eng Science and Education Publishing Applied Mathematics and Physics 2013-11-07 1 4 120 125 10.12691/amp-1-4-4 AMP2013144 article Pushpa N. Rathie pushpanrathie@yahoo.com 1 Prabhata K. Swamee 2 Luan Carlos de S. M. Ozelim 3 Department of Statistics, University of Brasilia, Brasilia, Brazil Department of Civil Engineering, ITM University, Gurgaon, India Department of Civil and Environmental Engineering, University of Brasilia, Brasilia, Brazil Nonlinear problems arise in most of the scientific fields. In general, such behavior is represented by a nonlinear equation, whose solution is sought. Analytical and numerical methods have been applied to the solution of this class of equations, notwithstanding, in cases where highly nonlinear phenomena are analyzed, the number of iterations and computational effort necessary to achieve the minimum required accuracy is very high. Lagrange´s Inversion Theorem (LIT) has been applied to solve this kind of problems analytically, giving the solution as an infinite power series. This way, the accuracy can be as high as necessary by taking more terms from the series solution, which is easily computationally implemented. Also, in some cases it is possible to relate the series obtained to the expansion of special and elementary functions, which enables one to exactly solve the desired equation. In the present review paper, a total of eleven applications have been discussed in order to show the role of LIT in various areas of nonlinear sciences. http://pubs.sciepub.com/amp/1/4/4/amp-1-4-4.pdf Lagrange´s Inversion TheoremCivil engineeringstatisticsGraph theoryalgebraic equationschemical engineering