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: Find the gradient of w=x2y3z at (1,2,1). Problem 2P: Starting from the point (1,1), in what direction does the function =x2y2+2xy decrease most rapidly? Problem 3P: Find the derivative of xy2+yz at (1,1,2) in the direction of the vector 2ij+2k. Problem 4P: Find the derivative of zexcosy at (1,0,/3) in the direction of the vector i+2j. Problem 5P: Find the gradient of =zsinyxz at the point (2,/2,1). Starting at this point, in what direction is ... Problem 6P: Find a vector normal to the surface x2+y2z=0 at the point (3,4,25). Find the equations of the... Problem 7P: Find the direction of the line normal to the surface x2y+y2z+z2x+1=0 at the point (1,2,1). Write the... Problem 8P: (a) Find the directional derivative of =x2+sinyxz in the direction i+2j2k at the point (1,/2,3). (b)... Problem 9P: (a) Given =x2y2z, find at (1,1,1). (b) Find the directional derivative of at (1,1,1) in the... Problem 10P: For Problems 10 to 14, use a computer as needed to make plots of the given surfaces and the... Problem 11P: For Problems 10 to 14, use a computer as needed to make plots of the given surfaces and the... Problem 12P: For Problems 10 to 14, use a computer as needed to make plots of the given surfaces and the... Problem 13P: For Problems 10 to 14, use a computer as needed to make plots of the given surfaces and the... Problem 14P: For Problems 10 to 14, use a computer as needed to make plots of the given surfaces and the... Problem 15P: Repeat Problem 14b for the following points and directions. (a) (4,2),i+j (b) (3,1),4i+3j (c)... Problem 16P: Show by the Lagrange multiplier method that the maximum value of d/ds is . That is, maximize d/ds... Problem 17P: Find r, where r=x2+y2, using ( 6.7) and also using (6.3). Show that your results are the same by... Problem 18P: As in Problem 17, find the following gradients in two ways and show that your answers are... Problem 19P: As in Problem 17, find the following gradients in two ways and show that your answers are... Problem 20P: As in Problem 17, find the following gradients in two ways and show that your answers are... Problem 21P: Verify equation ( 6.8 ); that is, find f in spherical coordinates as we did for cylindrical... format_list_bulleted