
Theory And Problems Of Differential Calculus In Rn: With Solutions
Jose Manuel Mazon Ruiz(Author)
World Scientific Europe Ltd (Publisher)
Will be published approx. on 14. February 2026
Book
Hardback
250 pages
978-1-80061-838-1 (ISBN)
Description
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 Frechet and Gateaux 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.
More details
Series
Language
English
Place of publication
London
United Kingdom
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 19 mm
Weight
546 gr
ISBN-13
978-1-80061-838-1 (9781800618381)
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Schweitzer Classification