Integrals of rational functions
Nika Hren · PeFprints (University of Ljubljana) · 2013
The intention of this diploma thesis is to present the procedure of partial fractions decomposition of rational functions and its use for integration of real and complex rational functions. Laplace theorem, quoted at the beginning, leads us to use complex numbers in the decomposition of rational functions. We use the theorem to show the reason for the partial fraction decomposition, and to emphasize the difference between the decomposition using either real or complex numbers. This difference is later also seen in the procedure of integration. The first two chapters are devoted to finding partial fraction decompositions and their uniqueness. In the next chapter, we present the integration procedures using either real or complex decomposition, and show that they both give the same result.