We define different varieties of business conducted over the Internet or supported by this technology, which are called e-Business. These businesses can range from sell or Internet auctions to manage internal business processes -distribution, production, supply, finance, etc. using such technology. Differential equations are a powerful and versatile tool for solving problems from the most diverse horizons: from mechanics to biology, economics electricity, etc. The first step in solving these problems is modeling, ie the "translation" in mathematical relationships of the most important of the situation in question intrinsic aspects.The mathematical treatment of a problem from technical or other branch of science can be a difficult job, it is the combination of two different domains: the phenomena being studied (financial, ecological, economic, etc) and mathematics.Solving a problem basically comprises the following steps:1) Determination of intrinsic qualitative aspects of the problem: choosing a reference system of independent variables and unknown variables.2) Writing equations. These essentially they translate laws or physical, biological, economic behavior, etc.3) Processing and study of the equations obtained. Analytical or approximate solutions of the unknowns are being looked for.4) Interpretation of the mathematical results by comparison with experience.We understand mathematical model to approximate representation of a phenomenon by mathematical relationships (usually equations, differential equations in our case). This approach is appropriate if the conclusions that can be drawn have sufficient similarity to the observed phenomena. Its formulation corresponds to steps 1) and 2) mentioned above. It is virtually impossible for a model to represent all facets of the phenomenon. Therefore we insist on the need to take into account the most relevant aspects of the situation in question. Sometimes the same model can be reformulated facilitating its resolution. As well as the equations are also involved data models, inaccuracies in measuring these entail errors in the results. In most cases there is no analytical solution of the mathematical model by which we must pass numerical modeling. This is another source of inaccuracies and in the context of numerical analysis can establish error bounds between the solution of the numerical model and the exact solution of the mathematical model. The mathematical model is disturbed numeric character as mathematical operations as the derivation or integration are not accurate. The numerical model for its size or complexity may require computer processing involves the disturbance arithmetic, since the representation of real numbers and elementary arithmetic is about. In this book, we will try to figure out how the essential bookkeeping condition is utilized to keep all bookkeeping records in adjust. We broke down business exchanges to perceive how they influenced each piece of the bookkeeping condition. Money, credit, income and cost, withdrawals, and speculation exchanges were inspected for a specific business. It should be kept in mind that a solid comprehension of the fundamental bookkeeping condition is the way to understanding the impacts of any business exchange. In conclusion, the resolution of a problem for numerical computation, the result cascading different types of errors, rarely produces an exact solution.
About the Author: Ivan Stanimirovic gained his PhD from University of Nis, Serbia in 2013.His work spans from multi-objective optimization methods to applications of generalized matrix inverses in areas such as image processing and computer graphics and visualisations. He is currently working as an Assistantprofessor at Faculty of Sciences and Mathematics at University of Nis on computing generalized matrix inverses and its applications.