MATH 2210-3 Calculus III

MATH 2210-3 Calculus III - Fall 2007

Last modified: $LastChangedDate: 2007-12-08 21:28:27 -0700 (Sat, 08 Dec 2007) $

Class information

Time: 6pm-7:30pm
Days: Monday and Wednesday
Where: LCB 219
Textbook: Calculus, Varberg, Purcell and Rigdon (9th edition, Prentice Hall)
Material covered: Multivariate calculus (Chapters 11-14)
Prerequisites: MATH 1210 and MATH 1220 or equivalent.

Contact information

Instructor:Fernando Guevara Vasquez
Office: LCB 212
Office hours:MWF 10:30am-11:30am or by appointment (please see announcements below for any changes)
Phone: 801-581-7467
Email: fguevara(AT)math(DOT)utah(DOT)edu

Homework assignments and other announcements

Dec 8 2007

Typo: One of your colleagues pointed a typo in the mock exam that I posted online. In the solution to problem 1.b. the y component of r'(t) should be 10/(2*sqrt(10*t)) and not 5/(2*sqrt(10*t)). The corrected version is here: final_practice.pdf

Dec 6 2007

Reminder: The final exam is Monday Dec 10, 6pm-8pm in LCB 219.
The mock exam (+ correction) that we went over on Wed Dec 5 is available here: final_practice.pdf.

Nov 30 2007

Homework assignment #10 is due on Monday Dec 3. It is optional and will count as extra credit for up to half of a normal homework. It consists of 5 exercises:
14.2: 7, 19

14.3: 3, 13

14.4: 1 (a direct application of Green's Theorem (Theorem 14.4.A))
The program until the final is:
Mon 12/3: Collect HW10. Green's Theorem in the plane. Midterm #3 correction.

Wed 12/5: Get graded HW10 back. Review session for the final (we will go over a mock final exam).

Mon 12/10: Final exam (the conditions of the exam will be announced shortly).

Nov 16 2007

Here is a little write up that shows how thinking about the order of integation first can simplify your life when evaluating triple integrals: 13_7_21.pdf. It is a good exercise to verify that the different iterated integrals there represent the same triple integral.
And here are the Matlab files that I used in class to demonstrate transformations from the plane to the plane (change of variables): cov1.m, cov2.m, cov3.m, and cov4.m.

Nov 12 2007

Homework Assignemnt #9 is due on Monday Nov 19 2007 and contains 8 exercises.
13.5: 8

13.6: 13, 15

13.7: 25, 27

13.8: 9, 11, 21
Midterm #3 will be on Wed Nov 28, during class time and will cover Chapter 13. There will be a review on Mon Nov 26. More details on the last midterm will follow.
As a reminder the final exam is on Mon Dec 10 2007, at 6pm. This will be a comprehensive exam, i.e. it covers all the material we've seen in class. Our last class on Wed Dec 5 2007 will be a review.

Oct 29 2007

Homework assignment #8 is due on Mon. November 12 2007. It consists of 9 exercises. More than half of the problems have solutions in the book, this should help you avoid calculation errors. The answer to 13.3.22 can be easily checked using (area of base) x height / 3.

13.2: 10, 23

13.3: 7, 15, 22, 34

13.4: 5, 9 (see page 544 Example 3), 20

Office hours on F 11/9 and M 11/12 are cancelled. Substitute office hours: on Th 11/8 10am-11am, and on M 11/12 2pm-3pm.
I will give back your midterm #2 on Wednesday.

Oct 22 2007

Homework assignment #7 is due on Wed. October 24 2007. This is an extra credit assignment (worth one half of a normal assignment) that I recommend you do as practice for the Midterm. It is only one exercise: 12.9.22.
There will be no office hours on Wed. October 24 2007, since I am out of town to give a talk. I will be back in time for class though.

Oct 15 2007

Homework assignment #6 is due on Monday October 22 and consists of 11 problems.

