General Remarks. Governing Equations. Classification of Differential Equations. Well-Posed Problems. Numerical Methods. The Finite DIfference Method. Basic Principles. The One-Dimensional Case. The Two-Dimensional Case. The Three-Dimensional Case. Stability and Convergence. Hyperbolic PDEs. Explicit Finite Analytic Method. Introduction to Grid Generation. Elliptic Grid Generation. Equations in E and n Coordinates. Diagonal Cartesian Method. FA Method on Diagonal Cartesian Coordinates. Solving Momentum and Continuity. Non-Staggered Grid Methods. Boundary Conditions. Laminar Flows. Laminar Convective Heat Transfer. Turbulent Flows. Turbulent Convective Heat Transfer. Complex Flows. Conjugate Heat Transfer. Appendix A: The One-Dimensional Case. Appendix B: The Two-Dimensional Case. Appendix C: FA 2-D Laminar Code.;This book contains the fundamental development of the finite analytic method and gives a systematic coverage of knowledge needed for numerical computation of fluid flows and heat transfer. It will be helpful to many including graduate students studying computational fluid dynamics and heat transfer.