1 Infinite Series, Power Series 2 Complex Numbers 3 Linear Algebra 4 Partial Differentitation 5 Multiple Integreals 6 Vector Analysis 7 Fourier Series And Transforms 8 Ordinary Differential Equations 9 Calculus Of Variations 10 Tensor Analysis 11 Special Functions 12 Series Solutions Of Differential Equations; Legendre, Bessel, Hermite, And Laguerre Functions 13 Partial Differential Equations 14 Functions Of A Complex Variable 15 Probability And Statistics expand_more
6.1 Introduction 6.2 Applications Of Vector Multiplication 6.3 Triple Products 6.4 Differentiation Of Vectors 6.5 Fields 6.6 Directional Derivative; Gradient 6.7 Some Other Expressions Involving 6.8 Line Integrals 6.9 Green's Theorem In The Plane 6.10 The Divergence And The Divergence Theorem 6.11 The Curl And Stokes' Theorem 6.12 Miscellaneous Problems expand_more
Problem 1P: Evaluate the line integral x2y2dx2xydy along each of the following paths from (0,0) to (1,2). (a)... Problem 2P: Evaluate the line integral (x+2y)dx2xdy along each of the following closed paths, taken... Problem 3P: Evaluate the line integral xydx+xdy from (0,0) to (1,2) along the paths shown in the sketch. Problem 4P Problem 5P: Find the work done by the force F=x2yixy2j along the paths shown from (1,1) to (4,2). Problem 6P Problem 7P: For the force field F=(y+z)i(x+z)j+(x+y)k, find the work done in moving a particle around each of... Problem 8P: Verify that each of the following force fields is conservative. Then find, for each, a scalar... Problem 9P: Verify that each of the following force fields is conservative. Then find, for each, a scalar... Problem 10P: Verify that each of the following force fields is conservative. Then find, for each, a scalar... Problem 11P: Verify that each of the following force fields is conservative. Then find, for each, a scalar... Problem 12P: Verify that each of the following force fields is conservative. Then find, for each, a scalar... Problem 13P: Verify that each of the following force fields is conservative. Then find, for each, a scalar... Problem 14P: Verify that each of the following force fields is conservative. Then find, for each, a scalar... Problem 15P: Verify that each of the following force fields is conservative. Then find, for each, a scalar... Problem 16P: Given F1=2xi2yzjy2k and F2=yixj (a) Are these forces conservative? Find the potential corresponding... Problem 17P: Which, if either, of the two force fields F1=yi+xj+zk,F2=yi+xj+zk is conservative? Calculate for... Problem 18P: For the force field F=yi+xj+zk, calculate the work done in moving a particle from (1,0,0) to (1,0,)... Problem 19P: Show that the electric field Eofapointcharge[equation(8.11)] is conservative. Write in ( 8.13) in... Problem 20P: For motion near the surface of the earth, we usually assume that the gravitational force on a mass m... Problem 21P: Consider a uniform distribution of total mass m over a spherical shell of radius r The potential... format_list_bulleted