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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
Grading policy
Your overall grade for the course will be a combination of:
- 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.
- 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.
- 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.
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:
| Overall grade | Letter grade |
|---|---|
| 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.
General advice
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 |