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The aim of this book is to lead the reader out from the ordinary routine of computing and calculating by engaging in a more dynamic process of learning. This Learning-by-Doing Approach can be traced back to Aristotle, who wrote in his Nicomachean Ethics that "For the things we have to learn before we can do them, we learn by doing them".
The theory is illustrated through many relevant examples, followed by a large number of exercises whose requirements are rendered by action verbs: find, show, verify, check and construct. Readers are compelled to analyze and organize analytical skills.
Rather than placing the exercises in bulk at the end of each chapter, sets of practice questions after each theoretical concept are included. The reader has the possibility to check their understanding, work on the new topics and gain confidence during the learning activity. As the theory unfolds, the exercises become more complex - sometimes they span over several topics. Hints have been added in order to guide the reader in the process.
This book stems from the Differential Calculus course which the author taught for many years. The goal of this book is to immerse the reader in the subtleties of Differential Calculus through an active perspective. Particular attention was paid to continuity and differentiability topics, presented in a new course of action.
List of contents
Ch 1. Vectors and Sets Ch 2. Functions of several variables Ch 3. Limits and continuity Ch 4. Differentiable functions Ch 5. Chain rule and the Mean Value Theorem Ch 6. Directional derivative Ch 7. Higher order derivatives Ch 8. Taylor's theorem and approximations Ch 9. Inverse and Implicit Function Theorem Ch 10. Maxima and Minima Ch 11. Constrained optimisation and applications Ch 12. Solutions
About the author
Marius Ghergu is an Associate Professor at University College Dublin. He holds a Ph.D. from Universite de Savoie, France. His interests lie at the interface of Calculus and Partial Differential Equations. He is the author and co-author of four research monographs. He has published over 60 research articles in major journals in the field and has been invited to give talks at various international meetings such as conferences and summer schools for graduate students.
Summary
The aim of this book is to lead the reader out from the ordinary routine of computing and calculating by engaging in a more dynamic process of learning. This Learning-by-Doing Approach can be traced back to Aristotle who wrote “For the things we have to learn before we can do them, we learn by doing them”
