ABSTRACT
This chapter presents methods to solve problems with one independent variable involving first-order differential equation and first-kind boundary condition. Therefore, every mathematical model just approximately reproduces the relationships among the involved variables during real processes or phenomena. For instance, during the process of heat exchange between the body and environment, temperature will vary along positions inside the body. In addition, during the process of solution, one is involved with several equations to which various mathematical techniques may be applied. To show few details regarding the application of method of weighted residuals as well as comparisons between various solutions, consider the same problem of the heated batch reactor. Of course, such problems can only be solved by numerical methods, mainly by commercial computational fluid dynamics programs. Obviously, the solution of problems does not require the transformation of variables into dimensionless variables. Laplace transform is a powerful tool for solving ordinary as well as partial differential equations.
