Numerical Methods and Analysis with Mathematical Modelling (Textbooks in Mathematics)

Description

What sets this book apart is the modeling aspects utilizing numerical analysis (methods) to obtain solutions. The authors cover the basic numerical analysis methods first with simple examples to illustrate the techniques and discuss possible errors. The modeling prospective reveals the practical relevance of the numerical methods in context to real world problems.

At the core of this text are the real-world modeling projects. Chapters are introduced and techniques are discussed with common examples. A modeling scenario is introduced that will be solved with these techniques later in the chapter. Often the modeling problems require more than one previously covered technique presented in the book.

Fundamental exercises to practice the techniques are included. Multiple modeling scenarios per numerical methods illustrate the applications of the techniques introduced. Each chapter has several modeling examples that are solved by the methods described within the chapter.

The use of technology is instrumental in numerical analysis and numerical methods. In our text, we illustrate MAPLE, EXCEL, R, and Python. Our goal is not to teach technology but illustrate its power and limitations to perform algorithms and reach conclusions.

This book fulfills a need in the education of all students who plan to use technology to solve problems whether using physical models or true creative mathematical modeling, like discrete dynamical systems.