# Multivariate Calculus and Geometry

• Seán Dineen
Textbook

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

1. Front Matter
Pages i-xiv
2. Seán Dineen
Pages 1-12
3. Seán Dineen
Pages 13-23
4. Seán Dineen
Pages 25-34
5. Seán Dineen
Pages 35-45
6. Seán Dineen
Pages 47-53
7. Seán Dineen
Pages 55-67
8. Seán Dineen
Pages 69-81
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Pages 83-92
10. Seán Dineen
Pages 93-102
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Pages 103-120
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Pages 121-134
13. Seán Dineen
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15. Seán Dineen
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17. Seán Dineen
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18. Seán Dineen
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19. Seán Dineen
Pages 217-227
20. Back Matter
Pages 229-257

### Introduction

Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations.

In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions.

Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.

### Keywords

Curvature and Torsion of Curves Double and Triple Integrals Frenet-Serret Equations Gaussian Curvature Geodesic Curvature Lagrange Multipliers Line Integrals Stokes Theorem Surface Integrals The Hessian The Weingarten Mapping

#### Authors and affiliations

• Seán Dineen
• 1
1. 1.School of Mathematical SciencesUniversity College DublinDublinIreland

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4471-6419-7
• Copyright Information Springer-Verlag London 2014
• Publisher Name Springer, London
• eBook Packages Mathematics and Statistics
• Print ISBN 978-1-4471-6418-0
• Online ISBN 978-1-4471-6419-7
• Series Print ISSN 1615-2085
• Series Online ISSN 2197-4144
• Buy this book on publisher's site
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