Calculus I

• Jerrold Marsden
• Alan Weinstein
Book

Part of the Undergraduate Texts in Mathematics book series (UTM)

1. Front Matter
Pages i-xv
2. Jerrold Marsden, Alan Weinstein
Pages 1-11
3. Jerrold Marsden, Alan Weinstein
Pages 13-14
4. Jerrold Marsden, Alan Weinstein
Pages 15-48
5. Jerrold Marsden, Alan Weinstein
Pages 49-97
6. Jerrold Marsden, Alan Weinstein
Pages 99-137
7. Jerrold Marsden, Alan Weinstein
Pages 139-199
8. Jerrold Marsden, Alan Weinstein
Pages 201-249
9. Jerrold Marsden, Alan Weinstein
Pages 251-306
10. Jerrold Marsden, Alan Weinstein
Pages 307-335
11. Back Matter
Pages 337-388

Introduction

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 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.

Keywords

Fundamental theorem of calculus calculus derivative differential equation intermediate value theorem logarithm maximum mean value theorem minimum

Authors and affiliations

• Jerrold Marsden
• 1
• Alan Weinstein
• 2
1. 1.California Institute of TechnologyControl and Dynamical Systems 107-81PasadenaUSA
2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-5024-1
• Copyright Information Springer-Verlag New York 1985
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-90974-5
• Online ISBN 978-1-4612-5024-1
• Series Print ISSN 0172-6056