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What sets Numerical Methods and Analysis with Mathematical Modelling apart are the modelling aspects utilizing numerical analysis (methods) to obtain solutions. The authors cover first the basic numerical analysis methods with simple examples to illustrate the techniques and discuss possible errors. The modelling 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 modelling projects. Chapters are introduced and techniques are discussed with common examples. A modelling scenario is introduced that will be solved with these techniques later in the chapter. Often, the modelling problems require more than one previously covered technique presented in the book. Fundamental exercises to practice the techniques are included. Multiple modelling scenarios per numerical methods illustrate the applications of the techniques introduced. Each chapter has several modelling examples that are solved by the methods described within the chapter. The use of technology is instrumental in numerical analysis and numerical methods. In this text, Maple, Excel, R, and Python are illustrated. The goal is not to teach technology but to 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.
About the Authors.
Preface.
Acknowledgements.
Review of Differential Calculus.
Mathematical Modelling and Introduction to Technology: Perfect Partners.
Modelling with Discrete Dynamical Systems and Modelling Systems of Discrete Dynamical Systems.
Numerical Solutions to Equations in One Variable.
Interpolation and Polynomial Approximation.
Numerical Differentiation and Integration.
Modelling with Numerical Solutions to Differential Equations—Initial Value Problems for Ordinary
Differential Equations.
Iterative Techniques in Matrix Algebra.
Modelling with Single-Variable Unconstrained Optimization and Numerical Methods.
Multivariable Numerical Search Methods.
Boundary Value Problems in Ordinary Differential Equations.
Approximation Theory and Curve Fitting.
Numerical Solutions to Partial Differential Equations.
Answers to Selected Exercises.
Index