Corral's vector calculus

Description

Preface......Page 5 Contents......Page 6 1.1 Introduction......Page 9 1.2 Vector Algebra......Page 17 1.3 Dot Product......Page 23 1.4 Cross Product......Page 29 1.5 Lines and Planes......Page 41 1.6 Elementary surfaces......Page 51 1.7 Curvilinear Coordinates......Page 59 2.1 Vector-Valued Functions......Page 64 2.2 Arc Length......Page 74 2.3 Curvature......Page 78 3.1 Functions of Two or Three Variables......Page 82 3.2 Partial Derivatives......Page 88 3.3 Tangent Plane to a Surface......Page 92 3.4 Directional Derivatives and the Gradient......Page 95 3.5 Maxima and Minima......Page 101 3.6 Numerical Methods......Page 108 3.7 Lagrange Multipliers......Page 115 4.1 Double Integrals......Page 122 4.2 Double Integrals Over a General Region......Page 127 4.3 Triple Integrals......Page 134 4.4 Numerical Approximation of Multiple Integrals......Page 138 4.5 Change of Variables in Multiple Integrals......Page 143 4.6 Application: Center of Mass......Page 150 4.7 Application: Probability and Expected Value......Page 155 5.1 Line Integrals......Page 163 5.2 Properties of Line Integrals......Page 172 5.3 Green's Theorem......Page 180 5.4 Surface Integrals and the Divergence Theorem......Page 187 5.5 Stokes' Theorem......Page 197 5.6 Gradient, Divergence, Curl and Laplacian......Page 210 5.7 Other coordinate systems......Page 215 Bibliography......Page 221 Appendix A: Answers and Hints to Selected Exercises......Page 223 GNU Free Documentation License......Page 226 History......Page 234 Index......Page 235