In what is a rigorous treatment of multivariable differential and integral calculus, this book explains key theorems including Stokes's as well as covering extrema such as Lagrange multipliers. It explores Riemann integration in n dimensions in detail.

Contains a number of examples as well as section-by section problems, ranging from simple to complex Problems illustrate the application of concepts introduced as well as further developments Extensive hints and solutions are provided Full chapter on extrema, including examples when the Lagrange method appears to "fail"

Klappentext

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.

Inhalt

Preliminaries.- Functions between Euclidean Spaces.- Differentiation.- Inverse and Implicit Function Theorems.- Extrema.- Riemann Integration in Euclidean Space.- The General Stokes Theorem.- Solutions.