## Multivariate Calculus and Geometry (3rd Edition)

**Author(s):**

Seán Dineen

**Publisher:**

Springer

**Pages:**257

**Further Actions:**

**Categories:**

### AVAILABLE FORMATS

Paperback - 9781447164180

29 September 2014

* $44.99*

Free Shipping

**In stock**

Ebook - 9781447164197

18 September 2014

* $34.99*

**In stock**

Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook not only follows this programme, but additionally provides a...

Show More

Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook not only follows this programme, but 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.

Show Less

Places the differential and integral calculus of several variables in its natural geometric environment

Presents interesting non-trivial applications of the differential calculus

Shows how the differential calculus and classical geometry evolved into differential geometry

Introduction to Differentiable Functions

Level Sets and Tangent Spaces

Lagrange Multipliers

Maxima and Minima on Open Sets

Curves in Rn

Line Integrals

The Frenet–Serret Equations

Geometry of Curves in R3

Double Integration

Parametrized Surfaces in R3

Surface Area

Surface Integrals

Stokes’ Theorem

Triple Integrals

The Divergence Theorem

Geometry of Surfaces in R3

Gaussian Curvature

Geodesic Curvature.

“The book is very useful for those who wish to learn the theory properly. … the book is very clearly written–the theory is nicely presented with important topics being well explained and illustrated with examples.… Each chapter begins with an outline of its content, and ends with suitably constructed exercises, with solutions given at the end of the book. … it is also an excellent reference text on multivariate calculus and the basics in differential geometry.” (Peter Shiu, The Mathematical Gazette, Vol. 100 (547), 2016)

“A textbook aimed at undergraduate mathematics students. … The text is accompanied with a large number of figures and explanatory text. Each chapter is concluded by a collection of exercises of both routine and more theoretical nature. The textbook is written in a readable way, especially it is one of rare cases of multivariate calculus texts consequently linked to the geometric roots of the subject.” (Vladimír Janiš, zbMATH 1312.26001, 2015)