The third of a three-volume work, this book is the outgrowth of the authors' experience teaching calculus at Berkeley. It covers multivariable calculus and begins with the necessary material from analytical geometry. It goes on to cover partial differention, the gradient and its applications, multiple integration, and the theorems of Green, Gauss and Stokes. The authors motivate the study of calculus using its applications. Features many solved problems and extensive exercises.

Calculus III (Undergraduate Texts in Mathematics)

Science & Math

Weinstein, Alan

Marsden, Jerrold

Mathematics

Springer

Basic Multivariable Calculus fills the need for a student-oriented text devoted exclusively to the third-semester course in multivariable calculus. In this text, the basic algebraic, analytic, and geometric concepts of multivariable and vector calculus are carefully explained, with an emphasis on developing the student's intuitive understanding and computational technique. A wealth of figures supports geometrical interpretation, while exercise sets, review sections, practice exams, and historical notes keep the students active in, and involved with, the mathematical ideas. All necessary linear algebra is developed within the text, and the material can be readily coordinated with computer laboratories. Basic Multivariable Calculus is the product of an extensive writing, revising, and class-testing collaboration by the authors of Calculus III (Springer-Verlag) and Vector Calculus (W.H. Freeman &amp; Co.). Incorporating many features from these highly respected texts, it is both a synthesis of the authors' previous work and a new and original textbook.

Basic Multivariable Calculus

MARSDEN, Jerrold E.

Tromba, Anthony

W.H.Freeman

Basic Multivariable Calculus & Study Guide

These notes are based on a course entitled ``Symplectic Geometry and Geometric Quantization'' taught by Alan Weinstein at the University of California, Berkeley (fall 1992) and at the Centre Emile Borel (spring 1994). The only prerequisite for the course needed is a knowledge of the basic notions from the theory of differentiable manifolds (differential forms, vector fields, transversality, etc.). The aim is to give students an introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role these ideas play in formalizing the transition between the mathematics of classical dynamics (hamiltonian flows on symplectic manifolds) and quantum mechanics (unitary flows on Hilbert spaces). These notes are meant to function as a guide to the literature. The authors refer to other sources for many details that are omitted and can be bypassed on a first reading.

Lectures on the Geometry of Quantization (Berkeley Mathematical Lecture Notes ; Vol 8) BMLN/8

Bates, Sean

Amer Mathematical Society

Geometry of the Laplace Operator (Proceedings of Symposia in Pure Mathematics, V. 36)

Osserman, Robert

American Mathematical Society

Ams Symposium on the Geometry of the Laplace Operator

Symposium in Pure Mathematics University of Hawaii 1979

Hamiltonian Lie Algebroids

Blohmann, Christian

Providence, RI : American Mathematical Society

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