Calculus III (MATH V1201-002, Spring 2008)


Basic information

Day & Time: Monday and Wednesday 11:00 am-12:15pm

Location:  312 Mathematics Building

Instructor: Christophe Breuil

Office Hours: Wednesday 4.00 pm-6.00 pm in Math 415

Teaching Assistants : Melanie Busch and Michael Lock 

Textbook: James Stewart, Calculus: Early Transcendentals sixth edition, Brooks/Cole-Thomson Learning, Belmont, CA, 2003. ISBN 0534393217. It is available at the University bookstore.

Prerequisites: Calculus I, II (or the equivalent).

Examinations: There will be two in class tests. The first will be on Feb. 20 and the second on March 31. The final exam is scheduled on Monday, May 12, 9.00 am-12.00 am in  Math 312.



Policies & Procedures

Goals: At the end of the course, students should be able to:
(i) make calculations with agility, accuracy, intelligence and flexibility;
(ii) explain the basic concepts of calculus clearly and reason logically with them;
(iii) solve extended problems, with good judgment in the choice of tools and in checking answers.

Expectations: To achieve these goals, students are expected to:
(i) read each section of the textbook before the material is presented in class;
(ii) attend the lectures;
(iii) complete all homework assignments;
(iv) eventually discuss mathematics with other students.

Assessment: The course grades will be computed as follows:
20% Homework
20% First test
20% Second test
40% Final exam

Tests and Exams: There are no makeups for missed tests.

Homework: There will be two kinds of homework each week:
(i) Exercises to practice. They give you a chance to refine your basic calculus skills. They will not be collected but are important.
(ii) Exercises due. They consist of a few exercises that will be collected at the beginning of the next Monday class.
Late homework will not be accepted. Graded homework can be found on a box on a table near the office 415.

Written work: We write to communicate. Please bear this in mind as you complete assignments and take exams. You must explain your work in order to obtain full credit. AN ASSERTION IS NOT AN ANSWER. For specific suggestions see A guide to writing in mathematics classes.

Contacting me: I only meet students during my office hours (unless the issue is very urgent) and I do not answer emails.

Help: Help is available if you have trouble with homework or lecture material at the Mathematics Help Room (333 Milbank Hall, on the Barnard campus). You may drop by whenever the Help Room is open as no appointment is necessary.

Calculators: Calculators — in particular graphing calculators — are not required for this course. If you have one, you are welcome to use it when you do your homework. However, calculators will not be allowed during any tests or exams.

Disabilities: People with disability problems that have extended time at midterms and exams must pass their midterms/exams at the Office of Disability.




 Schedule

Class Topic Read   Exercises to practice
Exercises due
Jan.23
Coordinates
§12.1 p.769 Ex.1, 2, 3, 5, 9, 10, 11
p.769 Ex.13,14,15,16,21,33  (due Jan.28)
Jan.28
Vectors and coordinates §12.2 p.777 Ex.2,3,4,5,6,7-12,13-16
p.777-778 Ex.17,19,24,37,38,39,41 (due Feb.4)
Jan.30
Dot product §12.3 p.784-785 Ex.1,2,3-10,13,15,16,17
p.785 Ex.19,25,26,27,34,41,50 (due Feb.4)
Feb.4
Cross product §12.4 p.792 Ex.1-7,8,9-12,13,14,15
p.792-793 Ex.16,19,29,37,38,43,44 (due Feb.11)
Feb.6
Equations of lines and planes
§12.5 p.802 Ex.6-12,19,20,23,24,27,43
p.803-804 Ex.49,56,58,59,63,64,73 (due Feb.11)
Feb.11
Polar and spherical coordinates §10.3,15.8
p.647-648 Ex.1,2,3,4,5,6,7-12
p.1010 Ex.1,2,3,4,5,6
p.648 Ex.14,30,35,36,46,51 (due Feb.18)
p.1010 Ex.7,8 (due Feb.18)
Feb.13 Cylindrical coordinates, cylinders and quadric surfaces §12.6,15.7
p.811 Ex.11-20,21-28
p.811 Ex.32,34,43,45,46,49 (due Feb.18)
Feb.18 Review: Practice midterm I  Solutions: here


Feb.20 Midterm I  Solutions: here



Feb.25 Complex numbers. Complex exponentials App. H p.A64 Ex.1-14,15-17
p.A64 Ex.21,24,27,29,36,47,48 (due Mar.3)
Feb.27 Vector functions and space curves §13.1 p.822 Ex.1,2,3-6,7,8,15,16
p.822-823 Ex.9,13,18,19-24,26,38 (due Mar.3)
Mar.3 Derivative and integral of vector functions §13.2 p.828-829 Ex.1,2,3,4,5,9,10,11,12
p.828-829 Ex.8,14,16,18,26,37,48,51 (due Mar.10)
Mar.5 Arc length and curvature
§13.3 p.836 Ex.1,2,3
p.836 Ex.4,5,6,14,15,16 (due Mar.10)
Mar.10 Curvature, normal vectors and osculating circles
§13.3 p.837 Ex.17-19,21-23,33,43,45
p.837-838 Ex.20,24,44,46,49,51,53 (due Mar.24)
Mar.12 Velocity and acceleration §13.4 p.846-847 Ex.3-8,9-14
p.847 Ex.15,21,22,23,25,29 (due Mar.24)
Mar.24 Tangential and normal components of acceleration §13.4 p.847 Ex.33,34
p.847 Ex.36,37,38 (due Mar.31)
Mar.26 Review: Practice midterm II  Solutions: here



Mar.31
Midterm II  Solutions: here


Apr.2 Functions of several variables §14.1 p.866-867 Ex.6,7,10,11,12,16,17,21 p.866-868 Ex.8,9,14,15,20,26,40,42 (due Apr.7)
Apr.7 Limits and continuity §14.2 p.877 Ex.5,6,7,8,9,11,12,13,17,18 p.877 Ex.6,10,14,15,22,30,41 (due Apr.14)
Apr.9 Partial derivatives §14.3 p.889-890 Ex.15-21,57-60,61-68
p.889-890 Ex.22,28,37,42,73,76,77 (due Apr.14)
Apr.14
Tangent planes, linear approximations §14.4 p.899 Ex.1-6,11-16,17
p.899-900 Ex.18,19,25-30 (due Apr.21)
Apr.16 The chain rule §14.5 p.907 Ex.1-5,7-11
p.907-909 Ex.6,12,13,20,23,24,46 (due Apr.21)
Apr.21 The gradient vector I
§14.6 p.920 Ex.4,5,6,7,8,9,11,12,13,14
p.920-922 Ex.10,15,17,18,20,28,35 (due Apr.28)
Apr.23 The gradient vector II §14.6 p.920-921 Ex.21-24,39,40,41,43
p.920-922 Ex.25,26,32,42,44,49,53 (due Apr.28)
Apr.28 Maximum and minimum values §14.7 p.931 Ex.5-15
 p.931-932 Ex.18,20,34,42,49 (due May 5)
Apr.30
Lagrange multipliers §14.8 p.940 Ex.3-11
 p.940-941 Ex.12,17,18,21,41 (due May 5)
May 5
Review: Practice final  Solutions: here



May 12
Final exam  Solutions: here