12.6: 2, 12, 22

12.7: 4, 10, 16, 22

12.8: 4, 12, 16, 35 (note on problem 12.8.35: only the way to get to the answer will be evaluated, not the answer itself, as it is given in the book)

Midterm #2: will be on Wed October 31 at the regular class time and location (6pm-7:30pm, LCB219). The program is Chapter 12, and there will be a review session on Mon October 29. The test conditions will be the same as for Midterm #1, except that a calculator will be allowed. Any calculator with scientific functions should be enough.
Midterm evaluations: Look for an e-mail from the University of Utah Center for Teaching and Learning Excellence for further instructions. The evaluation is a simplified version of the evaluation at the end of the semester and runs from 10/15 to 10/22.

Oct 1st 2007

Homework assignment #5 is due on October 15 (Monday after the fall break)

12.3: 30

12.4: 4, 8, 18, 22

12.5: 6, 12, 14, 20, 30

The Matlab files that I used in class today are here: tgtplane.m which illustrates a tangent plane to a surface and gradfield.m for a gradient field.
The office hours of Friday Oct 4th are moved to Thursday Oct 3rd at the same time. There will be no office hours during the fall break. Questions by email are welcome anytime (including during the break).

Sept 24 2007

Homework assignment #4 is due on October 1st 2007.

12.1: 10, 20, 32

12.2: 16, 18, 34, 46a

12.3: 2, 6, 12

Sept 17 2007

The midterm of Wednesday September 19 is on Chapter 11 and will take place at the usual class time/location (6pm-7:30pm, LCB 219). Here are some guidelines for the exam:

Test problems will be along the lines of the textbook examples and homework problems. Please see the sample test problems that appear at the end of Chapter 11 (pp 614 -- 615)
The test will be 1.5 hours long
No calculators are allowed. The objective of the test is to find out if you understand the methods and concepts, so you will not be heavily penalized for little calculation mishaps.
A one sided, letter size (8.5" x 11"), handwritten, formula sheet is allowed, with reasonably sized font. Books (including the textbook) are NOT allowed.
Some students asked me about the possibility of taking the test earlier on Wednesday (4pm-5:30pm). If you are interested and really need to take the test earlier, please let me know by email as soon as possible
There will be no office hours on Friday Sept 21. If you have questions about Chapter 11, please feel free to email me or come by my office.

Sept 6 2007

Homework assignment #3 is short, and is due W Sept 12 in class.
11.7: 12, 18, 36, 46, 56, 60

Sept 3 2007

I will be out of town for the lectures of W Sept 5 and M Sept 10. These lectures will be given by Dan Ciubotaru.

Prof. Ciubotaru will return the graded HW1 and collect HW2, which is still due on W Sept 5.
There will be a short HW3 assigned on W Sept 5 (covering only 11.7). There will be no homework assigned on W Sept 12.
The midterm exam will be delayed to W Sept 19, with the lecture on M Sept 17 being a review of the material covered by the exam.
The office hours are cancelled up to M Sept 10. However, if you have questions please feel free to email me.

Aug 30 2007

Adeel will be giving weekly group tutoring sessions scheduled on Thursdays 6pm, room 152 of the Benny Rushing Mathematics Center (adjacent to LCB and JWB). The first session is next week (Sept 6).

Aug 29 2007

Homework #2, due W 09/05 in class.
11.4: 2, 4, 8, 18, 36

11.5: 6, 10, 12, 28, 40

11.6: 2, 6, 10, 14, 18, 24, 30

11.7: 6
Here are the curvature circle demos that I ran today. These are programs written for Matlab (or the open source alternative Octave): curv1.m (parabola) and curv2.m (ellipse). NOTE: there will be no Matlab assignments, so it's completely optional to look at these.

