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Multivariable Analysis (Paperback, 2011 ed.)
Loot Price: R2,362
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Multivariable Analysis (Paperback, 2011 ed.)
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This book provides a rigorous treatment of multivariable
differential and integral calculus. Implicit function theorem and
the inverse function theorem based on total derivatives is
explained along with the results and the connection to solving
systems of equations. 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 expounded in
the last chapter. With a focus on clarity rather than brevity, this
text gives clear motivation, definitions and examples with
transparent proofs. Much of the material included is published for
the first time in textbook form, for example Schwarz' Theorem in
Chapter 2 and double sequences and sufficient conditions for
constrained extrema in Chapter 4. A wide selection of problems,
ranging from simple to more challenging, are included with
carefully formed 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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