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...International journal of mathematics trends and technology ijmtt volume issue april on the calculus dirac delta function with some applications khalid abd elrazig awad alla elnour assistant professor department preparatory dean ship najran university kingdom saudi arabia abstract in this paper we present different properties provided simple proof definite integral obtain results derivative discontinuous functions an important problem to change traditional mathematical approach concept first order differential equations is developing by using it solution real life problems keywords generalized sifting laplace transform i introduction size bold ii was introduced p at end s effort create tool for field quantum theory can be regarded as a or probability dynamics known impulse very useful that appear many places physics such mechanics electromagnetism optics engineering various way defining its application determination see interesting discussion statistic plays role idealization radar circ...