Aug 22 2007

Homework #1, due W 08/29 in class. (references relative to ninth edition of textbook).
11.1: 8, 14, 16, 18, 22, 28

11.2: 4, 6, 10, 12, 14, 18
11.3. 6, 8, 12, 14, 18, 20, 24, 26, 32, 34, 44, 54, 56, 66, 68, 74

General guidelines: Show your work. A right answer without proper explanation or the manipulations that lead to it, will not count for full credit. You may work in groups, however you must submit your own writeup of the solution.
Homework problem sets will be posted online, after class. Unless noted otherwise, homework is due in class.
Let me know if you have problems registering for the class because it is full.
The Mathematics tutoring center offers free, drop-in tutoring for students enrolled in this class. Hours are M-Th 8am-8pm, and F 8am-6pm (closed on weekends and university holidays). Group tutoring and group study rooms are available. Check the link above for more information. If there is enough interest, we can setup a regular (weekly) tutoring session.

Aug 20 2007

Homework assignments will be given in class, on this webpage and by email. Other announcements such as office hour changes, will go here also.

Homework, exams and withdrawal policies

Homeworks 30%, Final 30%, Midterms 40%
Expect one weekly homework assignment. No late homework will be accepted, but the two lowest homework scores will be dropped when finding the homework mean for the term.
Three midterms, tentatively on Monday Sep 17, Wednesday Oct 24 and Wednesday Nov 26.
Final exam date: Monday Dec 10 6pm-8pm in LCB219.
See the following links for the University of Utah withdrawal policy and the Fall 2007 academic calendar.

Students with Disabilities

The University of Utah seeks to provide equal access to its programs, services and activities for people with disabilities. If you will need accommodations in the class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Olpin Union Building, 581-5020 (V/TDD). CDS will work with you and the instructor to make arrangements for accommodations.

All written information in this course can be made available in alternative format with prior notification to the Center for Disability Services.

Also, please let me know at the beginning of the course, should you need special accomodations.

Tentative Calendar

M Aug 20	11.1, 11.2, 11.3	Cartesian coordinates, vectors, dot product.
W Aug 22	11.4, 11.5	Cross product, vector valued functions.
M Aug 27	11.5, 11.6	Curvilinear motion, lines, and tangent lines.
W Aug 29	11.7	Curvature and acceleration.
M Sep 3	Labor day
W Sep 5	11.8	Surfaces in dimension three.
M Sep 10	11.8, 11.9	Cylindrical and spherical coordinates.
W Sep 12	Review
M Sep 17	Midterm exam
W Sep 19	12.1, 12.2	Multivariate functions, partial derivatives
M Sep 24	12.3	Limits and continuity.
W Sep 26	12.4, 12.5, 12.6	Differentiability, directional derivatives and gradients, the chain rule.
M Oct 1	12.7	Tangent planes and approximations.
W Oct 3	12.8, 12.9	Maxima and minima, Lagrange multipliers.
M Oct 8	Fall break
W Oct 10	Fall break

M Oct 15	13.1, 13.2	Double integrals over rectangles, iterated integrals.
W Oct 17	13.3	Integrals over non-rectangular regions.
M Oct 22	Review
W Oct 24	Midterm exam
M Oct 29	13.4, 13.5, 13.6	Double integrals in polar coordinates, applications, surface area.
W Oct 31	13.7, 13.8	Triple integrals (cartesian, cylindrical and spherical coordinates).
M Nov 5	13.9	Change of variables in multiple integrals.
W Nov 7	14.1, 14.2	Vector fields, line integrals.
M Nov 12	14.3	Path independence of line integrals
W Nov 14	14.4	Green's theorem in the plane.
M Nov 19	14.5	Surface integrals.
W Nov 21	Review
M Nov 26	Midterm exam
W Nov 28	14.6	Gauss's divergence theorem.
M Dec 3	14.7	Stokes theorem. Review for final.
W Dec 5	Review
M Dec 10	Final exam.

