## Exploring Multivariable Calculus with Maple

This text was published in 1996 by John Wiley and Sons, Inc. (ISBN 0-471-13753-7).

It was written by C-K. Cheung, Jerry Keough (both at Boston College), and Tim Murdoch. It directly supplements "Multivariable Calculus - Preliminary Edition" by the Calculus Consortium based at Harvard (McCallum, Hughes-Hallett, Gleason et al.).

C-K Cheung (ck.cheung@bc.edu) handles most support questions for this text.

### These links allow you to download the mvcal2 library referenced in the text, together with installation instructions, according to the version of Maple you are running:

• Maple Releases I, II, and III. (this link will be active shortly)
• Maple Release IV. (this link will be active shortly)
• Maple Release V. (this link will be active shortly)

### An errata list for this text follows, given in order by page number. This list was last updated on Monday, December 14, 1999.

• p.5 line 14 from the top, should read a := 'a'; (*Both are apostrophes.*)
• p.16 line 2 from the bottom, delete the phrase "(both should be 1)"
• p.37 line 2 from the top, replace "grid lines" by "cross sections".
• p.56 line 8 from the bottom, replace "drawhyperbolid1" with "drawhyperboloid1".
• p.60 line 8 from the top, replace "w = [ , , ];" with "w := [ , , ];"
• p.79 line 11 from the top, replace "plot3d(sin(x^2+y^2), x=-3..3,y=-3..3);" with plot3d(f(x,y), x=-3..3, y=-3..3);
• p.79 line 4 from the bottom, replace "plot( f(x,y), x = , y = );" with "plot3d(f(x,y), x= , y= );"
• p.80 line 12 from the bottom, replace the two Maple commands with subs(x=1, y=2, diff(f(x,y), x)); subs(x=1, y=2, diff(f(x,y),y));
• p.85 line 2 from the top, replace "Make up a polynomial ........." with Consider a polynomial ..........
• p.86 line 5 from the top, it should be: df := ( )*dx+( )*dy+( )*dz;
• p.86 line15 from the bottom, "Linear function L(x,y) = ________" should read Linear function L(x,y,z) = ________________
• p.97 line 4 from the bottom, the Maple command should read limit( (f( , ) - f(1, 2) )/h, h = 0);
• p.101 In example 2.1, the Maple output is shown incorrectly. When we copied the commands from the text to Maple, somehow the negative signs were all lost, and Maple gave the result at the point (1, 2) instead of (-1,2).
• p.111 line 3 from the bottom, "At (1, -1) and (-1, 1)..." should be "At (1, -1) and (-1,-1)...."
• p.116 line 12 from the top, the Maple command should read plot3d(f(x,y), x=-1.1..-0.9, y=0.9..1.1);
• p.123 line 8 from the bottom, the Maple command should read line1 := plot( 2*x+5, x=-5..5) :
• p.127 line 9 from the top, the Maple command should read f := (x, y) -> x^2 +x*y +2*y^2 ;
• p.137 line 3 from the top, the Maple command should read dydxplot(y=0..1-x, x=0..1);
• p.139 line 8 from the top, the Maple command should read: dzdxdyplot( z= .. , x = .. , y = .. );
• p.158 line 8 from the bottom, replace "This means R is bounded ......." with "This means T is bounded.... ".
• p.164 line 1 from the top, replace "(0, 1)" with "(1, 0)".
• p.164 line 7 from the bottom. This experiment should be numbered 1.3 (not 1.2).
• p.165 line 2. This discovery should be numbered 1.4 (not 1.3).
• p.166 line 1. This example should be numbered 1.5 (not 1.4).
• p.169 problem 1d), the question should be "An ellipse centered at the point (1, 3) traveling in a counter-clockwise direction and passing through the points (2,3), (0,3), (1,0) and (1,6)."
• p.176 problem 5 iii), the equation of the ellipsoid should be x^2+y^2+2*z^2 = 4.
• p.187 line 6 from the top, in the Maple command, the interval should be t = 0..1 instead.
• p.187 line 20 from the top, The work done on this curve is negative in the first and _third_ quadrants, and positive in the _second_ and fourth quadrants.
• p.188 line 12 from the bottom, The tracecurve command has an incorrect y(t) parameter. the command should be tracecurve([cos(2*(Pi-t)), Pi-t, t=0..Pi]);
• p.189 line 14 from the bottom, the curve C:(sint, sin^2t, sin(sint)), should have intervals, -Pi/2 < t < Pi/2.
• p.192 line 3 from the bottom, delete the extra parenthesis at the end of the command.
• p.195 line 17 from the bottom. Delete the third word "that" in the phrase "To check that if ..."
• p.196 line 12 from the top, the parameterization of the ellipse is wrong -- it contains an incorrect y-coordinate (cosine instead of sine). The parameterization should be (a*cos(t) + b, c*sin(t) + d).
• p.197 line 14 from the top, we need an additional Maple command, F := [F1, F2] ;
• p.198 line 4. The captions below the diagrams should _both_ have a second line reading "condition of Green's Theorem". (delete the extra "the")
• p.202 problem 3, the j-component of F should be x^3 - 2xysin(xy^2) - y sin(y)
• p.202 problem 3, part v) the new vector field should be: V = 3x^2i + 2xy j
• p.206 line 11 from the top, the Maple command should be drawvfsurface([p*cos(q), p*sin(q), p], [(x-2*z),-y,0], p=1..4, q=0..2*Pi);
• p.206 line1 from the bottom, the answer should be 0.
• p.207 line 6, the term x^3 inside the double integral should be x^2 instead.
• p.207 line3 from the bottom, the Maple command should be int(int((r*(cos(theta))^2-2*r*cos(theta)-r*(sin(theta))^2)*r, theta=0..2*Pi), r=1..4);
• p.210 the two Maple commands in problem 4 should read drawvfgraph(z=sqrt((1-x^2-y^2)/2),[ , , ], x=-1/2..1/2, y=-1/2..1/2);
• p.212 line 7 from the bottom, it should read "At (1, 1, 0), div F = 4/5, ....... "
• p.212 line 3 from the bottom, it should read "At (-1, -0.5, 0), div F = -3/5, ......"
• p.216 line 4 from the top, the x and y intervals should read -1 < y < 1 , -1/sqrt(2) < x < 1/sqrt(2).
• p.220 line 13 from the top, should be: "To calculate ... around (the vector) k", not the vector i.
• p.220 In the table of experiment 1.1, the label for each column should be a line integral divided by (Pi r^2).
• p.222 line 9 from the bottom, replace "curl F(1, 1, 0) = 2/ 3 k" with "curl F(1, 1, 0) = 4/3 k".
• p.222 line 3 from the bottom, replace "curl F (-1, -1, 0) = -2/3 k" with "curl F(-1, -1, 0) = -4/ 3 k".
• p.224 line 7 from the bottom, in the fluxintegral command, replace "F" with "curl[F, [x,y,z]]
• p.225 line 6 from the bottom, the Maple command should be lineintegral(F, curve, t=0..2*Pi);
• p.226 line 1 from the bottom. the figure reference should be for figure 7 (there is no figure 8, except perhaps in ice skating).