The meaning of key mathematical concepts used for the analysis of fluid dynamics and heat/mass transfer processes by Computational Fluid Dynamics (CFD) codes, are described without assuming prior knowledge of calculus by the readers. These include the concepts of derivativesDerivative, integralsIntegral, gradientGradient, divergenceDivergence, and Taylor seriesTaylor series. The divergence theoremDivergence theorem is formulated for both three-, two-, and one-dimensional cases. In the latter case, this theorem reduces to theLeibniz-Newton theorem Leibniz-Newton theorem. The mathematical concepts described in the chapter are used for the formulation of the equations solved by CFD codes, including those of conservation of mass, momentumNavier-Stokes equation (the Navier-Stokes equation), and energy. It is pointed out that these equations have a similar structure that appears to be helpful in the development of numerical methods for their solution. Various approaches to modelling turbulent flowsTurbulent flows are discussed, including the Direct Numerical Simulation (DNS)Direct Numerical Simulation (DNS), Large Eddy Simulation (LES)Large Eddy Simulation (LES), and the approaches based on the Reynolds AveragedNavier-Stokes equation Navier-Stokes (RANS)Reynolds Averaged Navier-Stokes (RANS) equations equations. The latter include the Reynolds stress and k- \(\epsilon \) models- model. The ranges of applicability of equations of stateEquations of state for ideal and real gasesReal gases are described. CFD approaches to modelling chemical and electromagneticElectromagnetic processes are briefly summarised.