Dec 8 2007	Typo: One of your colleagues pointed a typo in the mock exam that I posted online. In the solution to problem 1.b. the y component of r'(t) should be 10/(2sqrt(10t)) and not 5/(2sqrt(10t)). The corrected version is here: final_practice.pdf
Dec 6 2007	Reminder: The final exam is Monday Dec 10, 6pm-8pm in LCB 219. The mock exam (+ correction) that we went over on Wed Dec 5 is available here: final_practice.pdf.
Nov 30 2007	Homework assignment #10 is due on Monday Dec 3. It is optional and will count as extra credit for up to half of a normal homework. It consists of 5 exercises: 14.2: 7, 19 14.3: 3, 13 14.4: 1 (a direct application of Green's Theorem (Theorem 14.4.A)) The program until the final is: Mon 12/3: Collect HW10. Green's Theorem in the plane. Midterm #3 correction. Wed 12/5: Get graded HW10 back. Review session for the final (we will go over a mock final exam). Mon 12/10: Final exam (the conditions of the exam will be announced shortly).
Nov 16 2007	Here is a little write up that shows how thinking about the order of integation first can simplify your life when evaluating triple integrals: 13_7_21.pdf. It is a good exercise to verify that the different iterated integrals there represent the same triple integral. And here are the Matlab files that I used in class to demonstrate transformations from the plane to the plane (change of variables): cov1.m, cov2.m, cov3.m, and cov4.m.
Nov 12 2007	Homework Assignemnt #9 is due on Monday Nov 19 2007 and contains 8 exercises. 13.5: 8 13.6: 13, 15 13.7: 25, 27 13.8: 9, 11, 21 Midterm #3 will be on Wed Nov 28, during class time and will cover Chapter 13. There will be a review on Mon Nov 26. More details on the last midterm will follow. As a reminder the final exam is on Mon Dec 10 2007, at 6pm. This will be a comprehensive exam, i.e. it covers all the material we've seen in class. Our last class on Wed Dec 5 2007 will be a review.
Oct 29 2007	Homework assignment #8 is due on Mon. November 12 2007. It consists of 9 exercises. More than half of the problems have solutions in the book, this should help you avoid calculation errors. The answer to 13.3.22 can be easily checked using (area of base) x height / 3. 13.2: 10, 23 13.3: 7, 15, 22, 34 13.4: 5, 9 (see page 544 Example 3), 20 Office hours on F 11/9 and M 11/12 are cancelled. Substitute office hours: on Th 11/8 10am-11am, and on M 11/12 2pm-3pm. I will give back your midterm #2 on Wednesday.
Oct 22 2007	Homework assignment #7 is due on Wed. October 24 2007. This is an extra credit assignment (worth one half of a normal assignment) that I recommend you do as practice for the Midterm. It is only one exercise: 12.9.22. There will be no office hours on Wed. October 24 2007, since I am out of town to give a talk. I will be back in time for class though.
Oct 15 2007	Homework assignment #6 is due on Monday October 22 and consists of 11 problems. 12.6: 2, 12, 22 12.7: 4, 10, 16, 22 12.8: 4, 12, 16, 35 (note on problem 12.8.35: only the way to get to the answer will be evaluated, not the answer itself, as it is given in the book) Midterm #2: will be on Wed October 31 at the regular class time and location (6pm-7:30pm, LCB219). The program is Chapter 12, and there will be a review session on Mon October 29. The test conditions will be the same as for Midterm #1, except that a calculator will be allowed. Any calculator with scientific functions should be enough. Midterm evaluations: Look for an e-mail from the University of Utah Center for Teaching and Learning Excellence for further instructions. The evaluation is a simplified version of the evaluation at the end of the semester and runs from 10/15 to 10/22.
