Multivariate Calculus and Geometry

• Main Author: Dineen, Seán (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London : Imprint: Springer, 2014.
• Edition: 3rd ed. 2014.
• Series: Springer Undergraduate Mathematics Series,
• Subjects: Mathematics.; Mathematics, general.

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...

Table of 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
• Parametrized Surfaces in R3
• Surface Area
• Surface Integrals
• Stokes’ Theorem
• Triple Integrals
• The Divergence Theorem
• Geometry of Surfaces in R3
• Gaussian Curvature
• Geodesic Curvature.