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
4.1 Introduction And Notation 4.2 Power Series In Two Variables 4.3 Total Differentials 4.4 Approximations Using Differentials 4.5 Chain Rule Or Differentiating A Function Of A Function 4.6 Implicit Differentiation 4.7 More Chain Rule 4.8 Application Of Partial Differentiation To Maximum And Minimum Problems 4.9 Maximum And Minimum Problems With Constraints; Lagrange Multipliers 4.10 Endpoint Or Boundary Point Problems 4.11 Change Of Variables 4.12 Differentiation Of Integrals; Leibniz' Rule 4.13 Miscellaneous Problem expand_more
Problem 1P: Use the Taylor series about x=a to verify the familiar second derivative test for a maximum or... Problem 2P: Using the two-variable Taylor series [say ( 2.7)] prove the following second derivative tests for... Problem 3P: Use the facts stated in Problem 2 to find the maximum and minimum points of the functions in... Problem 4P: Use the facts stated in Problem 2 to find the maximum and minimum points of the functions in... Problem 5P: Use the facts stated in Problem 2 to find the maximum and minimum points of the functions in... Problem 6P: Use the facts stated in Problem 2 to find the maximum and minimum points of the functions in... Problem 7P: Given z=yx2y2x2, show that z has neither a maximum nor a minimum at (0,0), although z has a minimum... Problem 8P: A roof gutter is to be made from a long strip of sheet metal, 24cm wide, by bending up equal amounts... Problem 9P: An aquarium with rectangular sides and bottom (and no top) is to hold 5 gal. Find its proportions so... Problem 10P: Repeat Problem 9 if the bottom is to be three times as thick as the sides. An aquarium with... Problem 11P: Find the most economical proportions for a tent as in the figure, with no floor. Problem 12P: Find the shortest distance from the origin to the surface z=xy+5. Problem 13P: Given particles of masses m, 2m, and 3m at the points (0,1),(1,0), and (2,3), find the point P about... Problem 14P: Repeat Problem 13 for masses m1,m2,m3 at x1,y1,x2,y2,x3,y3. Show that the point you find is the... Problem 15P: Find the point on the line through (1,0,0) and (0,1,0) that is closest to the line x=y=z. Also find... Problem 16P: To find the best straight line fit to a set of data points xn,yn in the least squares sense means... Problem 17P: Repeat Problem 16 for each of the following sets of data points. (a) (1,0),(2,1),(3,8) (b)... format_list_bulleted