Oct 1st 2007	Homework assignment #5 is due on October 15 (Monday after the fall break) 12.3: 30 12.4: 4, 8, 18, 22 12.5: 6, 12, 14, 20, 30 The Matlab files that I used in class today are here: tgtplane.m which illustrates a tangent plane to a surface and gradfield.m for a gradient field. The office hours of Friday Oct 4th are moved to Thursday Oct 3rd at the same time. There will be no office hours during the fall break. Questions by email are welcome anytime (including during the break).
Sept 24 2007	Homework assignment #4 is due on October 1st 2007. 12.1: 10, 20, 32 12.2: 16, 18, 34, 46a 12.3: 2, 6, 12
Sept 17 2007	The midterm of Wednesday September 19 is on Chapter 11 and will take place at the usual class time/location (6pm-7:30pm, LCB 219). Here are some guidelines for the exam: Test problems will be along the lines of the textbook examples and homework problems. Please see the sample test problems that appear at the end of Chapter 11 (pp 614 -- 615) The test will be 1.5 hours long No calculators are allowed. The objective of the test is to find out if you understand the methods and concepts, so you will not be heavily penalized for little calculation mishaps. A one sided, letter size (8.5" x 11"), handwritten, formula sheet is allowed, with reasonably sized font. Books (including the textbook) are NOT allowed. Some students asked me about the possibility of taking the test earlier on Wednesday (4pm-5:30pm). If you are interested and really need to take the test earlier, please let me know by email as soon as possible There will be no office hours on Friday Sept 21. If you have questions about Chapter 11, please feel free to email me or come by my office.
Sept 6 2007	Homework assignment #3 is short, and is due W Sept 12 in class. 11.7: 12, 18, 36, 46, 56, 60
Sept 3 2007	I will be out of town for the lectures of W Sept 5 and M Sept 10. These lectures will be given by Dan Ciubotaru. Prof. Ciubotaru will return the graded HW1 and collect HW2, which is still due on W Sept 5. There will be a short HW3 assigned on W Sept 5 (covering only 11.7). There will be no homework assigned on W Sept 12. The midterm exam will be delayed to W Sept 19, with the lecture on M Sept 17 being a review of the material covered by the exam. The office hours are cancelled up to M Sept 10. However, if you have questions please feel free to email me.
Aug 30 2007	Adeel will be giving weekly group tutoring sessions scheduled on Thursdays 6pm, room 152 of the Benny Rushing Mathematics Center (adjacent to LCB and JWB). The first session is next week (Sept 6).
Aug 29 2007	Homework #2, due W 09/05 in class. 11.4: 2, 4, 8, 18, 36 11.5: 6, 10, 12, 28, 40 11.6: 2, 6, 10, 14, 18, 24, 30 11.7: 6 Here are the curvature circle demos that I ran today. These are programs written for Matlab (or the open source alternative Octave): curv1.m (parabola) and curv2.m (ellipse). NOTE: there will be no Matlab assignments, so it's completely optional to look at these.
Aug 22 2007	Homework #1, due W 08/29 in class. (references relative to ninth edition of textbook). 11.1: 8, 14, 16, 18, 22, 28 11.2: 4, 6, 10, 12, 14, 18 11.3. 6, 8, 12, 14, 18, 20, 24, 26, 32, 34, 44, 54, 56, 66, 68, 74 General guidelines: Show your work. A right answer without proper explanation or the manipulations that lead to it, will not count for full credit. You may work in groups, however you must submit your own writeup of the solution. Homework problem sets will be posted online, after class. Unless noted otherwise, homework is due in class. Let me know if you have problems registering for the class because it is full. The Mathematics tutoring center offers free, drop-in tutoring for students enrolled in this class. Hours are M-Th 8am-8pm, and F 8am-6pm (closed on weekends and university holidays). Group tutoring and group study rooms are available. Check the link above for more information. If there is enough interest, we can setup a regular (weekly) tutoring session.
Aug 20 2007	Homework assignments will be given in class, on this webpage and by email. Other announcements such as office hour changes, will go here also.