Math 235: Calculus III (Spring 2017)

Contents

Syllabus

Download the course syllabus here. The syllabus contains essential information about the course (textbook, prerequisites, course description, material covered, etc.).

Textbook

The official textbook for this course is: Calculus, Early Transcendentals by W. Briggs, L. Cochran and B. Gillett, published by Pearson. See this link for the full reference.

Note: Although the syllabus only mentions the first edition, getting the second edition is also fine. You may also get a digital version of the book. All you want to make sure is that your edition/version of the book contains chapters 11-14 (Multivariable Calculus), which are the only chapters we will cover in this course.

Class time and location & Office hours

Class time and location:

Monday: 9:30am-11:20am, Smith Hall B-25
Wednesday: 9:30am-11:20am, Smith Hall B-25

Office hours:

Monday: 2-3pm, Smith Hall 308
Wednesday: 2-3pm, Smith Hall 308

Course policies

1. Your global quiz grade $G_1$. There will be about 10 quizzes in the semester. Your quiz grades will be automatically scaled to grades out of 100 and then averaged to a global quiz grade, after dropping the lowest two grades.
2. Your global midterm grade $G_2$. There will be two midterm exams, whose grades will be automatically scaled to grades out of 100 and then averaged to a global midterm grade.
3. Your final exam grade $G_3$. There will be a final exam, whose grade will also be automatically scaled to a grade out of 100.
Note: Although your homework assignements will not be collected nor graded, they will often provide a basis for the quiz questions.

The formula for your overall grade $G$ for the course will be: $G = c_1 G_1 + c_2 G_2 + c_3 G_3$, where the coefficients $c_1$, $c_2$ and $c_3$ will be around $c_1 = 35\%$, $c_2 = 30\%$ and $c_3 = 35\%$. These coefficients may be subject to marginal change.

Finally, you will be assigned a letter grade for the course depending only on your overall grade $G$, according to the following table:

90% ≤ G ≤ 100% A
80% ≤ G < 90% B+
70% ≤ G < 80% B
60% ≤ G < 70% C+
50% ≤ G < 60% C
40% ≤ G < 50% D
0% ≤ G < 40% F

Note: There will be no exceptions to the grading policy described above.

Attendance & Excused absence policy

Attendance is mandatory: you are required to attend every class.

If you must miss a class for a legitimate reason, you are required to inform me as soon as possible and provide documentation for your absence. If you miss a midterm exam, there will not be automatically a make-up exam if the reason of absence is not serious or the notice is too short. There will be no make-up quizzes, even if you miss a quiz with a valid reason of absence.

Textbook vs Lecture notes

Although we will follow the outline of the textbook (Chapters 11 through 14) very closely, your lecture notes should always be your primary source of information. You can only be expected to know the contents of the lectures, unless you are explicitely asked to review specific segments of the textbook. Nevertheless, the textbook is a great secondary source of information and will be the main source of problems, which are of the utmost importance.

Calculator

You will never need to use a calculator in this course. Calculators will not be allowed during quizzes or exams.

Our goal is to provide all the resources necessary for you to succeed and learn great mathematics in the process, regardless of your background coming in. Nevertheless, you may find multivariable calculus very challenging. Attending every class is absolutely necessary to meet the challenge but in no way will it be sufficient. The key to your success rests on yourself: it will require hard work, including hours of study, lots of problem solving, and your active involvement in learning both in and outside of the classroom. Of course, you will be assisted in your efforts, and I encourage you to reach me as often as you need.

Contact

My e-mail is brice@loustau.eu. I encourage you to write with any questions.

My office is 308 in Smith Hall. You are welcome during office hours (see above), you may also see me outside of office hours by appointment (first send me an e-mail).

Course schedule

For general important dates in the semester, see the academic calendar here.

Refer to the course schedule below very regularly. It contains among other things the homework assignments and the past quizzes and exams.

This course schedule is only tentative: it is very much subject to change. Always refer to last version online, and make sure that you refresh the page.

