Purdue Calumet
MA 26100
Multivariate Calculus
Spring, 2016

Professor Roger Kraft
Office: Classroom Office Building, Room 368
Office phone: (219) 989-2696
Office hours: 2:00--4:00 MW, after class, and by appointment.
E-mail: roger@purduecal.edu

This page documents what we do in class. It contains reading and homework assignments from our textbook, and links to illustrations, demonstration programs, or other sources of information.

The quiz today is on Sections 13.7, 11.9, and 13.8.

The final exam will be Wednesday, May 4, at 6:00pm.

Study for the final exam by making sure that you can solve all the problems from the three midterm exams and the 12 quizzes. Also, look at the review problems at the end of each chapter that were assigned for each midterm exam.

Here are review sheets of what we have covered this semester.

Here are two review sheets on integration from MA 16400.

The quiz on Wednesday is on Sections 13.7, 11.9, and 13.8.

For Wednesday, read Section 13.8.

The homework problems for Section 11.9 are

The homework problems for Section 13.8 are

If you would like to read some other explanations of cylindrical and spherical coordinates, try looking at the following references.

If you would like to read some other explanations of triple integrals in cylindrical and spherical coordinates, try looking at the following references.

The quiz today is on Section 13.6.

For Monday, read Section 11.9 (we need to cover Section 11.9 before we can cover Section 13.8) and Section 13.8.

The homework problems for Section 13.7 are

If you would like to read some other explanations of triple integrals, try looking at the following references.

Today we will go over Section 13.6 and start Section 13.7

The quiz Wednesday will be on Section 13.6.

For Wednesday, read Section 13.7.

The homework problems for Section 13.6 are

The homework problems for Section 13.7 are

If you would like to read another explanation of the double integral for surface area, try looking at the following reference.

Third midterm exam is today.

For the Monday, read Section 13.6.

The third exam is this Wednesday. See the review material just below.

Today we will go over Section 13.5.

The quiz today is on polar coordinates (Sections 10.5 & 10.6) and Section 13.4.

The third exam will be next Wednesday, April 13. It will be on Sections 13.1, 13.2, 13.3, 13.4, 13.5, and Sections 10.5, 10.6.

Here is a review sheet of what you should know for the exam.

Here is a list of review problems, from the end of Chapter 13, that you should look at as you study for the exam.

The homework problems for Section 13.5 are

When you read Section 13.5, you may need to go back and review the material on moments and center of mass from Section 6.6.

If you would like to read some other explanations of densities, moments, and center of mass, try looking at the following reference.

The quiz Wednesday is on polar coordinates (Sections 10.5 & 10.6) and Section 13.4.

For Wednesday, read Section 13.5.

The quiz today is on Section 13.3.

Today and Monday we will go over polar coordinates.

The homework problems for Section 13.4 are

If you would like to read some other explanations of double integrals in polar coordinates, try looking at the following references.

The quiz Wednesday is on Section 13.3.

Today we will finish Section 13.3.

For Wednesday, read Section 13.4.

When you read Section 13.4, you may need to go back and review the material on polar coordinates from Sections 10.5, 10.6, and 10.7.

The following web pages review polar coordinates and area in polar coordinates (what our textbook covers in Sections 10.5, 10.6, and 10.7).

The quiz today is on Sections 13.1 and 13.2

Here is a brief summary of double and iterated integrals.

The homework problems for Section 13.3 are

If you would like to read some other explanations of non-rectangular regions of integration, try looking at the following references.

The quiz Wednesday is on Sections 13.1 and 13.2

For Wednesday, read Section 13.3.

The homework problems for Section 13.1 are

The homework problems for Section 13.2 are

If you would like to read some other explanations of double integrals, try looking at the following references.

If you would like to read some other explanations of iterated integrals, try looking at the following references.

  • Second midterm exam is today.

    • For next Monday, read Sections 13.1 and 13.2.

  • The second midterm exam is Wednesday.

    • Today we will finish Section 12.8.

    Spring break.

    Spring break.

    The second exam will be Wednesday, March 16. It will be on Section 11.8, and Chapter 12, Sections 12.1, 12.2, 12.4, 12.5, 12.6, 12.7, and 12.8.

    Here is a review sheet of what you should know for the exam.

    These are slightly more detailed summaries of tangent plane, gradient vector, and directional derivatives.

    Here is a list of review problems, from the end of Chapter 12, that you should look at as you study for the exam.

    The homework problems for Section 12.7 are

    The homework problems for Section 12.8 are

    If you would like to read some other explanations of tangent plane approximations, try looking at the following references.

