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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 Note that the syllabus only mentions the first edition of the textbook but it is outdated: you should get the second edition (see below).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Note: The syllabus only mentions the first edition but it is outdated: you should get the second edition.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 814 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: 9:30am11:20am, Smith Hall B25
Wednesday: 9:30am11:20am, Smith Hall B25
Office hours:
Monday: 1:302:30pm, Smith Hall 308
Wednesday: 1:302:30pm, Smith Hall 308
Course policies
Grading policy
Your overall grade for the course will be a precise combination of:
 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.
 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.
 Your final exam grade $G_3$. There will be one final exam, whose grade will also be automatically scaled to a grade /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 makeup exam if the reason of absence is not serious or the notice is too short. There will be no makeup 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.
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 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 email 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 email).
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 VectorValued 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 

Last ADD day 01/24 

Wed 01/24  11.2 Vectors in 3D Space 
Review Lecture Notes (11.1 Review Exercises) 11.1 Exercises 1747, 5975 

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. 912, 1520, 2326, 4550, 57, 6772 

Mon 02/05 
Generalities on Sets and Functions 11.5 Lines and Curves in 3D Space 
Review Lecture Notes 11.3 Ex. 924, 66, (7680), 8487 11.4 Ex. 78, 1338, 4952 
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 VectorValued Functions 
Review Lecture Notes 11.5 Ex 932, 4748, 67, (5055, 6066, 7576) 
Quiz #3 Quiz #3 Solutions 
Wed 02/14  11.7 Motions in Space 
Review Lecture Notes 11.6 Ex 730, 4166, 6871, 7883 

Mon 02/19  11.7 Motions in Space 
Review Lecture Notes 11.7 Ex 718, 2536, 4346, 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 3742, 53, 58, (70, 71, 80) 

Mon 02/26  Review Session 
Review Lecture Notes 11.8 Ex 926, 4150, 5153, (62, 63) 11.9 Ex 1120, 2734, 4148 (not torsion), (5054, 80) Chapter 11 Review Ex 47, 5657, 5962, 7071 
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 1138, 4770, (7278), 79, 8089, (9093) 
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 1138, 4770, (7278), 79, 8089, (9093) 12.2 Ex 1129 
Quiz #5 Quiz #5 Solutions 
Wed 03/21  CLASS CANCELLED 
Review Lecture Notes 12.2 Ex 1138 
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 1138 
No Quiz (Will be given as homework) 
Wed 03/28  12.8 Maximum/Minimum Problems 
Review Lecture Notes 12.4 Ex 1144 12.6 Ex 732, (3950, 6568) Quiz #6 Quiz #6 Solutions 

Mon 04/02  Review Session 
Review Lecture Notes 12.8 Ex 934, (36), 3942, 5356 (Chapter 12 Review Ex 23, 67, 2330, 3944, 5970, 8487) 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 536, (4350), 55 

Mon 04/16 
Chapter 14: Vector Calculus 14.1 Vector Fields 
Review Lecture Notes 13.1 Ex 536, (4350), 55 
Quiz #7 Quiz #7 Solutions 
Wed 04/18  14.2 Line Integrals 
Review Lecture Notes 14.1 Ex 616, 2531, 3740 

Mon 04/23  14.3 Conservative Vector Fields 
Review Lecture Notes 14.2 Ex 1124, 3138, 4748, 5455, (60) 
Quiz #8 Quiz #8 Solutions 
Wed 04/25  14.4 Green's Theorem 
Review Lecture Notes Homework Problem 14.3 Ex 919, 2729, 3336, 39 

Mon 04/30  Review Session 
Review Lecture Notes 14.4 Ex 1121, 33, 58, 60 
No Quiz 
Mon 05/07  FINAL EXAM  List of topics 
FINAL EXAM Time: 8:30  11:30am Location: Smith B25 