Date Topic Homework assignment Special
Wed 01/18 Discussion of course policies
Introduction to the course
11.1 Vectors in the plane
First day of class
Mon 01/23 11.1 Vectors in the plane
11.2 Vectors in 3D space
Review lecture notes
Wed 01/25 11.2 Vectors in 3D space
11.3 Dot products
Review lecture notes
11.1 Ex. 1-43, 53-69 (1st edition)
11.1 Ex. 1-47, 59-75 (2nd edition)
Mon 01/30 11.4 Cross products Review lecture notes
11.2 Ex. 1-24, 39-50, (57-70) (1st ed.)
11.2 Ex. 1-24, 35-48, (49-56) (2nd ed.)
Quiz #1
Wed 02/01 Generalities on functions, functions of several variables, vector valued functions Review lecture notes
11.3 Ex. 1-5, 9-18, (66-70, 74-78) (1st ed.)
11.3 Ex. 1-5, 9-24, (76-80, 84-88) (2nd ed.)
Mon 02/06 11.5 Lines and curves in 3D space Review lecture notes
11.4 Ex. 1-5, 7-18, 23-32, 41 (1st ed.)
11.4 Ex. 1-5, 7-20, 28-38, 49-52 (2nd ed.)
Quiz #2
Wed 02/08 11.5 Lines and curves in 3D space
11.6 Calculus of vector-valued functions
Review lecture notes
11.5 Ex. 9-16 (1st ed.)
11.5 Ex. 9-16 (2nd ed.)
Mon 02/13 11.6 Calculus of vector-valued functions
11.7 Motions in space
Review lecture notes
11.5 Ex. 1-23, 37 (1st ed.)
11.5 Ex. 1-33, 47-48 (2nd ed.)
Quiz #3
Wed 02/15 11.7 Motions in space Review lecture notes
11.6 Ex. 1-55, (62-67) (1st ed.)
11.6 Ex. 1-67, (78-83) (2nd ed.)
Mon 02/20 EXAM #1 List of topics
11.7 Ex. 7-14, 19-24, (29-32), 41, 49-55
11.7 Ex. 7-18, 25-30, (31-36), 53, 61-67
EXAM #1
Wed 02/22 Exam #1 solutions Review lecture notes
Mon 02/27 11.8 Lengths of curves
11.9 Curvature
Review lecture notes No Quiz
Wed 03/01 12.1 Planes and surfaces
12.2 Graphs and level curves
Review lecture notes
11.8 Ex. 1-5, 7-22, 35-39, 46, 48 (1st ed.)
11.9 Ex. 1-5, 9-36, 44-47, 58-61, 73-75 (1st ed.)
11.8 Ex. 1-5, 7-26, 41-55, 62, 64-66 (2nd ed.)
11.9 Ex. 1-5, 11-34, 50-53, 64-67, 79 (2nd ed.)
Mon 03/06 12.2 Graphs and level curves Review lecture notes
Chapter 11 review exercises:
1-15, 21-22, 30, 34-38 (1st ed.)
1-17, 29-30, 46, 50-53, 56-62 (2nd ed.)
Quiz #4
Quiz #4 Solutions
Wed 03/08 12.2 Graphs and level curves
12.4 Partial derivatives
Review lecture notes
Review section 12.1 in textbook
12.1 Ex. 1-6, 11-32, 37-40, 42, 61, 63 (1st ed.)
12.1 Ex. 1-4, 5-38, 47-50, 52, 71, 79 (2nd ed.)
Spring recess
03/11 - 03/19
Mon 03/20 12.6 Directional derivatives and Gradient Review lecture notes
Review section 12.2 in textbook
12.2 Ex. 2-7, 11-25, 27-31, 34, 49 (1st ed.)
12.2 Ex. 2-7, 11-26, 29-35, 38, 53 (2nd ed.)
12.4 Ex. 1-4, 7-30, 53, 64-71, (77) (1st ed.)
12.4 Ex. 1-4, 11-44, 69, 80-87, (95) (2nd ed.)
Quiz #5
Wed 03/22 12.8 Maximum/Minimum problems Review lecture notes
12.6 Ex. 1-36 (1st ed.)
12.6 Ex. 1-42 (2nd ed.)
Mon 03/27 12.8 Maximum/Minimum problems
Review lecture notes
12.6 Ex. 1-36 (1st ed.)
12.6 Ex. 1-42 (2nd ed.)
Quiz #6
Quiz #6 Solutions
Wed 03/29 12.8 Maximum/Minimum problems Review lecture notes
12.8 Ex. 9-36, 53, 57, 71 (1st ed.)
12.8 Ex. 9-42, 61, 65, 79 (2nd ed.)
Mon 04/03 EXAM #2 List of topics EXAM #2
EXAM #2 Solutions
Wed 04/05 13.1 Double integrals over rectangular regions
Mon 04/10 13.2 Double integrals over general regions Review lecture notes
13.1 Ex. 9-26, 39-42 (1st ed.)
13.1 Ex. 5-34, 47-50 (2nd ed.)
Quiz #7
Quiz #7 Solutions
Wed 04/12 14.1 Vector fields Review lecture notes
13.2 Ex. 7-38 (1st ed.)
13.2 Ex. 7-52 (2nd ed.)
Mon 04/17 14.2 Line integrals Review lecture notes
14.1 Ex. 6-26, 25-43(1st ed.)
14.1 Ex. 6-16, 25-47 (2nd ed.)
Quiz #8
Quiz #8 Solutions
Wed 04/19 14.2 Line integrals
14.3 Conservative vector fields
Review lecture notes
14.2 Ex. 11-24, 31-38 (1st ed.)
14.2 Ex. 11-24, 31-38 (2nd ed.)
Mon 04/24 14.3 Conservative vector fields Review lecture notes
14.2 Ex. 11-24, 31-38, 52-53 (1st ed.)
14.3 Ex. 1-2, 9-14 (1st ed.)
14.2 Ex. 11-24, 31-48, 52-53 (2nd ed.)
14.3 Ex. 1-2, 9-14 (2nd ed.)
Quiz #9
Quiz #9 Solutions
Wed 04/26 14.3 Conservative vector fields
14.4 Green's theorem
Review lecture notes
14.3 Ex. 15-19, 27-29, 33-36, 39, (52-53) (1st)
14.3 Ex. 15-19, 27-29, 33-36, 39, (52-53) (2nd)
Mon 05/01 Review session Review lecture notes
14.4 Ex. 11-22 (1st edition)
14.4 Ex. 11-22 (2nd edition)
Mon 05/08 FINAL EXAM List of topics FINAL EXAM
Time: 8:30 - 11:30am
Location: Smith B-25