Satish Shirali – författare

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.

This book treats material concerning Metric Spaces, which is crucial for any advanced level course in analysis. Usually this is taught in the latter years of an undergraduate course. Often books on functional analysis have to be used, because there are so few books specifically on metric spaces - a gap that needs to be filled in the literature. It is a comprehensive introduction, with applications, containing a large number of worked examples and exercises for real and complex analysis, sequence spaces and the space of continuous functions. Each concept is followed by a large number of examples, some satisfying the requirements and others not, so that the concept is well understood.

This undergraduate textbook offers a self-contained and concise introduction to measure theory and integration.The author takes an approach to integration based on the notion of distribution. This approach relies on deeper properties of the Riemann integral which may not be covered in standard undergraduate courses. It has certain advantages, notably simplifying the extension to "fuzzy" measures, which is one of the many topics covered in the book.This book will be accessible to undergraduate students who have completed a first course in the foundations of analysis. Containing numerous examples as well as fully solved exercises, it is exceptionally well suited for self-study or as a supplement to lecture courses.