Course website for Fall 2008 16C (Short Calculus)

General information

Course code: MAT - 016C - 3
CRN: 79781
Professor: Alexander Coward
Main course textbook: Calculus: An Applied Approach, 7th Edition, by R. E. Larson, B. H. Edwards (Houghton Mifflin Co., 2006)
Sections to be covered: C.1-C.4; 7.1-7.6; 7.8-7.9; 10.1-10.6.

 

Lecture information

Lectures will all be held on Mondays, Wednesdays and Fridays at 1:10pm in Everson Hall, Room 176.

Because of Memorial Day, there will be no lecture on Monday, May 25th.

Homework

The homework for the course is listed below. It is set on a weekly basis. When you have finished a piece of homework, you should go to the Calculus Room or come to my office hours to get help with anything you don't understand and to get general feedback on your work. Remember, it is your responsibility to make sure you are keeping up with the course, and only by doing the homework will you know that you are keeping up.

Assessment

The assessment for this course will be in the form of two midterm exams and one final exam. The first midterm will take place in class on Monday, April 20th. The second midterm will take place in class on Monday, May 11th. The final examination will take place on Wednesday, June 10th at 8am.

Your overall grade will be calculated as follows. Your final will count for 50%. Your midterms will count for 25% each.

The use of calculators, books or notes will not be allowed in the examinations, but is positively encouraged when completing the homework. There'll be no make-up examinations.

Syllabus

The syllabus for the course is everything covered in lectures as well as everything in the relevant sections of the course book. The sylabus is based around the one available here.

How to get help

The are several ways that you can get help with this course. They are:
  1. The Calculus Room (Mathematical Sciences Building, Room 3118) This is open from 11am until 6pm, Monday to Friday and will usually be the best place for you to get help. There are people there who specialize in helping students out in Calculus, and they'll be happy to give you as much help as you need. Don't forget to take your homework along with you and ask them what's good about it, and how you could do better.
  2. My office hours You can come to see me in my office (Room 2214, Mathematical Sciences Building) on Mondays and Fridays between 2:10pm and 3pm.
  3. The Internet Calculus is an old subject and there are plenty of resources online that you may find helpful. In particular try visiting www.calculus.org.
  4. Each other Don't forget to talk to your friends about the course and help each other out.
One of the keys to your success in this course is accessing the support that is available to you. Make sure you get help when you need it.

Computer resources

There are several mathematical computer programs which will be illuminating for you to experiment with. I particularly like Maple and there others such as Mathematica and MatLab which you might also like to try. To use these programs you will need to set up an account. Follow this link to do so.

There is a good tool for plotting graphs here.

Course syllabus, timetable and homework

Week 1 (Commencing Monday, March 30th. Three lectures.)

Topics to be covered: Review of calculus from 16A and 16B. Definition of a differential equation. Solving differential equations by separating variables. Exponential growth and decay formulas.
Reading: Sections C.1 and C.2.
Homework: Chapter 6 Review Exercises: 5, 7, 13, 29, 31, 43; C.1: 13, 17, 28, 29, 45, 61; C.2: 5, 9, 10, 13, 16, 19, 22, 24, 26, 27, 29, 33, 37, 43. This should be done by Monday, April 6th.

Week 2 (Commencing Monday, April 6th. Three lectures.)

Topics to be covered: Solving linear first order differential equations using the integrating factor method. Identifying when to use the integrating factor and when to use separation of variables. Some applications of differential equations.
Reading: Sections C.3 and C.4.
Homework: C.3: 9, 11, 12, 13, 16, 18, 21, 27, 31, 33, 34; C.4: 5, 9, 15, 29. This should be done by Monday, April 13th.

Week 3 (Commencing Monday, April 13th. Three lectures.)

Topics to be covered: Three-dimensional coordinates. Planes and quadric surfaces. Functions of several variables. Level curves.
Reading: Sections 7.1, 7.2 and 7.3.
Homework: 7.1: 1, 7, 9, 15, 23, 25, 29, 33, 35, 47; 7.2: 1, 5, 9, 13, 15, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53; 7.3: 4ce, 13b, 15, 17, 20, 23, 24, 26, 27, 33, 35. This should be done by Monday, April 20th.

Week 4 (Commencing Monday, April 20th. Two lectures. Midterm One on Monday.)

Topics to be covered: Partial derivatives.
Reading: Section 7.4.
Homework: 7.4: 3, 8, 9, 14, 15, 16, 17, 21, 25, 29, 39, 40, 41, 49, 57, 59, 61, 66, 68a. This should be done by Monday, April 27th.

Week 5 (Commencing Monday, April 27th. Three lectures.)

Topics to be covered: Relative extrema for functions of two variables. Lagrange multipliers.
Reading: Sections 7.5 and 7.6.
Homework: 7.5: 7, 15, 19, 21-24, 25, 27, 34; Ch. 7 RE: 67; 7.6: 4, 5, 8, 11, 13, 16, 17, 20, 21, 33, 35. This should be done by Monday, May 4th.

Week 6 (Commencing Monday, May 4th. Three lectures.)

Topics to be covered: Double integrals. Applications of double integrals. Volume.
Reading: Sections 7.8 and 7.9.
Homework: 7.8: 2, 3, 9, 11, 14, 15, 20, 31, 33, 35, 36, 37, 38; 7.9: 15, 17, 22, 23. This should be done by Monday, May 11th.

Week 7 (Commencing Monday, may 11th. Two lectures. Midterm Two on Monday.)

Topics to be covered: Sequences and series. Meaning of convergence. Geometric series.
Reading: Sections 10.1 and 10.2.
Homework: 10.1: 5, 12, 13, 14, 17, 20-23, 27, 34, 35, 36, 38, 41. This should be done by Monday, May 18th.

Week 8 (Commencing Monday, March 30th. Three lectures.)

Topics to be covered: Tests for converence.
Reading: Section 10.3.
Homework: 10.1: 31, 37, 53, 55, 66, 69a, 71; 10.2: 20*, 24-27, 30, 34*, 39*, 44, 47, 51, 52, 53; 10.3 - 7, 9, 15, 17, 19-23, 41, 45-48. (* without a utility) This should be done by Monday, May 25th.

Week 9 (Commencing Monday, March 30th. Two lectures. No lecture on Monday because of Memorial Day.)

Topics to be covered: Power series, Taylor’s Theorem. Maclaurin series for sine and cosine, binomial series. Taylor polynomials.
Reading: Sections 10.4 and 10.5.
Homework: 10.4: 7, 10, 12, 15, 16, 25, 29, 30, 32, 33, 35, 41, 44, 45, 48, 51, 54; 10.5: 1, 3, 5, 17, 21, 23. This should be done by Monday, June 1st.

Week 10 (Commencing Monday, March 30th. Two lectures. Wednesday is the last lecture.)

Topics to be covered: Newton’s Method.
Reading: Section 10.6.
Homework: 10.6: 1, 3, 6, 7, 10, 13, 16, 31, 33, 35. This should be done by Monday, June 8th.