The text for the whole course is available on line:
The course consists of four blocks of material. There will be a test on each of these blocks in recitation about one week after all of the material has been covered in lecture.
The first block is focused on the differential calculus in several variables. The subtitle for this part of the course could be Gradients, Hessians, Jacobians, and what they are good for. This material is covered in Chapters 0, 1 and 2 of the text. (The short Chapter 0 will probably be a warm up review for most people).
The second block is devoted to the eigenvalue problem which is all about finding eigenvalues and eigenvectors of square matrices. In our case, this will be the Hessians adn Jacobians that we met in the first block. Many applications of the differential calculus require us to find eigenvalues and eigenvectors of Jacobian and Hesisan matrices. Jacobian matrices are not always square, and singular values are the relevant concept in that case. The material in this block is essential for effective application multivariable calculus in more than two variables, but it has many, many other uses as well, particulalry in graphics, computer vision and robotics. This material is covered in Chapters 3 and 4 of the text.
The third block is devoted to the prediction and description of motion. This is once again differential calculus per se. We will see how to describe curves through differential equations. A key concept here is a vector field as description of motion. We also study rigid body motion, which leads us into the space of three dimensional rotations. This material is covered in Chapter 5 of the text.
The fourth block is devoted to integration in several variables. Special emphasis will be placed on topics that are relevant to probability theory, and are designed to provide background for the probability course that is required in ther degree sequence. This material is covered in Chapter 6 of the text.
First Unit: The
Differential
Calculus of Functions of Several Variables
Week 1: (Aug 20, 22, 24, August 24 last day to register and/ or make schedule changes)
Both sections of Chapter 0 of the text. There are problems at the end
of each section. These are the homework, and will prepare you for the
first quiz,
which will be Thursday, Aug 28 in recitation.
Please think about forming study
groups, anywhere from 3-5 students is ideal.
You may also want to read about this material in the Salas and Hille textbook (Ninth edition), if you have it. Lines and planes, with reference to tangent lines and planes are discussed in section 15.4. Continuity is discussed in sectio 14.5 and 14.6. The theorem that applies continuity to minimum and maximum problems is in section 15.6.
Week 2: (Aug 27, 29,31)
Sections
1, 2 and 3 of Chapter 1. Do all of the problems at the end of each
section
for homework.
Suggested method: form a study group, and divide them up. Explain your
solutions to each other.
Quiz 1: August 28, in recitation, 20 minutes.
Week 3: (Sept 5, 7, Sept 3 is a holiday) Sections 4 and 5 of Chapter 1. Do all of the problems at the end of each section for homework.
Here are two practice quizzes. Quiz 2a, (solution), Quiz 2b (solution).
Quiz 2 on Sep 11 in recitation, 20 minutes.
Week 6: (Sep 24, 26, 28,
Progress report due for 1000 and 2000 level courses)
Sections
2 and 3 of Chpater 2. Do all of the problems at the end of each section
for homework.
Here is a java
applet in Newton's method in two variables that lets you see it in
action.
Test 1 on Sep 25 in recitation. 50 minutes.
Second Unit: Calculating
Eigenvalues
and Eigenvectors -- Iterative Methods
Week 7: (Oct 1, 3, 5)
Sections
1, 2 and 3 of Chapter 3. Do all of the problems at the end of each
section for homework.
Week 8: (Oct 10, 12, Oct 8, 9
fall recess, Oct 12 last day to withdraw from the course with `w') Sections 4 and 5 of Chapter 3. Do all of the problems at the end of
each section for homework.
Here is a Maple worksheet for Jacobi's algorithm
Quiz 3: October 11, in recitation. 20 minutes.
Prepquiz one (solution) and Prepquiz two (solution) .
Week 9: (Oct 15, 17, 19) Sections 1, 2 and 3 of Chapter 4. Do all of the problems at the end of each section for homework.
Here are additional
notes on the power method for finding eigenvectors. And here is a Maple
worksheet to go along with this. You must
have Maple installed to use this. If it is not on your own computer,
you can use it in one of the labs.
Third Unit: Prediction and description of motion
Please read over section 6 in chapter 4. This will be useful in what follows.
Week 12:
(Nov 5, 7, 9)
Sections 3 and 4 of Chapter 5. Do all of the problems at the end of
each section for homework.
Quiz 4:
November 6, in recitation. 20 minutes. Here is the first practice quiz, (solution) and here is the second practice quiz.
(solution)
Week 13: (Nov 12, 14, 16) Sections 5 and 6 of Chapter 5. Do all of the problems at the end of each section for homework.
Fourth Unit: Integration in several variables
Week 14: (Nov 19, 21, Nov 22-23 holiday, Thanksgiving) Finish Chapter 5. Do all of the problems at the end of each
section for homework.
Test 3: November 20, in
recitation. 50 minutes.
Week 15: (Nov 26, 28, 30)
Sections 1 and 2 of Chapter 6. Do all of the problems at the end of each section for
homework
Week 16: (Dec 3, 5, 7) Section 3 of Chapter 6 and review.
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December 10-14 Final Exam
The exam is cumulative.