Mathematical approaches are increasingly used in the field of computational biology to describe, analyze, and predict complex biological phenomena at molecular, cellular and population scales. This study discusses the applications of mathematical tools in computational biology such as differential equations, integral equations, linear algebra, matrix computation, and numerical solution techniques. Mathematical representations are created to describe interactions in biological systems, changes over time, regulation and quantitative relationships in biological systems. The use of differential equations represents the temporal behavior, and integral formulations represent cumulative biological effects. Linear algebra enables high dimensional processing of biological data, representation of networks and estimation of parameters. Numerical methods allow to solve models that do not have an analytical solution. The integrated framework exemplifies the enhancement of biological insights, biological simulations and predictive analysis through the use of mathematical computation. The results highlight the need for mathematical methods to further the development of computational modelling, biological data analysis and interdisciplinary science research in contemporary computational biology studies.