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Abstract
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Continuous calculus of differentiation and integration has been considered more in
undergraduate and graduate mathematics. However this calculus is more useful for continuous
physical and engineering phenomena, But there are many problems and phenomena in natural
sciences. When we want to build mathematical models for them we need to use discrete calculus.
In this paper, at first we introduce the fundamental concepts of discrete additive and multiplica-
tive differentiation and integration. Then for some elementary functions discrete derivative and
multiplicative integration of them are calculated. In further research, by using this newly intro-
duced calculus, we solve difference equations in linear and nonlinear cases. Difference equations are
associated to differential equations in continuous calculus. This calculus can be used and taught
in undergraduate mathematics and graduate courses in university for investigation and solving
discrete physical systems and other natural phenomena
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