Author | Marsden, Jerrold. author |
---|---|
Title | Calculus III [electronic resource] / by Jerrold Marsden, Alan Weinstein |
Imprint | New York, NY : Springer US, 1985 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5028-9 |
Descript | XV, 372 p. 75 illus. online resource |
13 Vectors -- 13.1 Vectors in the Plane -- 13.2 Vectors in Space -- 13.3 Lines and Distance -- 13.4 The Dot Product -- 13.5 The Cross Product -- 13.6 Matrices and Determinants -- 14 Curves and Surfaces -- 14.1 The Conic Sections -- 14.2 Translation and Rotation of Axes -- 14.3 Functions, Graphs, and Level Surfaces -- 14.4 Quadric Surfaces -- 14.5 Cylindrical and Spherical Coordinates -- 14.6 Curves in Space -- 14.7 The Geometry and Physics of Space Curves -- 15 Partial Differentiation -- 15.1 Introduction to Partial Derivatives -- 15.2 Linear Approximations and Tangent Planes -- 15.3 The Chain Rule -- 15.4 Matrix Multiplication and the Chain Rule -- 16 Gradients, Maxima, and Minima -- 16.1 Gradients and Directional Derivatives -- 16.2 Gradients, Level Surfaces, and Implicit Differentiation -- 16.3 Maxima and Minima -- 16.4 Constrained Extrema and Lagrange Multipliers -- 17 Multiple Integration -- 17.1 The Double Integral and Iterated Integral -- 17.2 The Double Integral Over General Regions -- 17.3 Applications of the Double Integral -- 17.4 Triple Integrals -- 17.5 Integrals in Polar, Cylindrical, and Spherical Coordinates -- 17.6 Applications of Triple Integrals -- 18 Vector Analysis -- 18.1 Line Integrals -- 18.2 Path Independence -- 18.3 Exact Differentials -- 18.4 Greenโs Theorem -- 18.5 Circulation and Stokesโ Theorem -- 18.6 Flux and the Divergence Theorem -- Answers