Calculus III / by Jerrold Marsden, Alan Weinstein.

Format:

Book

Author/Creator:

Marsden, Jerrold, author.

Weinstein, Alan, author.

Contributor:

SpringerLink (Online service)

Series:

Undergraduate texts in mathematics 0172-6056

Undergraduate Texts in Mathematics, 0172-6056

Language:

English

Subjects (All):

Functions of real variables.

Real Functions.

Local Subjects:

Real Functions.

Physical Description:

1 online resource.

Edition:

Second edition 1985.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1985.

System Details:

text file PDF

Summary:

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:

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.

Other Format:

Printed edition:

ISBN:

9781461250289

Access Restriction:

Restricted for use by site license.