Multivariate calculus & geometry

Aimed primarily at higher level undergraduates in the mathematical sciences, the author provides the reader with a deep understanding 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 tested 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 comprehensive and unified understanding of the Differential, Integral and Geometric Calculus of Several Variables.
"The author has taken the sensible approach of giving an adequate 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

Contents

• 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
• Parametrised Surfaces in R3
• Surface Area
• Surface Integrals
• Stokes'Theorem
• Triple Integrals
• The Divergence Theorem
• Geometry of Surfaces in R3
• Gaussian Curvature
• Geodesic Curvature
• Solutions
• Index