    If you would like to read some other explanations of maximums and minimums, try looking at the following references.

    The quiz on Wednesday will be on Sections 12.5 and 12.6.

    Today we will go over Section 12.6.

    For Wednesday, read Sections 12.7 and 12.8.

    The second exam will be postponed two weeks to Wednesday, March 16 (after Spring Break). It will be on Section 11.8, and Chapter 12, Sections 12.1, 12.2, 12.4, 12.5, 12.6, 12.7, and 12.8. More detailed review information will be here in a few days.

    The homework problems for Section 12.6 are

    If you would like to read some other explanations of the chain rule, try looking at the following references.

    No class today because of the snow.

    Here is today's quiz on Sections 12.4 and 12.5. It is a take home quiz. Print out the quiz, do the problems, and turn in the quiz at the beginning of class Monday.

    Here is a summary of the material from Section 12.5.

    The quiz on Wednesday will be on Sections 12.4 and 12.5.

    For Wednesday, read Section 12.6.

    The homework problems for Section 12.5 are

    If you would like to read some other explanations of directional derivatives, try looking at the following references.

    The quiz today is on Sections 12.1 and 12.2.

    For Monday, read Section 12.5.

    The homework problems for Section 12.4 are

    Here is a summary of the material from Section 12.4.

    If you would like to read some other explanations of the tangent plane, try looking at the following references.

    The quiz Wednesday will be on Sections 12.1 and 12.2.

    Today we will go over Sections 12.1 and 12.2.

    For Wednesday, read Section 12.4 (we shall skip Section 12.3).

    Here are a few online programs for graphing functions z=f(x,y) along with their level sets (horizontal cross sections) and partial derivatives (vertical cross sections).

    The quiz today is on Section 11.8.

    Today we will finish Section 12.1.

    The homework problems for Section 12.2 are

    If you would like to read some other explanations of partial derivatives, try looking at the following reference.

    The quiz Wednesday will be on Section 11.8

    For Wednesday, read Section 12.2.

    The homework problems for Section 11.8 are

    The homework problems for Section 12.1 are

    If you would like to read some other explanations of quadric surfaces, try looking at the following references.

    If you would like to read some other explanations of functions of two variables, try looking at the following references.

    First midterm exam is today.

    For Monday, read Sections 11.8 and 12.1 (and skip Section 11.7).

    Remember that the first midterm exam is this Wednesday.
    See the review material below.

    Today we will finish Section 11.6.

    The quiz today is on Section 11.5.

    Today we will start Section 11.6.

    Remember that the first midterm exam is next Wednesday.

    Here is a review sheet of what you should know for the exam.

    Review this summary of all the vector algebra rules from Sections 11.2, 11.3, 11.4.

    Here is a list of review problems that you should look at as you study for the exam, which will be on Chapter 11, Sections 11.1, 11.2, 11.3, 11.4, 11.5, 11.6.

    The homework problems for Section 11.6 are

    NOTE: When solving these problems, don't write the "symmetric equations" of a line, always write the "parametric equations".

    If you would like to read some other explanations of the parametric equations for a line, try looking at the following references.

    The quiz Wednesday will be on Section 11.5.

    The homework problems for Section 11.5 (pages 581-587 and skip the optional section on Kepler's Laws) are

    If you would like to read some other explanations of parametric curves, try looking at the following references.

    There will be a take home quiz handed out at the end of class today covering Sections 11.3 and 11.4. It will be due at the beginning of class Monday.

    For Monday, read Section 11.5 (pages 581-587 and skip the optional section on Kepler's Laws). In order to really understand Section 11.5, you will need to review a few previous sections from the textbook:

    The homework problems for Section 11.4 are

    Here is a summary of all the vector algebra rules from Sections 11.2, 11.3, and 11.4.

    If you would like to read some other explanations of the cross product, try looking at the following references.

    No class today.

    The quiz today is on Sections 11.1 and 11.2.

    For next Wednesday, read Section 11.4.

    Today we will start Section 11.3.

    The homework problems for Section 11.3 are

    If you would like to read some other explanations of the dot product, try looking at the following references.

    The first quiz will be Wednesday on Sections 11.1 and 11.2.

    For Wednesday, read Sections 11.3 and 11.4.

    Today we will cover Sections 11.1 and 11.2.

    The homework problems for Section 11.1 are

    The homework problems for Section 11.2 are

    If you would like to read some other explanations of 3D Cartesian coordinates, try looking at the following references.

    If you would like to read some other explanations of vectors, try looking at the following references.