Multivariate calculus and geometry POD (2^nd Ed.)

Aimed primarily at higher level undergraduates in the mathemati- cal sciences, the author provides the reader with a deep under- standing of the uses and limitations of multivariate calculus by the integrated use of geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. On reading this book the student will acquire the confidence and techniques necessary to tackle new problems. In this revised edition, which includes additional exercises and expanded solutions, Sen Dineen gives a solid description of the basic concepts, via simple familiar examples which are then te- sted in technically demanding situations. The author recognises the varied backgrounds students bring to the subject and only assumes the minimal prerequisite knowledge necessary for a com- prehensive and unified understanding of the Differential, Inte- gral and Geometric Calculus of Several Variables. "The author has taken the sensible approach of giving an adequa- te formulation of the theories, bakcked up by geometric insight and accompanied by reasonable explanations." The Mathematical Gazette "It is rare to find a text on multivariate analysis where the geometrical intuition is preserved so well." Zentralblatt für Mathematik und ihre Grenzgebiete

1. Introduction to Differentiable Functions.- 2. Level Sets and Tangent Spaces.- 3. Lagrange Multipliers.- 4. Maxima and Minima on Open Sets.- 5. Curves in Rn.- 6. Line Integrals.- 7. The Frenet-Serret Equations.- 8. Geometry of Curves in R3.- 9. Double Integration.- 10. Parametrised Surfaces in R3.- 11. Surface Area.- 12. Surface Integrals.- 13. Stokes'Theorem.- 14. Triple Integrals.- 15. The Divergence Theorem.- 16. Geometry of Surfaces in R3.- 17. Gaussian Curvature.- 18. Geodesic Curvature.- Solutions.- Index.

From the reviews of the second edition:"The author has taken the sensible approach of giving an adequate formulation of the theories, backed up by geometric insight and accompanied by reasonable explanations."The Mathematical Gazette"It is rare to find a text on multivariate analysis where the geometrical intuition is preserved so well."Zentralblatt für Mathematik und ihre Grenzgebiete"This is a nice introduction to multivariate calculus for higher level undergraduates. ... The text contains many worked out examples and a collection of additional exercises with solutions given in the appendix of the book." (F. Haslinger, Monatshefte für Mathematik, Vol. 139 (3), 2003)"In this revised edition, which includes additional exercises and expanded solutions, Seán Dineen gives a solid description of the basic concepts, via simple familiar examples, which are then tested in technically demanding situations. The author recognizes the varied backgrounds students bring to the subject and only assumes the minimal prerequisite knowledge necessary for a comprehensive and unified understanding of the differential, integral and geometric calculus of several variables. On reading this book the student will acquire the confidence and techniques necessary to tackle new problems." (L'Enseignement Mathematique, Vol. 47 (3-4), 2001)"Dineen deals with many of the topics you would find in a typical text on advanced calculus but he does so in a much more sophisticated way. ... All the new terms are defined as they appear and all the necessary theorems are stated ... . The book is ... very clearly written, and there are lots of useful diagrams and worked examples. The approach ... is one that students who are going on will want to learn sooner or later." (Peter Saunders, The Mathematical Gazette, Vol. 86 (505), 2002)"Aimed primarily at higher level undergraduates in the mathematical sciences, the author provides the reader with an understanding of the uses and limitations of multivariate cal