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.