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Full Description
This widely used textbook demonstrates the power of numerical methods in the context of solving complex engineering and scientific problems. The book helps to prepare future engineers and assists practicing engineers in understanding the fundamentals of numerical methods, especially their applications, limitations, and potentials.
Each chapter contains many computational examples, as well as a section on applications that contain additional engineering examples. Each chapter also includes a set of exercise problems.
The problems are designed to meet the needs of instructors in assigning homework and to help students with practicing the fundamental concepts. Although the book was developed with emphasis on engineering and technological problems, the numerical methods can also be used to solve problems in other fields of science.
The text is most appropriate for a first course in numerical methods, so students would only need basiccalculus and matrix algebra.
The book offers three general parts: (1) introduction to numerical methods; (2) the process and application of numerical methods; (3) optimization of engineering data. In all chapters, a proper balance between theory and the application of the numerical methods is provided.
Outstanding Features:
· Presents a balanced mix of theory and engineering concepts
· Emphasizes theoretical background, and engineering applications
· Introduces fundamental concepts in a self-contained manner
· Provides numerous examples and applications to illustrate key computational algorithms
· Provides end-of-chapter exercise problems
A solutions manual is available for instructors.
Some textbooks focus on the theoretical aspects of numerical methods. Students of the 21st century prefer a more applied education. While the background theory will be provided, the emphasis of the textbook will be the application of the methods. Sufficient theory will be provided to enable the students to program the methods and to understand the limitations of the procedures. Since students have access to many different programming languages, programmed algorithms will not be included; instead the general solution procedure will be a focus of the theory.
In the past, function fitting has been limited in undergraduate curricula to analytical least squares. This limits examples to linear, polynomial, and log-linear (power) model forms. Many statistical software packages allow for the option of other forms, as problems in optimization go beyond the simple models. While the proposed text will discuss the analytical fitting of functions, the test will include basic material on the methods for numerical optimization, which will be a distinguishing feature from other books on numerical methods.
Rationale and Pedagogy
Engineering students are motivated to learn a concept when they see applications that they believe would be relevant to their career paths. While applications should not be the primary educational focal point, they are an important motivational factor and a necessary ingredient to the retention of the educational concepts. While one type of engineering student (e.g., mechanical) may prefer the applications to be solely from that discipline, the student still appreciates applications in other engineering disciplines (e.g., electrical), as the student then recognizes the breadth of the concepts. This focus on the broad application of numerical methods is a primary educational objective of our proposed textbook.
Students need different types of illustrating examples. First, they need computational examples that illuminate the nuances of the underlying theoretical concepts; these are simple calculations that focus on setting up solutions and number crunching. Second, students need engineering applications which show that learning the methods will be of value to them in applied engineering. The textbook will include both types of illustrating examples—the simple computation-oriented problem solving and the more retailed, engineering-oriented, real-world applications.
Contents
Preface Acknowledgements 1. Numerical Methods: The Past and Future 2. Matrices 3. Background for Numerical Methods 4. Roots of Equations 5. Simultaneous Linear Equations 6. Numerical Interpolation 7. Differentiation and Integration 8. Differential Equations: Fundamentals 9. Differential Equations of Higher-Order, Boundary Value and Integrals 10. Curve Fitting and Regression Analysis 11. Numerical Optimization Solutions to Selected Problems
