tailieunhanh - Modeling Tools for Environmental Engineers and Scientists Episode 4

Tham khảo tài liệu 'modeling tools for environmental engineers and scientists episode 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | CHAPTER 3 Primer on Mathematics CHAPTER PREVIEW This chapter contains a review of mathematical methods and tools as they apply to environmental modeling. It is assumed that the readers have taken a formal sequence of college-level course work in mathematics leading up to partial differential equations. In the first part of this chapter reviews of different types of mathematical formulations are summarized. Analytical and numerical procedures for solving them are outlined. Then ways to implement some of the more common procedures in the computer environment are demonstrated. MATHEMATICAL FORMULATIONS IN the previous chapter several steps and tasks involved in the model development process were identified. It goes without saying that a clear understanding of mathematical formulations and analyses is a necessary prerequisite in this process. A strong mathematical foundation is required to transmute subject matter knowledge into mathematical forms such as functions expressions and equations. Knowledge of analytical procedures in mathematical calculi such as simplifying transforming and solving is essential to select and develop the appropriate computational procedures for computer implementation. The selection of an appropriate computer software package to complete the model also requires a good understanding of the mathematics underlying the model. As pointed out in Chapter 1 different formulations can be developed to describe the same system hence the ability to choose the optimal one that can meet the goals requires a strong mathematical foundation. The advantage of reducing the formulations to standard mathematical forms has been pointed out before. For modeling purposes a wide variety of environmental systems can be categorized as deterministic with continuous 2002 by CRC Press LLC variables. Deterministic systems can be described either by static or dynamic formulations. This chapter will therefore focus on the mathematical calculi for continuous .