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Applied Mathematics: A Computational Approach aims to provide a basic and self-contained introduction to Applied Mathematics within a computational environment. The book is aimed at practitioners and researchers interested in modeling real-world applications and verifying the results — guiding readers from the mathematical principles involved through to the completion of the practical, computational task.
Important skills for the digital era and the effective utilization of digital systems would include high-level cognitive skills for whom automated operations and routine-basis procedures are neither being expected, nor openly proposed for deployment in the most recent years. Beyond the average years of schooling, skills complexity, and geographical factors, the prospects for education and training would include appropriate cognitive skills, e.g., active learning, complex problem solving, creativity, critical thinking, strategic thinking, along with the selection and utilization of adequate learning methods.
In that manner, a book on Applied Mathematics should overview a number of contents, covering basic notions while providing an enhanced approach to important Calculus subjects. This text is directed to post-secondary readers, or university students in the initial years, being the required concepts and tools introduced as needed. With a computational approach aiming at the understanding of new situations, creative problem-solving, and decision-making, the experimental focus is supported either in the analytical confirmation of necessary conditions or in the visual verification of sufficient conditions. It is thus envisaged the book can be effective for students of STEM fields, Economics and Management Science, Social Sciences and Humanities, and for readers interested in a computational point of view.
The text contents include Applied Mathematical tools that support judgment and decision-making, with the readers being initiated into a simple case, and facing simple issues. Then they have the opportunity to focus on more challenging situations, to select and use the appropriate procedures, and creatively solve them with the proper mathematical manipulations and computational reasoning. The importance of observation and verification, and experimental focus is illustrated through the application of diverse mathematical tools, within a typical differential calculus path that aims at integral calculus. Namely, such path includes real numbers sequences, function limits, continuity, derivation, and the main results of differential calculus then integral calculus is introduced, by including integral sums, indefinite integrals, and definite integrals finally, important concepts on sum series are addressed too.
Preface
First Notes on Real Functions
Sequences of Real Numbers
Limit of a Function
Continuity
Derivative of a Function
Sketching Functions and Important Theorems
First Steps on Integral Sums
Indefinite Integral
Definite Integral
Series