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 and 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 22, 24, August
26 last day to register and/ or make schedule changes,
registration closes at 4 pm)
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, Sep 1
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 (10-th 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.
Concerning the Projects: Please create a web papge for the submission of the projects and send me the URL. The deadline for this is August 26 Midnight. This is the place where you will put all your projects for me to download.
Week 2: (Aug 29, 31)
Sections 1 and 2 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: Thursday, Sep 1, in
recitation, 20 minutes. Lecture
on Gradients
Week 3: (Sept 7, Sept 5 is a school holiday) Sections 3 and 4 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: Thursday Sep
15 in recitation, 20 minutes.
Week 6: (Sep 26, 28; Sep 30
Progress report due for 1000 and 2000 level courses)
Sections 1 (this is a review of Newton's method) and 2 (This deals
with optimizaation problems with more than one constraint) of
Chapter 2. Do all of the problems at the end of each section for
homework. Start reading Section 1 of Chapter 3.
There
will be a review session on Monday September 26 from 6-8 pm in
Skiles 202
Test 1 on Tuesday Sep 27 in recitation . 50 minutes. Everything we covered until and including Sep 21 might be on the test.
Second Unit:
Calculating Eigenvalues and Eigenvectors -- Iterative
Methods
Week 7: (Oct 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 14
last day to withdraw from the course with `W' by 4 pm) Sections
4 and 5 of Chapter 3. Do all of the problems at the end of each
section for homework.
Quiz 3: Thursday, October 13, in recitation. 20 minutes.
Prepquiz
3A (solution)
and Prepquiz
3B (solution)
.
Week 9: (Oct 19) (Oct 15-Oct 18 Fall recess) Sections 1 and 2 of Chapter 4. Do all of the problems at the end of each section for homework.
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 7, 9) Sections 3 and 4 of
Chapter 5. Do all of the problems at the end of each section for
homework.
Quiz 4:
Thursday, November 10 in recitation. 20 minutes.
Here is Prepquiz
4A, (solution)
and here is Prepquiz
4B.
(solution)
Week 13: (Nov 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 21, 23) (Nov 24-25 holiday, Thanksgiving) Finish Chapter 5.
Read Sections 1 and 2 of Chapter 6. Do all of the problems at
the end of each section for homework.
There will be a review session on Monday
November 21 from 6-8 pm in Skiles 202
Test 3: Tuesday
November 22, in reciation. 50 minutes. Everything
we covered until and including Nov 16 might be on the test.
Week 15: (Nov 28, 30) Continue reading Sections
1 and 2 of Chapter 6. Do all of the problems at the end of each
section for homework
Week 16: (Dec 5, 7) Section 3 of Chapter 6 and
review.
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The
Final Exam is on Monday, December 12, 2:50-5:40 pm in
Weber SSTIII Room 2
The exam is cumulative.