Course Title MATH 1201-Q-2 CALCULUS III
Time (7/6 - 8/14) MTWR 1:00-2:35pm
Location Room 520, Mathematics Building
Instructor Qing Lu
Email qinglu(at)math.columbia.edu
Office Hour RM 408, Wednesdays 2:40P - 3:40P
TA Ion Mihalescu
Email igm2103(at)columbia.edu
Help Room RM 406, Mathematics Building. Schedule: http://www.math.columbia.edu/department/mathhelp.shtml
(You are encouraged to visit the Help Room to ask questions about the course material. If it is not a special question related to this class only, you can ask any TA there.)
HOMEWORK LINK
http://sites.google.com/site/summercalculus3/
COURSE DESCRIPTION
This is a standard Calculus III course. The course will follow the textbook closely, covering (not exhaustively) Chapters 12, 13, 14.
The first half of this course is not about calculus but about algebraic techniques for describing geometry in two and three dimensions. For example, there are special ways of "multiplying" points in the plane (the product of complex numbers) and points in space (the cross product of vectors), both of which have geometric as well as algebraic significance.
The second half of the course is about differential calculus applied to functions of two variables and to curves in space. The lines and planes studied in the first part here appear as first order approximations, i.e. derivatives. Conics (ellipses and hyperbolas) appear as second order approximations, allowing us to distinguish maxima, minima and saddle points.
TEXTBOOK
Calculus, Early Transcendentals, by James Stewart (6th edition)
LECTURES SCHEDULE
This schedule is tentative and may be modified as necessary.
| Week | Date | Topic | Sections | |
| 1 | 07/06/08 | Monday | Three-dimensional Coordinate Systems | Sec 12.1 |
| 07/07/08 | Tuesday | Vectors | Sec 12.2 | |
| 07/08/08 | Wednesday | The Dot Product | Sec 12.3 | |
| 07/09/08 | Thursday | The Cross Product | Sec 12.4 | |
| 2 | 07/13/08 | Monday | Equations of Lines and Planes | Sec 12.5 |
| 07/14/08 | Tuesday | Cylinders and Quadric Surfaces | Sec 12.6 | |
| 07/15/08 | Wednesday | Vector Functions and Space Curves | Sec 13.1 | |
| 07/16/08 | Thursday | Derivatives and Integrals of Vector Functions | Sec 13.2 | |
| 3 | 07/20/08 | Monday | Arc Length and Curvature | Sec 13.3 |
| 07/21/08 | Tuesday | Motion in Space: Velocity and Acceleration | Sec 13.4 | |
| 07/22/08 | Wednesday | Review | Sec 12.1 - 13.4 | |
| 07/23/08 | Thursday | Midterm | Sec 12.1 - 13.4 | |
| 4 | 07/27/08 | Monday | Functions of Several Variables | Sec 14.1 |
| 07/28/08 | Tuesday | Limits and Continuity | Sec 14.2 | |
| 07/29/08 | Wednesday | Partial Derivatives | Sec 14.3 | |
| 07/30/08 | Thursday | Tangent Plane and Linear Approximations | Sec 14.4 | |
| 5 | 08/03/08 | Monday | More about Parital Derivatives; The Chain Rule | Sec 14.5 |
| 08/04/08 | Tuesday | Directional Derivatives and the Gradient Vector | Sec 14.6 | |
| 08/05/08 | Wednesday | Maximum and Minimum Values | Sec 14.7 | |
| 08/06/08 | Thursday | Lagrange Multipliers (1) | Sec 14.8 | |
| 6 | 08/10/08 | Monday | Lagrange Multipliers (2) | Sec 14.8 |
| 08/11/08 | Tuesday | Review | ||
| 08/12/08 | Wednesday | Review | ||
| 08/13/08 | Thursday | Final Exam | ||
COURSE REQUIREMENT
Homework
- There will be homework assignments every week. The homework will be due on Thursdays before class or at the beginning of class.
- No late homework will be accepted. No exceptions.
- Please
staple your homework.
Quizzes
- There will be short quizzes (about 10 minutes) every Monday. These are to make sure that you study regularly.
Exams
- Midterm: July 23.
- Final exam: August 13 or 14.
Grading Scheme
The final grade will be determined from the following (tentative) weights:
- Homework: 20%
- Quizzes: 15%
- Midterm: 25%
- Final exam: 40%
POLICIES
Attendance
Attendance is not required, but strongly encouraged, as this summer course is very intensive. You will have to work everyday to keep up with the class, but you can see your harvest at the end of the course.
Reading Assignments
- It
is strongly suggested that you read over the textbook after the class,
review the definitions and theorems, go through the examples,
understand (not just memorize) the underlying principles, etc. If you
have questions during reading, please do not hesitate to see the
instructor or TA. Don't leave a question for too long.
- You are encouraged to preview the textbook before each class.
- I may sometimes assign reading materials in the book which we do not have time to cover in class.
Class Participation
- You are welcomed to raise any question during the class. There is no stupid
question. And your question would be inspiring for the other students and the instructor, too.
- Do not hesitate to tell me if I am going too fast, too slow, or if you want me to speak louder, etc. I deeply appreciate your help on improving my teaching.
Make-up Exams
There will be no make-up exam without a note from a doctor or the dean.
ENJOY IT!
Calculus
is exciting and full of fun! Just imagine how elegantly it
describes the orbits of planets around the sun ... Make some effort,
and you will manage this powerful tool to explore the Nature, the
financial world, etc.