Continuous Functions of Vector Variables

Alberto Guzman

ISBN 10: 0415139937 / ISBN 13: 9780415139939

Published by Birkhäuser, 68, 2002

About this Item

Text in English. 207 pp. This text is an axiomatic treatment of the properties of continuous multivariable functions and related results from topology. In the context of normed vector spaces, the author covers boundedness, extreme values, and uniform continuity of functions, along with the connections between continuity and topological concepts such as connectedness and compactness. The order of topics deliberately mimics the order of development in elementary calculus. This sequencing allows for an elementary approach, with analogies to and generalizations from such familiar ideas as the Pythagorean theorem. The reader is frequently reminded that the pictures suggested by geometry are powerful guides and tools. The definition-theorem-proof format resides within an informal exposition, containing numerous historical comments and questions within and between the proofs. The objective is is to present precise proofs, but in a structure and tone that teach the student to plan and write proofs, both general and specifically for the real analysis course that will follow this one. Applications are included where they provide interesting illustrations of the principles and theorems presented. Problems, solutions, bibliography and index complete this book. Continuous Functions of Vector Variables is suitable for a course in multivariable calculus aimed at advanced undergraduates preparing for graduate programs in pure mathematics. Required background includes a course in the theory of single variable calculus and the elements of linear algebra.

Seller Inventory # 3331

Bibliographic Details

• Title: Continuous Functions of Vector Variables
• Publisher: Birkhäuser, 68
• Publication Date: 2002
• ISBN 10: 0415139937
• ISBN 13: 9780415139939
• Binding: Soft Cover
• Edition: 1st Edition.
• Condition: Near Fine
• Seller catalogs:
  • Mathematics

About this title

Synopsis

Four Approaches to Counselling and Psychotherapy provides an essential introduction to and overview of the main therapeutic approaches used in psychotherapy and counselling today. Written clearly and concisely, it will have international appeal as an ideal introductory text for all those embarking on psychotherapy and counselling courses. The authors trace the development of counselling and psychotherapy, and examine the relationship between the two. They then consider the four main models of psychotherapy - psychodynamic, humanistic, integrative and cognitive-behavioural - before focusing on the most popular approach from each, including: person-centred, rational emotive behavioural, and multimodal. Each approach is clearly examined in terms of its historical context and development, its main theoretical concepts, and its aims. In the final chapter these approaches are compared, with the examination of a case vignette from the point of view of each approach by four well-known therapists.

About the Author

Windy Dryden is Professor of Counselling at Goldsmiths College. Jill Mytton is Senior Lecturer at the University of East London.