Mathematics 13                              Winter 2004                              tentative Syllabus

 Day Date Topic Sections in text Homework

 1 1-5 Review vectors, dot and cross products, lines, planes, determinants.  Matrix multiplication 1.1-1.6 webwork and Section 1.3: 11;  Section 1.6: 11 2 1-7 Polar, cyclindrical and spherical coordinates.  (Standard bases will not be covered.) 1.7 webwork and 1.7:  19, 23, 25, 31, 33 3 1-9 Review functions of several variables 2.1-2.3 webwork

 4 1-12 Derivative of vector-valued functions 2.3 webwork and 2.3: 21, 23, 25, 35(a) 5 1-14 Chain rule 2.4, 2.5 webwork and 2.5: 15, 17, 19 6 1-16 Directional derivatives and the gradient, start curves 2.6, start 3.1 webwork

No class Monday the 19th.  Class meets Tuesday the 20th during X-hour.

 7 1-20 More curves, arc length parametrizations 3.1, 3.2 webwork and 3.2: 3.  Also, find the arc length or unit speed parametrization of the curve in this problem.  Answer: x(s) = the expression for x(t) given in the problem, but replace t with (s/2 + 1)^(2/3) - 1. 8 1-21 Vector fields 3.3 webwork 9 1-23 Divergence, Curl, Gradient and the Del operator 3.4 webwork and 3.4: 13,  14.

 10 1-26 Intro to Volumes, Cavalieri's principle 5.1 webwork and 5.1:  7, 13 11 1-28 Double integrals 5.2 webwork 12 1-30 More double integrals 5.2 webwork and 5.2:  5, 7, 11, 13

Last quarter's first math 13 test is here.
Here are some suggested review problems from the book:  1.8:  13, 15, 17;  2.5:  13;  3.2:  12;  3.3:  17, 23;  3.4:  5, 7, 11(Can the vector in this problem be the curl of some vector field?)   5.1:  3, 7;  5.2:  3.

The first exam on Monday, on Feb. 2, in Bradley 101, from 6:00 to 8:00pm covers up to and including day 11.
Solutions to the first exam.

 13 2-2 Changing the order of integration 5.3 webwork and 5.3:  9, 13 14 2-4 Triple integrals 5.4 webwork and 5.4:  11, 13, 21 15 2-6 Change of variables 5.5 webwork and 5.5:  9, 11, 15, 17, 21

No class Friday the 13th.  Class meets Tuesday the 10th during X-hour.

 16 2-9 More change of variables 5.5 webwork.  Optional problem: Find the volume of the solid {(x,y,z): (x/(1+z^3))^2 + (y/(1 - z^3))^2 < or = 1,  -1 < z < 1} by changing variables, and check your work by using Cavalieri's  principle. 17 2-10 Applications of multiple integrals 5.6 webwork and 5.6:  9, 17 18 2-11 Scaler and vector line integrals 6.1 webwork and 6.1:  20 (answer:  25 (pi - 2) )

 19 2-16 More Scaler and vector line integrals 6.1 webwork and 6.1: 15 20 2-18 Green's theorem 6.2 webwork and 6.2: 13, 15 21 2-20 Conservative vector fields 6.3 webwork and 6.3: 13

The second exam on Wednesday,  Feb. 25, in Bradley 101, from 6:00-8:00pm covers days 12 through 21.
Last quarter's second math 13 test is here.
Here are some suggested review problems from the book: pages 371-374:  3, 5, 11, 19 and pages 412-413: 14, 19, 21

 22 2-23 Parametrized surfaces 7.1 webwork 23 2-25 Areas of surfaces 7.1 webwork 24 2-27 Surface integrals 7.2 webwork and  7.2:  1, 5, 7, 11

 25 3-1 Stokes's theorem 7.3 webwork and 7.3: 3, 5 26 3-3 Stoke's and Gauss's theorems 7.3 webwork 27 3-5 Stoke's and Gauss's theorems 7.3 webwork

Some review problems from the book covering material from the latter part of the course that might help you prepare for the final:  5.6: 3, 11;  5.7:  5, 13;  6.2: 1;  6.4: 11;  7.2: 3;  7.3: 1, 7;  7.5: 1a, 2(Just set up the integral. answer:  Integral of theta from 0 to 2 pi , integral of z from -a to a of (1 + 2z^2)^.5 ) ), 8(answer: (4 pi/3)(2^1.5 - 1))

Most of an old math 13 final is here.  (There were two more questions on this final involving material we did not cover.)