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Theory And Problems Of Differential Calculus In Rn: With Solutions

Jose Manuel Mazon Ruiz (Autor)

Buch | Softcover

250 Seiten

2026
World Scientific Europe Ltd (Verlag)
978-1-80061-855-8 (ISBN)

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This book offers both a theoretical and practical introduction to Differential Calculus of several real variables, tailored for students embarking on their first semester of study in the subject. Designed especially for those in Mathematical and Physical Sciences, as well as Engineering disciplines, it assumes only a foundational understanding of single-variable calculus and basic linear algebra.The book begins with a study of finite-dimensional Euclidean spaces, including geometry, metrics, convergence, compactness, and convexity. It then progresses to continuous and differentiable functions, exploring directional derivatives, the chain rule, vector fields, and Fréchet and Gâteaux differentials. Further chapters address higher-order derivatives, Taylor's formula, and the conditions for local extrema, before delving into essential theorems such as the Inverse and Implicit Function Theorems. The final chapter introduces differentiable manifolds and constrained optimization using Lagrange multipliers.Each topic is supported by a selection of thoughtfully designed problems that reinforce both conceptual understanding and practical skills. Complete solutions are provided at the end of the book, making it a valuable resource for classroom use and self-study alike. This is a clear and rigorous foundation for anyone beginning their journey into multivariable calculus.

Erscheint lt. Verlag	14.2.2026
Reihe/Serie	Essential Textbooks in Mathematics
Verlagsort	London
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
ISBN-10	1-80061-855-7 / 1800618557
ISBN-13	978-1-80061-855-8 / 9781800618558
Zustand	Neuware