Announcements
Solutions to midterm exam
Here is the final exam and my solutions.
- In pdf: final.pdf.
- In pdf: final_answers.pdf.
- For LaTeX source, check the directory: final/.
Have a great holiday and see you in the new year for math 208.
Homework for the weekend
Read through sections 9.6 on the derivatives of functions defined implicitly. The worked examples in section 9.7 should be very helpful guides for doing the exercises in section 9.8. Here are some problems to work on this weekend:
- Miscellaneous: Exercises 3, 4, 13 from Section 8.24
- Derivatives of functions defined implicitly: Ex 1, 4, 6 from Section 9.8.
There will be an extra review class 9:30-11:30am Tuesday, December 16 in Kiely 319.
Final Exam
The final exam is on Tuesday, December 23 from 4:00-6:00pm in Kiely 326.
The exam will cover all of chapters 1, 2, 3, 4, 5, 8 in the book, sections 7.1-7.12, and sections 9.6, 9.7.
The final exam will be on Tuesday, December 23 from 4:00-6:00pm in Kiely 326.
Homework for the weekend
This weekend, study all of chapter 8 in Apostol. We covered everything, except the chain rule, so be sure to pay particular attention to material on the chain rule so you can do the problems from section 8.22.
- Section 8.14: 1a, 2a, 3, 4, 10, 11
- Section 8.22: 8, 9a, 10, 11b, 14, 15
- Section 8.24: 2
On Tuesday, I'll ask each of you to put your solutions to these problems on the board.
Homework for the Wednesday
Read through sections 8.13 in the book and do a few exercises.
- Sec 8.5: 1e, 1h, 4, 5, 6, 8
- Sec 8.5: 1, 2, 3, 4, 5, 6, 10, 11
My plan for Wednesday is to go over the material in 8.10-8.13, and I'll probably get to the chain rule (sec 8.15).
Homework for the weekend
We'll be spending the rest of the semester doing nonlinear analysis. To prepare for class next week, read sections 8.1-8.2 in the book and do the following exercises in section 8.3 (page 245-247).
- 1a, 2a, 2b, 2g 2h, 3a, 3c, 4a, 4b, 5a, 5c, 5e, 6a, 6b, 6c, 6d, 6e, 6f, 6i, 6j, 6k, 7b, 7c, 8a, 8d, 8e, 9a, 9b, 10, 12
Feel free to read ahead about continuity and differentiability, but be sure to spend a significant amount of time studying the basic material in 8.1 and 8.2 on open balls and open sets.
Solutions to midterm exam
Here is the midterm exam and my solutions.
- In pdf: midterm.pdf.
- In pdf: midterm_answers.pdf.
- For LaTeX source, check the directory: midterm/.
Have a great holiday. Be sure to read through the first few sections of chapter 8.
Practice Exam Answers
Here are answers and notes about the practice exam.
- Practice Exam practice_exam_answers.pdf or LaTeX: practice_exam_answers.tex
Practice Exam and reminder
There will be an exam in class on Tuesday, November 25 over linear algebra with applications to approximating functions and differential equations. In addition to the problems already assigned, I assembed some problems into a practice exam. Get started early and work on it over the weekend and early next week.
Remember, there will be no class and no office hours on Tuesday, November 18. So, post questions to the forum or bring them to class on Thursday next week.
- Practice Exam practice_exam.pdf or LaTeX: practice_exam.tex
I briefly began "nonlinear analysis". If you want to take a break from linear algebra problems, read through the first few sections of chapter 8.
Homework for the weekend
I organized lecture notes from today's class into a few problems, beginning with the problem about finding exp(B) from problem set 2. I called it problem set 2.5. Do it over the weekend.
Homework and Problem Set 2 due date
Confusingly, I put the wrong due date on the recent problem set. It's due on Tuesday, November 4.
Here's another problem to do for homework this weekend: diagonlize the symmetric matrix below by explicitly following the proof of the spectral theorem.
As a starting point, the vector is an eigenvector.
Reading, problems, and a problem set
We finished chapter 4 and are up to section 5.6 in the book. Here are some exercises:
- Section 4.8, exercises 3, 4, 6, 7, 13, 14
- Section 4.10, exercises 1, 2, 4, 7, 8
- Section 5.5 exercises 3, 4, 6, 7, 9
I picked out a few problems from the text and made one or two up for a problem set to be turned in on October 31.
Reading and problems
After finishing with determinants, we defined eigenvectors and eigenvalues in class on Thursday, The revelevant sections in the book are 4.1, 4.2, 4.3. Be sure to study the statements and work through the proofs of the basic theorems. Here are a few problems that involve knowing the the definition of an eigenvalue and eigenvector:
- Section 4.4, exercises 1, 2, 3, 4, 6, 10.
Reading and problems
Be sure you've read all of chapter 2 in the book and the beginning of chapter 3 (up to 3.10). Here's some homework, due Tuesday, October 13.
- Section 2.16, exercises 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13
- Section 2.20, exercises 1, 3, 5, 7, 9, 11, 13
- Section 2.21, exercises 1, 2, 3, 4, 7, 8
- Section 3.6: exercise 1, 2, 6
- Section 3.11: exercise 1, 7
Problem set 1 solutions
Here are my solutions to the problem set:
A few announcements
Here's a schedule for the next few weeks:
- Tuesday, September 23: No Class
- Tuesday, September 25: No Class
- Tuesday, September 30: Problem Set 1 Due
- Thursday, October 2: No Class
Also, I revised the problem set, making it a little more coherent, so be sure to get a revised copy: ps1.pdf
As indicated on the schedule above, we don't have class again until the problem set is due. So, if you have questions, get them answered! Find answers in the book (relevant sections are 1.1--2.11 (pages 1-49) and/or post questions on the forum.
Reading
To prepare for Thursday's class, read sections 2.1, 2.2, and 2.3 in the book (this is just three pages).
To test your understanding of the definition, do exercises 1-28 in section 2.4 (pages 35-36).
Problem set 1
I wrote a few problems for you to work on. Due Monday, September 29.
Homework for the weekend
Be sure you've read through all of chapter 1 in the book. Pay particular attention to orthogonal projection and the Gram-Schmidt algorithm in sections 1.15 and 1.16, which are the only subjects in chapter 1 that we haven't covered in class yet.
Do the following exercises in Section 1.17 on page 30:
- 1, 2, 4, 5, 6, 7, 8, 9, 10
Homework
We've covered all the material through section 1.10 in the text. Next, read sections 1.11 and 1.12 and do the following exercises in section 1.13:
- 1, 4, 7, 8, 9, 10, 11, 12, 13.
Also, here's quiz1.pdf from class today.
Homework
Read sections 1.1 through 1.9 (pages 1-13) in the book. Here are some exercises from Section 1.10 (pages 13-14) :
- Exercises 1-20, 21, 22, 23 (a) (d) (e) (g) (h) and 24.
Information about Piazza
The math 207 discussion forum is hosted on Piazza. I encourage you to post questions and answers about the course on the Q & A page of the forum. The link to the forum is piazza.com/qc.cuny.edu/fall2014/math207.
Welcome to Math 207
This page will contain announcements. For now, take a look at the syllabus, which has practical information such as references, office hours, and a calendar.