Math 300 [A02] – Advanced Calculus and Introductory Analysis
Course Outline
Department of Mathematics and Statistics, UVIC
September 2010.
INSTRUCTOR
Slim Ibrahim (ibrahim[at]math.uvic.ca); SSM Building A547; Phone: 853-3294.
Please do no leave a message; send an e-mail instead.
OFFICE HOURS
Mondays 3:30-4:30 & Thursdays 3:30-4:30, or by appointment.
COURSE WEBPAGE
http://www.math.uvic.ca/∼ibrahim/MATH300− fall10.html
Note: Announcements and Homework Assignments will be posted on the course webpage. Please
check the webpage regularly.
PREREQUISITES
Math 200 or 205 AND one of Math 110, 133, 211 or 233A.
LECTURES
Monday, Wednesday & Thursday: 2:30-3:20 pm, in CLE, D132.
TEXT
Advanced Calculus, by Gerald B. Folland, Prentice Hall 2002.
Used copies may be available at the UVic Bookstore or SUBtext.
TOPICS
Theory and applications of functions in multidimensional Euclidean space (Sections 1.1-1.3).
Basic topological properties of n-dimensional space: convergence, uniform continuity, completeness, compactness and connectedness (Sections 1.4 - 1.8).
Differentiation: chain rule, multidimensional Taylor’s theorem, applications to optimization (Sections 2.1-2.7 and 2.10).
Implicit and Inverse function theorems (Sections 3.1 - 3.4).
Integration over multidimensional volumes and surfaces: change of variables (Sections 4.4 - 4.6).
Divergence and Stokes’ theorems and applications (Sections 5.2 - 5.5, and 5.7).
Sequences and series of vectors and functions: convergence and uniform convergence of functional
series (Sections 6.1 - 6.4, and 7.1 - 7.3).
Fourier series: derivation, computation, convergence and applications (Sections 8.1-8.3).
HOMEWORK ASSIGNMENTS
Homework assignments will be given approximately every two weeks, and they will be collected
for marking. These marks will count for 15% of your final numerical grades.
EXAMINATIONS AND GRADING
There will be TWO MIDTERM TESTS on Wednesday October 20, and Wednesday November 17, and A FINAL EXAMINATION scheduled by the university (during December 06 - 20, 2010).
Calculators will not be permitted for midterm and final exams. If you have a legitimate
reason for missing the midterm (with documentation), then the weight of the midterm will be added
to that of the final exam. There will be NO make-up midterm.
Off-scheduled final examinations are not given except in cases of Illness, Accident or Family
Affiction at Exam Time, as per UVic calendar. To pass the course, you must pass the final
examination. Among those passing the final examination, their final numerical grades will be
determined as follows:
[1] Homework Assignments: 15%
[2] Two Midterm Tests: 25%
[3] Final Examination: 60%.
FINAL GRADE
The conversion of the final numerical grades to letter grades will be done using the Department
of Mathematics and Statistics Multi-Section Grading Policy. Details may be found online at
http://www.math.uvic.ca
Copies of this policy are also available at the department office (SSM Building, A425).
The following scale is customarily used to convert scores to final grades; (the department reserves
the right to modify this conversion scale).
90–100 85–89 80–84 75–79 70–74 65–69 60–64 55–59 50–54 0–49
A+
A
A–
B+
B
B–
C+
C
D
F
Guidelines on Religious Observances
1. Where classes or examinations are scheduled on the holy days of a religion, students may notify
their instructors, at least two weeks in advance, of their intention to observe the holy day(s) by
absenting themselves from classes or examinations.
2. Instructors will provide reasonable opportunities for such students to make up work or missed
examinations.
3. Students will cooperate by accepting the provision of reasonable opportunities for making up
work or missed examinations.
4. The University Secretary’s Office will distribute a multi-faith calendar to each academic unit
annually.
Posting of Grades
The practice developed for posting grades after the introduction of the Freedom of Information and
Protection of Privacy legislation has been changed. All four B.C. universities have agreed to post
grades by using the full student number, sorted numerically.
Two important provisos are that the students’ names are stripped and that students are given the
option at the beginning of the course to not have their grades posted.
Commitment to Inclusivity and Diversity
The University of Victoria is committed to promoting, providing and protecting a positive, and
supportive and safe learning and working environment for all its members.
Final Examination Period Students are strongly advised NOT to make final plans for travel or
employment during the exam period since special arrangements will NOT be made for examinations
that may conflict with such plans.