approximating definite integrals using numerical techniques. There are many situations where numerical integration is needed. For example, several well defined functions do not have an anti-derivative, i.e. their anti-derivative cannot be expressed in terms of primitive function. A popular example is the function e��x2 whose anti-derivative does not exist. This function arises in a variety of applications such as those related to probability and statistics analyses. Furthermore, many applications in science and engineering are represented by integral differential equations that require a special treatment for the integral terms (e.g. expansion, liberalization, closure …).
Therefore, numerical integration does not only provide a means for evaluating integrals numerically, but also grants us the ability to approximate special functions that are defined in terms of integrals. Without loss of generality, there are two classes of problems where numerical integration is needed. In the first class, one wishes to evaluate the integral of a well defined function. In this case, the integrand can be evaluated a various points because and numerical integration techniques help define the optimum number of these points as well as their locations. The second class of problems for applying numerical integration is found in differential equations the most common of which are those that express conservation principles. For example, the population balance equation, a well known partial

VU MTH603 VU Current GDB Solution Spring 2013

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