Current homework assignments

Due Thursday, 12 March, 1998:

The homework due on the final Thursday of the course will not be collected and graded, but you should be prepared to work the following in recitation.

Chapter 9: Do problems 2,5,8.
Chapter 10: Do problems 5,9,13,14,16,17,18.
Chapter 11: Do problems 2,7,11,13.

Current contests

Past homework assignments

Chapter 1: Do problems 15, 16, and 20 changed so that it applies to the true monkey saddle (der echte Affensattel, for those who prefer German):
    z = x^3 - 2 x y^2.

Chapter 2, problems 6,8,10,15,16,18,20,22.

Due Thursday, 22 January, 1998:

There was a test on this date, so the homework was not collected to be graded. Instead, here are some recommended study problems.

Practice problems include all the problems in the following:

Recommended exercises from Cain-Herod include all those in chapters 1 and 2 (since there are not so many).

Recommended exercises from Grossman include:
Section 11.1, all drills.
Section 11.2, all drills, especially #19-32. Also #35,36,40.
Section 11.3, #31-34.
Section 11.4, all drills and #44,46,50,53.
Section 11.5, #4-6,12,13,24,25.
Section 11.6, all drills, especially #29-34,35,43,44.
Section 11.7, all drill.

In addition, a Maple worksheet is available for you to study projections onto lines, vectors, and planes, and gain some experience with the dot product, and another worksheet illustrates the basics of multidimensional graphs with Maple.

Due Thursday, 29 January, 1998:

Chapter 3: Do problems 1,13,14,23
Chapter 4: Do problems 1,2,5,9,11.

In addition, work through the Maple worksheet on tangents, normals, and curvature. In particular, do the exercise given in the worksheet.

The part of Grossman's book which correlates with Chapter 4 of Cain-Herod is chapter 12.

Due Thursday, 5 February, 1998:

There was a test on this date. Study suggestions included all the problems in chapters three, four, and five, which you have not yet done.

Recommended exercises from Grossman included:
Section 12.1, all drills, and problems 41,43,45
Section 12.2, drills 11-16, and problems 35,36
Section 12.3, all drills
Section 12.4, drills 24-30
Section 12.5, all drills, and problems 31,32
Section 12.6, all drills, and problems 42,43,46,48,49,50-54,61,62.

Due Thursday, 12 February, 1998:

Chapter six: Do problems #1,2,4,8,11,12.

Solve the following matrix problems:

A. Find a 2X2 matrix which has the effect of stretching a figure in the plane by a factor of 3 along the line y = -2 x and then reflecting the result through the y-axis.
Hint. In class we learned that there are two strategies for this sort of problem:

1. Simplify the problem by rotating the line to a standard line such as one of the axes, solve the problem there, and rotate back.
2. Project e_k onto the plane and use the results to build the columns of the matrix.

B. Find a function which has the effect of projecting a vector in the plane onto the line y = -2 x and then shifting the result up (j direction) by 2. Then use the result to find a function which has the effect of projecting a vector in the plane onto the line y = -2 x + 2.
Note: These are affine functions, not linear functions.

Due Thursday, 19 February, 1998:

A. Find a 3X3 matrix which has the effect of stretching a figure in R³ by a factor of 3 along the x-axis then rotating it counterclockwise around the z-axis (as seen from above) by pi/4 radians, then rotating it clockwise around the x-axis (as seen from x positive) by pi/3 radians.

Hints.

C. Find the unique 2X2 matrix A which has the following action:
    A (i + 2 j) = 2 i
    A (i - 2 j) = i + j.

Chapter 7: Do problems 1,2,6

Due Thursday, 26 February, 1998:

There was a test on this date, so the homework was not be collected to be graded. Instead, here are some recommended study problems.

Do all the problems in chapters 5-7 of the text by Cain and Herod and in chapter 8 up through section 8.4.

Recommended exercises from Grossman include:
Section 13.2, #31,43
Section 13.3, all drills, #43,
Section 13.4, all drills
Section 13.5, all drills
Section 13.6, all drills
Section 13.7, all drills, #31,34
Section 13.8, all drills, #25,28

Neither Grossman nor Cain has many exercises of the form "Find a linear - or affine - mapping which does something or other." The best source for them is the Maple worksheet on modeling linear functions with matrices, which contains some exercises. (It does not take specialized knowledge of Maple to read this worksheet.)

Due Thursday, 5 March, 1998:

Find the line of the form y = m x + b which best matches the following
data, and plot the data with the line:

        x       y

        1975    19948
        1980    28861
        1985    41086
        1990    65673
        1995    81555

If these numbers represent exports (in kilodollars) of an industry in
Georgia, give an estimate of the level of exports in 1998.

Chapter 8: Do problems 17,19,21.

A newsgroup called git.math.class.harrell has been created on the Georgia Tech computer system. Please use it to post questions and comments for the other students or the professor.

Old contests

The student who used the Maple graphing commands
    plot
    plot3d
    contourplot
    spacecurve
    cylinderplot
to draw the most recognizable and convincing animal - a frog - was Bob Lyons

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