Assignments: Math 221, Sec02, Fall, 2001
Assignments Math 221 Sec. 02
08/29/01 Notes p.1-4; H.W. Handout Class #1, Prob. 1-6.
(Vectors)
09/31/01 Notes p.4-6; H.W. Handout Class #2, Prob. 1-8.
(Inner Product)
09/05/01 Notes p.5-8; H.W. Problems in Notes, 1-5 ,and unnumbered
problem starting on p.9
bottom of the page and ending on p.10.
(Wedge products and the * Operator)
09/07/01 Notes p.10-15, H.W. Problems in Notes 1-9,p.14&15
(Planes,systems of equations,linear transformations,matrices)
09/10/01 Notes p.10-15, H.W.In text p868,Probs.15-25
09/12/01 Notes p.16-20 H.W.Problems in Notes p.20,Probs 1-3.
09/14/01 Review
09/17/01 Notes p.21-22
09/18/01 Test #1
09/19/01 Introduction to the study of vector-valued functions of
a vector variable--
the linear case. Notes, p.21-22. H.W. Handout
09/21/01 Review of Test #1; the tangent plane to a two dimensional surface at a point: Notes p.23-26
09/24/01 The tangent plane to a general surface, partial derivatives,
the gradient, the differential,
directional derivatives. Notes p.26-32. H.W. Handout
09/25/01 Ten point summary of the material on differentiation.
09/26/01 Same as 09/24/01.H.W. (in text)Problems as indicated in class
09/28/01 Solution to H.W. problems and general questions
10/01/01 The chain rule. Notes p. 32-34.H.W.Problems assigned
in the text p.958 and
3 prblems in the Notes p.33-34
10/02/01 Problems on the chain rule reviewed
10/03/01 Critical points and max/min with restraints. H.W. p.981#5,27,29,31,45; p.991#19,25,29,35,39
10/05/01 Classification of critical points; Taylor's theorem with
remainder
H.W. Handout (Test #2 announced for 10/16/01)
10/08/01 Technique for classification of critical points. H.W. Text p.981 #5 - 17 (odd), p.991 #15,17
10/09/01 Review of problems on local max and min with and without
restraints and
classification of critical points
10/10/01 Review for Test #2. Work old test #2.
10/12/01 Evaluating multiple integrals. H.W. Text, p. 1022, 7 - 27 odd
10/15/01 Review of Test # 2, H.W. Text, p. 1050, 3 - 19 odd
10/17/01 Change of variable in multiple integrals. H.W. Text, p.
1028, 7 - 13 odd, p. 1057,
7 - 11 odd, 17-23 odd, p. 1067, 11 - 17 odd.
10/19/01 Change of variable: spherical and cylindrical coordinates
10/22/01 Surface integrals, text, p.1042, 1-11(odd) and two exercises put on the board
10/24/01 -10/31 Additional problems on multiple integration
11/02/01 Introduction to Stokes' Theorem, boundaries,sample Test #3 distributed
11/05/01 Problems on sample test discussed.
11/06/01 Test #3
11/07/01 Differential Forms, H.W. Handout
11/09/01 Vector fields,Integration of one-forms and line integrals,
Text, p.1091,13-25 (odd), p.1125, 17,39,p.1138,
19-27 (odd)
11/12/01 Review of Test#3
11/13/01 p-forms and integration of vector fields over surfaces.
11/14/01 grads, curls, and divs and their relation to differential forms, H.W. (to be assigned)
11/16/01 Stokes' Theorem and applications, H.W. p. 1154, 15, 17, 19,27,29,31,32,33,35,36
11/19/01 More applications, interpretation of the curl and div.
11/26/01 Closed, Exact forms, independence of path (for 1-forms).
H.W. Text, p.1101, 13-17 (odd), 19-27 (odd),
28, 33, 34. p. 1115, 13-21 (odd).
09/03/97 Notes p.8-12; H.W. Handout Class #4, 1-12 .
(Planes)
09/06/97 Notes p.12-16; H.W. Problems in Notes p.14,
Prob. 1-9 &
Handout Class #5, Prob. 10.
(systems of linear equations,matrices,linear tranformations)
09/08/97 Notes p.12-16,Assignment of 09/06/97 continued.
Test #1 announced for 09/16/97.
09/09/97 Notes 16-18(top of page); H.W. Problems in Notes #1-4.
(curves)
09/10/97 Notes p.18-20; Problems in Notes p.20 , #1-3.
