Math 235: Calculus III (Spring 2018)

Contents

Syllabus

Download the course syllabus here. The syllabus contains essential information about the course (textbook, prerequisites, course description, material covered, etc.). Note that the syllabus only mentions the first edition of the textbook but it is outdated: you should get the second edition (see below).

Textbook

The official textbook for this course is: Multivariable Calculus (2nd Edition) by W. Briggs, L. Cochran and B. Gillett, published by Pearson. Click here for the full reference.

Note: The syllabus only mentions the first edition but it is outdated: you should get the second edition. Note that Multivariable Calculus (2nd Edition) corresponds to Chapter 8-14 of the book Calculus: Early Transcendentals (2nd Edition), so it is fine if you have the latter.

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: 1:30-2:30pm, Smith Hall 308
Wednesday: 1:30-2:30pm, Smith Hall 308

Course policies

Your overall grade for the course will be a precise combination of:

1. Your global quiz grade $G_1$. There will be about 9 quizzes in the semester. Each quiz grade will be automatically scaled to a grade /100, and at the end all the quiz grades, dropping the lowest two, will be averaged to a global quiz grade.
2. Your global midterm grade $G_2$. There will be two midterm exams, whose grades will be automatically scaled to grades /100, and then averaged to a global midterm grade.
3. Your final exam grade $G_3$. There will be one final exam, whose grade will also be automatically scaled to a grade /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 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 this course 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 01/17 Discussion of Course Policies
Introduction to the Course
Chapter 11: Vectors and Vector-Valued Functions
11.1 Vectors in the Plane
First day of class
Mon 01/22 11.1 Vectors in the Plane Review Lecture Notes No Quiz
Last DROP day
01/23
01/24
Wed 01/24 11.2 Vectors in 3D Space Review Lecture Notes
(11.1 Review Exercises)
11.1 Exercises 17-47, 59-75
Mon 01/29 11.2 Vectors in 3D Space
11.3 Dot Products
Review Lecture Notes Quiz #1
Quiz #1 Solutions
Wed 01/31 2x2 and 3x3 Determinants
11.4 Cross Products
Review Lecture Notes
11.2 Ex. 9-12, 15-20, 23-26, 45-50, 57, 67-72
Mon 02/05 Generalities on Sets and Functions
11.5 Lines and Curves in 3D Space
Review Lecture Notes
11.3 Ex. 9-24, 66, (76-80), 84-87
11.4 Ex. 7-8, 13-38, 49-52
Quiz #2
Quiz #2 Solutions
Wed 02/07 11.5 Lines and Curves in 3D Space Review Lecture Notes
Mon 02/12 11.6 Calculus of Vector-Valued Functions Review Lecture Notes
11.5 Ex 9-32, 47-48, 67, (50-55, 60-66, 75-76)
Quiz #3
Quiz #3 Solutions
Wed 02/14 11.7 Motions in Space Review Lecture Notes
11.6 Ex 7-30, 41-66, 68-71, 78-83
Mon 02/19 11.7 Motions in Space Review Lecture Notes
11.7 Ex 7-18, 25-36, 43-46, 63, 65
Quiz #4
Quiz #4 Solutions
Wed 02/21 11.8 Lengths of Curves
11.9 Curvature and normal vectors
Review Lecture Notes
11.7 Ex 37-42, 53, 58, (70, 71, 80)
Mon 02/26 Review Session Review Lecture Notes
11.8 Ex 9-26, 41-50, 51-53, (62, 63)
11.9 Ex 11-20, 27-34, 41-48 (not torsion), (50-54, 80)
Chapter 11 Review Ex 47, 56-57, 59-62, 70-71
No Quiz
Wed 02/28 EXAM #1 List of topics EXAM #1
EXAM #1 Solutions
Mon 03/05 Chapter 12: Functions of Several Variables
12.1 Planes and Surfaces
12.2 Graphs and Level Curves
No Quiz
Wed 03/07 CLASS CANCELLED Review Lecture Notes
12.1 Ex 11-38, 47-70, (72-78), 79, 80-89, (90-93)
CLASS CANCELLED (University closed for weather conditions)
Spring recess
03/10 - 03/18
Mon 03/19 12.1 Planes and Surfaces
12.2 Graphs and Level Curves
Review Lecture Notes
12.1 Ex 11-38, 47-70, (72-78), 79, 80-89, (90-93)
12.2 Ex 11-29
Quiz #5
Quiz #5 Solutions
Wed 03/21 CLASS CANCELLED Review Lecture Notes
12.2 Ex 11-38
CLASS CANCELLED (University closed for weather conditions)
Last WITHDRAW day
03/26
Mon 03/26 12.4 Partial Derivatives
12.6 Directional Derivatives and Gradient
Review Lecture Notes
12.2 Ex 11-38
No Quiz (Will be given as homework)
Wed 03/28 12.8 Maximum/Minimum Problems Review Lecture Notes
12.4 Ex 11-44
12.6 Ex 7-32, (39-50, 65-68)
Quiz #6
Quiz #6 Solutions
Mon 04/02 Review Session Review Lecture Notes
12.8 Ex 9-34, (36), 39-42, 53-56
(Chapter 12 Review Ex 2-3, 6-7, 23-30, 39-44, 59-70, 84-87)
Exam #2 Review Exercises
No Quiz
Wed 04/04 EXAM #2 List of topics EXAM #2
EXAM #2 Solutions
Mon 04/09 Chapter 13: Multiple Integration
13.1 Double Integrals over Rectangular Regions
No Quiz
Wed 04/11 13.7 Change of variables in multiple integrals Review Lecture Notes
13.1 Ex 5-36, (43-50), 55
Mon 04/16 Chapter 14: Vector Calculus
14.1 Vector Fields
Review Lecture Notes
13.1 Ex 5-36, (43-50), 55
Quiz #7
Quiz #7 Solutions
Wed 04/18 14.2 Line Integrals Review Lecture Notes
14.1 Ex 6-16, 25-31, 37-40
Mon 04/23 14.3 Conservative Vector Fields Review Lecture Notes
14.2 Ex 11-24, 31-38, 47-48, 54-55, (60)
Quiz #8
Quiz #8 Solutions
Wed 04/25 14.4 Green's Theorem Review Lecture Notes
Homework Problem
14.3 Ex 9-19, 27-29, 33-36, 39
Mon 04/30 Review Session Review Lecture Notes
14.4 Ex 11-21, 33, 58, 60
No Quiz
Mon 05/07 FINAL EXAM List of topics FINAL EXAM
Time: 8:30 - 11:30am
Location: Smith B-25