Calculus II / 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 leam 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, modelIed almost exactly on the exam- pIes; 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 students. 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:

7 Basic Methods of Integration

7.1 Calculating Integrals

7.2 Integration by Substitution

7.3 Changing Variables in the Definite Integral

7.4 Integration by Parts

8 Differential Equations

8.1 Oscillations

8.2 Growth and Decay

8.3 The Hyperbolic Functions

8.4 The Inverse Hyperbolic Functions

8.5 Separable Differential Equations

8.6 Linear First-Order Equations

9 Applications of Integration

9.1 Volumes by the Slice Method

9.2 Volumes by the Shell Method

9.3 Average Values and the Mean Value Theorem for Integrals

9.4 Center of Mass

9.5 Energy, Power, and Work

10 Further Techniques and Applications of Integration

10.1 Trigonometric Integrals

10.2 Partial Fractions

10.3 Arc Length and Surface Area

10.4 Parametric Curves

10.5 Length and Area in Polar Coordinates

11 Limits, L'Hôpital's Rule, and Numerical Methods

11.1 Limits of Functions

11.2 L'Hôpital's Rule

11.3 Improper Integrals

11.4 Limits of Sequences and Newton's Method

11.5 Numerical Integration

12 Infinite Series

12.1 The Sum of an Infinite Series

12.2 The Comparison Test and Alternating Series

12.3 The Integral and Ratio Tests

12.4 Power Series

12.5 Taylor's Formula

12.6 Complex Numbers

12.7 Second-Order Linear Differential Equations

12.8 Series Solutions of Differential Equations

Answers.

Other Format:

Printed edition:

ISBN:

9781461250265

Access Restriction:

Restricted for use by site license.