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Multivariable Analysis [electronic resource] / by Satish Shirali, Harkrishan Lal Vasudeva.

By: Shirali, Satish [author.].
Contributor(s): Vasudeva, Harkrishan Lal [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: London : Springer London, 2011Description: V, 393p. 18 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780857291929.Subject(s): Mathematics | Mathematics | Real FunctionsDDC classification: 515.8 Online resources: Click here to access online
Contents:
Preliminaries -- Functions between Euclidean Spaces -- Differentiation -- Inverse and Implicit Function Theorems -- Extrema -- Riemann Integration in Euclidean Space -- The General Stokes Theorem -- Solutions.
In: Springer eBooksSummary: This book provides a rigorous treatment of multivariable differential and integral calculus. Inverse and implicit function theorems based on total derivatives are given and the connection with solving systems of equations is included. There is an extensive treatment of extrema, including constrained extrema and Lagrange multipliers, covering both first order necessary conditions and second order sufficient conditions. The material on Riemann integration in n dimensions, being delicate by its very nature, is discussed in detail. Differential forms and the general Stokes' Theorem are explained in the last chapter. With a focus on clarity rather than brevity, this text gives clear motivation, definitions and examples with transparent proofs. Some of the material included is difficult to find in most texts, for example, double sequences in Chapter 2, Schwarz’ Theorem in Chapter 3 and sufficient conditions for constrained extrema in Chapter 5. A wide selection of problems, ranging from simple to challenging, is included with carefully written solutions. Ideal as a classroom text or a self study resource for students, this book will appeal to higher level undergraduates in Mathematics.
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Preliminaries -- Functions between Euclidean Spaces -- Differentiation -- Inverse and Implicit Function Theorems -- Extrema -- Riemann Integration in Euclidean Space -- The General Stokes Theorem -- Solutions.

This book provides a rigorous treatment of multivariable differential and integral calculus. Inverse and implicit function theorems based on total derivatives are given and the connection with solving systems of equations is included. There is an extensive treatment of extrema, including constrained extrema and Lagrange multipliers, covering both first order necessary conditions and second order sufficient conditions. The material on Riemann integration in n dimensions, being delicate by its very nature, is discussed in detail. Differential forms and the general Stokes' Theorem are explained in the last chapter. With a focus on clarity rather than brevity, this text gives clear motivation, definitions and examples with transparent proofs. Some of the material included is difficult to find in most texts, for example, double sequences in Chapter 2, Schwarz’ Theorem in Chapter 3 and sufficient conditions for constrained extrema in Chapter 5. A wide selection of problems, ranging from simple to challenging, is included with carefully written solutions. Ideal as a classroom text or a self study resource for students, this book will appeal to higher level undergraduates in Mathematics.

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