Math/MTHE 280

Advanced Calculus
Math/MTHE 280, Fall 2016

Home     Schedule and Homework
Daniel Offin (408 Jeffery Hall, 613-533-2407)
The lecture on Tuesday October 25, at 9:30 will be held as usual. NO cancellation.
Course overview:
How does one measure the luminosity of a star or a galaxy, or a light bulb? Calculus was invented in the late 17th century, to be able to understand complicated dynamical problems in three spatial dimensions, and one time dimension. Newton's solution of the two body problem (the sun and one planet as a first approximation) as parameterized curves in space, was a tour de force which revolutionized our understanding and gave the power of precise prediction for such dynamical problems. When Newton turned his attention to the dynamics of three bodies interacting with mutual gravitational attraction, his inability to solve this led him to remark to the astronomer John Machin that " his head never ached but with his studies on the moon". The 3-body problem thus became the most celebrated problem in mathematics. With the intervening years, calculus became an indispensible tool in the analysis and understanding of problems in geometry, topology, mechanics, dynamics, functional analysis, and probability. We will try to uncover the basics of this vast subject with attention to the basic principles of continuity, differentiability and integrability of real valued and vector valued functions and their operations. Computation and interpretation of derivatives, and integrals over various domains forms an important goal in the course. Luminosity turns out to be one example of what can be calculated with flux or surface integrals. Water flow or fluid flow or heat flow through a membrane are other examples. We will study these towards the end of the semester with the higher dimensional analogs of the fundamental theorem of calculus. .
TUES, 9:30-10:20 in 201 kINGSTON Hall
THURS, 8:30-9:20 in 201 Kingston Hall
Friday, 10:30-11:20 in 201 Kingston Hall
Tutorials will start second week of classes

Monday, 8:30-9:20 in 101 Jeffery Hall.
Tuesday, 8:30-9:20 in Stirling Hall Rm 414.
Tuesday, 2:30-3:20 in 101 Jeffery Hall.
I will prepare questions before each tutorial and post them on the website. Students are strongly encouraged to try to find solutions for these and other questions before the tutorial. Other questions in the problem sections at the back of each section we cover are relevant (see list of such questions on Schedule link), and should be attempted.
Office Hours:
Wednesday, 15:30-16:30, Tues, 15:30-16:30,Room 201 Jeffrey Hall and by appointment
There will be a ninety-minute midterm exam and a three-hour final exam. The midterm exam will be held on October 26 (evening), from 7:00 to 8:30 p.m. in Room TBA. The time and location for the final exam will be announced as they become available.
There will be ten homework assignments during the semester. Homework will be posted on the web page of the course and solutions will be posted after the homework is collected. Assignments will be due on Thursdays. You should submit your homework in class or in my office by 14:00. The marking should follow a simple pattern. I will ask markers to look at 3 questions, and mark each question out of 5. The student should get 5 for a complete or more or less complete answer, 2 or 3 marks if there is something important missing, and 0 if the question is answered incorrectly or has sigificant missing components. If the student does not prepare his or her solutions so that they can be read without spending too much time trying to decipher, then the marker should assign a mark of 0 or 2. Questions or comments are welcome! In calculating the total score for the homework, the lowest score will be dropped.
You should try the homework by yourself and then, for those questions you are unable to solve, get together with a few students and work on them together. Do not simply ask someone who has already solved a problem for the solution and do not copy a solution. If you solve a problem with a few other students you should write the solution out by yourself and make sure you understand the solution. Ask yourself if you could correctly answer the same question if it were to appear on the term test or the final examination. If you solve a problem with several other students and you all write the solution by yourselves the various solutions will be different at least in wording and presentation; as a general rule, the only way solutions will be identical (or nearly so) is if they are copied.
Vector Calculus by Susan Jane Colley, Third or Fourth Edition  
Students are also encouraged to look at and use other undergraduate texts on Vector Calculus or Multivariable Calculus in addition to the main text.
The final grade for the course will be calculated as follows:
Homework: 15%
Midterm exam: 25%
Final Exam: 60%
The numerical mark obtained by the above formula will then be converted to a letter grade according to the Queen's Official Grade Conversion Scale.
Academic Integrity:
Academic integrity (aka academic dishonesty) is taken seriously by the university, the faculty, and our department. The regulations dealing with academic integrity can be found at:
- for Arts and Science students, Regulation 1 in the Calendar or FAQ about Academic Integrity;
- for Applied Science students, Honesty.