Vector Calculus

Description

Preface Contents 1 Vectors in Euclidean Space 1.1 Introduction 1.2 Vector Algebra 1.3 Dot Product 1.4 Cross Product 1.5 Lines and Planes 1.6 Surfaces 1.7 Curvilinear Coordinates 1.8 Vector-Valued Functions 1.9 Arc Length 2 Functions of Several Variables 2.1 Functions of Two or Three Variables 2.2 Partial Derivatives 2.3 Tangent Plane to a Surface 2.4 Directional Derivatives and the Gradient 2.5 Maxima and Minima 2.6 Unconstrained Optimization: Numerical Methods 2.7 Constrained Optimization: Lagrange Multipliers 3 Multiple Integrals 3.1 Double Integrals 3.2 Double Integrals Over a General Region 3.3 Triple Integrals 3.4 Numerical Approximation of Multiple Integrals 3.5 Change of Variables in Multiple Integrals 3.6 Application: Center of Mass 3.7 Application: Probability and Expected Value 4 Line and Surface Integrals 4.1 Line Integrals 4.2 Properties of Line Integrals 4.3 Green's Theorem 4.4 Surface Integrals and the Divergence Theorem 4.5 Stokes' Theorem 4.6 Gradient, Divergence, Curl and Laplacian Bibliography Appendix A: Answers and Hints to Selected Exercises Appendix B: Proof of the Right-Hand Rule for the Cross Product Appendix C: 3D Graphing with Gnuplot GNU Free Documentation License History Index