Advanced Calculus of Several Variables

USD 40.00

Description

In this high-level treatment, the author provides a modern conceptual approach to multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, the book gives equal attention to the classical applications and computational methods responsible for much of the interest and importance of this subject. Beginning with a discussion of Euclidean space and linear mappings, Professor Edwards (University of Georgia) follows with a thorough and detailed exposition of multivariable differential and integral calculus. Among the topics covered are the basics of single-variable differential calculus generalized to higher dimensions, the use of approximation methods to treat the fundamental existence theorems of multivariable calculus, iterated integrals and change of variable, improper multiple integrals and a comprehensive discussion, from the viewpoint of differential forms, of the classical material associated with line and surface integrals, Stokes' theorem, and vector analysis. The author closes with a modern treatment of some venerable problems of the calculus of variations. Intended for students who have completed a standard introductory calculus sequence, the book includes many hundreds of carefully chosen examples, problems, and figures. Indeed, the author has devoted a great deal of attention to the 430 problems, mainly concrete computational ones, that will reward students who solve them with a rich intuitive and conceptual grasp of the material. Reprint of the Academic Press, New York, 1973 edition. differential forms;math textbooks;functional analysis;hilbert space;pure mathematics;differential equations;math students;ordinary differential;applied math;theory background;mathematics students;vector spaces;differential geometry;abstract mathematics;linear equations;numerical methods;modern texts;fourier transform;abstract algebra;self study;partial differential;classical mechanics;assigned textbook;math text;geometric proofs;linear algebra;mathematical background;exactly 200;graduate level;introductory text;integrals;matrices;deeper understanding;firm grasp;precalculus;farlow;coddington;pinsky;dieudonne;pugh;chapra;haberman;hamming;bostock;springer;tiles;krantz;strang;differentiable;yeh;tenenbaum;bartle;banach;mappings;bessel;boyce;coefficients;calc;normed;manifolds;laplace;spivak;axler;topological;lagrange;trig;euclidean;handbook;mendelson;diff;determinants;buck;compactness;self-study;cambridge;theoretical;discrete;stewart;topology;morse;manual;computational;theorems;pollard;odes;manga;solutions;taylor;physics;metric;applications;rigorous;exercises;books on differential equations;books on self studies;books on differential forms;books on numerical methods;books on applied maths;books on linear equations;books on mathematics students;books on pure mathematics;books on theory backgrounds;books on modern texts;books on math textbooks;books on math students;books on hilbert spaces;books on functional analysis;books on differential geometries;books on abstract mathematics