Several Real Variables / by Shmuel Kantorovitz.

Format:

Book

Author/Creator:

Kantorovitz, Shmuel., Author.

Series:

Springer Undergraduate Mathematics Series, 1615-2085

Language:

English

Subjects (All):

Functions of real variables.

Real Functions.

Local Subjects:

Real Functions.

Physical Description:

1 online resource (XII, 307 p. 16 illus.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Language Note:

English

Summary:

This undergraduate textbook is based on lectures given by the author on the differential and integral calculus of functions of several real variables. The book has a modern approach and includes topics such as: •The p-norms on vector space and their equivalence •The Weierstrass and Stone-Weierstrass approximation theorems •The differential as a linear functional; Jacobians, Hessians, and Taylor's theorem in several variables •The Implicit Function Theorem for a system of equations, proved via Banach’s Fixed Point Theorem •Applications to Ordinary Differential Equations •Line integrals and an introduction to surface integrals This book features numerous examples, detailed proofs, as well as exercises at the end of sections. Many of the exercises have detailed solutions, making the book suitable for self-study. Several Real Variables will be useful for undergraduate students in mathematics who have completed first courses in line ar algebra and analysis of one real variable.

Contents:

Continuity

Derivation

Implicit Functions

Integration

Solutions. .

Notes:

Bibliographic Level Mode of Issuance: Monograph

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-27956-4

OCLC:

939598667