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Catalogue Information
Field name	Details
Dewey Class	515.8
Title	Calculus III ([EBook]) / by Jerrold Marsden, Alan Weinstein.
Author	Marsden, Jerrold E.
Added Personal Name	Weinstein, Alan
Other name(s)	SpringerLink (Online service)
Edition statement	Second Edition.
Publication	New York, NY : Springer , 1985.
Physical Details	XV, 372 p. 75 illus. : online resource.
Series	Undergraduate texts in mathematics 0172-6056
ISBN	9781461250289
Summary Note	The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition. We list below some of the key features of the book. Examples and Exercises The exercise sets have been carefully constructed to be of maximum use to the students. With few exceptions we adhere to the following policies . • The section exercises are graded into three consecutive groups: (a) The first exercises are routine, modelled almost exactly on the exam ples; these are intended to give students confidence. (b) Next come exercises that are still based directly on the examples and text but which may have variations of wording or which combine different ideas; these are intended to train students to think for themselves. (c) The last exercises in each set are difficult. These are marked with a star (*) and some will challenge even the best studep,ts. Difficult does not necessarily mean theoretical; often a starred problem is an interesting application that requires insight into what calculus is really about. • The exercises come in groups of two and often four similar ones.:
Contents note	13 Vectors -- 13.1 Vectors in the Plane -- 13.2 Vectors in Space -- 13.3 Lines and Distance -- 13.4 The Dot Product -- 13.5 The Cross Product -- 13.6 Matrices and Determinants -- 14 Curves and Surfaces -- 14.1 The Conic Sections -- 14.2 Translation and Rotation of Axes -- 14.3 Functions, Graphs, and Level Surfaces -- 14.4 Quadric Surfaces -- 14.5 Cylindrical and Spherical Coordinates -- 14.6 Curves in Space -- 14.7 The Geometry and Physics of Space Curves -- 15 Partial Differentiation -- 15.1 Introduction to Partial Derivatives -- 15.2 Linear Approximations and Tangent Planes -- 15.3 The Chain Rule -- 15.4 Matrix Multiplication and the Chain Rule -- 16 Gradients, Maxima, and Minima -- 16.1 Gradients and Directional Derivatives -- 16.2 Gradients, Level Surfaces, and Implicit Differentiation -- 16.3 Maxima and Minima -- 16.4 Constrained Extrema and Lagrange Multipliers -- 17 Multiple Integration -- 17.1 The Double Integral and Iterated Integral -- 17.2 The Double Integral Over General Regions -- 17.3 Applications of the Double Integral -- 17.4 Triple Integrals -- 17.5 Integrals in Polar, Cylindrical, and Spherical Coordinates -- 17.6 Applications of Triple Integrals -- 18 Vector Analysis -- 18.1 Line Integrals -- 18.2 Path Independence -- 18.3 Exact Differentials -- 18.4 Green’s Theorem -- 18.5 Circulation and Stokes’ Theorem -- 18.6 Flux and the Divergence Theorem -- Answers.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4612-5028-9
Links to Related Works	Subject References: Functions of real variables . Mathematics . Real Functions . Authors: author . Marsden, Jerrold E. . Marsden, Jerrold E. . Weinstein, Alan . Corporate Authors: SpringerLink (Online service) . Series: Undergraduate texts in mathematics . Classification: 515.8 .

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Calculus III

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