( curves continued)
09/12/97 Notes p.21-22, Sample Quiz Distributed.
( linear functions from n-space to m-space)
09/15/97 Notes p.23, Prepare for Test #1
( functions from n-space to m-space)
09/16/97 Test #1
09/17/97 Test #1 Returned and Discussed; no further assignment.
(note:at this time two days behind schedule)
09/19/97 Notes p.24-26(top of page), H.W. Handout Class #8,Probs.1-5
(differentiability, tangent planes, the gradient and the differential for
real valued functions of two variables)
09/22/97 Notes p.26-32, H.W. Handout Class #9, Probs. 1-4
(the differential of vector valued functions of a vector variable, tangent
planes to
p-dimensional surfaces given parametrically and non-parametrically)
09/23/97 Notes p.32-34, H.W. Problems in Notes #1-3,p. 34.
(chain rule and discussion of implicit function theorem)
09/24/97 Notes p.35-36, H.W. Handout Class #10
(critical points and maxima and minima on surfaces)
09/26/97 Notes p.37-40, H.W. Handout Class #11
(Taylor's theorem in several variables, classification of critical points)
09/29/97 Problems on Max/Min and Critical Points
10/01/97 More Problems,Test #2 announced for10/07/97
10/03/97 Notes p.41-42
(Introduction to multiple and iterated integrals)
10/06/97 Typical Problems on Describing the Region of Integration,
H.W. Handout for Class #12 ,22 problems from
standard texts on double and triple integrals
10/07/97 Test #2 on Differentiation of Functions of Several Variables.
10/08/97 Review of Test #2, H.W. Redo of Test #2
10/10/97 Notes p.43-44, H.W. Handout Class #13 Probs. 1-11
(Change of Variable in Multiple Integrals)
10/13/97 Problems on Multiple Integration and Change of Variable, H.W. (continued)
10/14/97 Notes p.44-46, H.W. Handout for Class #14,probs. 1-6.
(Surface Integration of Scalar -Valued Functions)
10/15/97 Problems on Surface Integrals, H.W. (continued)
10/17/97 Notes p.47, Quiz 3 Announced as Take-home on 10/20/97 to
be returned 10/22/97.
(Introduction to Differential Forms)
10/20/97 Notes p.47-50, Take-home Quiz #3 handed out.
(The differential and boundary operators, integration of forms)
10/21/97 Problem Session (Lab) Cancelled due to Quiz #3
In the next three assignments the relavent Notes are found in pages 50-54:
10/22/97 Review of Quiz #3 and Use of the differential operator to compute grad, curl and div
10/24/97 Integrals of vector fields and the relation to integration of forms; STOKES' THEOREM
10/27/97 Problems on integration of vecor fields; the gravitational field and the solid angle form
In the next four exercises the relevant Notes are found in pages 54-57:
10/28/97 Integration over closed surfaces, exact forms and closed forms; relationship on any euclidean domain
10/29/97 Necessary and sufficient conditions for Conditions A, B
and C to be equivalent in the case of 1-forms,
Poincare's lemma for 1-forms
10/31/97 Finding scalar potentials: Problems
11/03/97 Poincare Lemma for p- forms, finding vector potentials,example problems
11/04/97 Review problems on all forms of Stokes's theorem,uniquenes
of solutions to Laplace's equation in
bounded regions
11/05/97 Integrating the unit normal vector field to find surface area ( Class notes )
11/07/97 Problem Session
11/10/97 The Gamma function, the Beta function, the volume of the n-ball ( Class notes )
11/11/97 Verification of existence of the improper integals of the
previous lecture,inductive formula for the volume
of
the n-ball, Quiz#4 announced for 11/18/97
11/12/97 Copies of previous final exams,copies of previous Quiz #4,
Problems in using the Gamma and Beta
funtion
to compute integrals and discussion on how to the use of this material
11/14/97 Gamma and Beta funtion used to compute improper integrals
11/17/97 Review in preparation for Quiz#4
11/18/97 Quiz#4
11/19/97 Completion of Quiz #4, Introduction to Curvilinear Coordinates
11/21/97 Orthonormal curvilinear coordinates, gradients,curls,
divs and Laplace's equation in curvilinear
coordinates.
Homework: Using polar,cylindrical and spherical coordinates find expressios
for
the gradient, divergence, curl and Laplace's equation.
All remaining classes will be used to review for the final examination.