INSTRUCTOR:
Dr. Angelo B. Mingarelli,
Office: Herzberg Physics #4250
Tel/Fax: (613) 520 3534
Electronic mail: amingare@math.carleton.ca
Office Hours: Fridays, 0930-1130 a.m.
TEXTBOOK(S):
Advanced Calculus (Third Edition) by A.E.Taylor and W.R. Mann
available at the Bookstore and, in case you wish to review your epsilon
and deltas, Chapter 6 of my,
Calculus by Angelo B. Mingarelli (bundled with the Solutions
Manual), cost: $59.95 +GST; available from the Bookstore or from the Instructor.
TOPICS COVERED:
Third Edition: Mainly Chapters 5, 6, and 7, topics from 8 and
9 and then Chapters 13, 15, 19, 20 and 21.
PREREQUISITES:
The prerequisites for this course are:
69.102 or 207, (see the Calendar for more information).
Students who have not passed the prerequisite courses may be automatically
de-registered during the term. Those that have done poorly in the prerequisites
are strongly urged to get advice from the Mathematics Undergraduate Advisor
Ken Small, in 4380 Herzberg Building.
EVALUATION
Your grade will be calculated as:
(i) Term Mark 40%;
(ii) Christmas Examination 30% and Final Examination, 30%
TERM MARK:
The term mark will be derived from: 8 term tests (40/40): best 5 chosen.
Weekly assignments will be given but need not be handed in. The solutions
may be discussed with your Teaching Assistant (or the Instructor).
Note:The "best x of y" rules allow you to miss some of the term
events for any reason (medical or otherwise).
Only under highly exceptional circumstances will a test be postponed
to a later date.
SUPPLEMENTAL EXAMINATION
No Supplemental examinations
CALCULATORS
You may use a non-programmable calculator for the examinations
and tests in this course:
The Sharp 531-L is available at the Bookstore for ca. $19.95
+ Tax. Programming in C++ is strongly encouraged (but not on the examinations!).
WITHDRAWAL
The last date for withdrawal from the course is November 5, 1999. If
you decide to leave the course before the end of term, it is much better,
in terms of your academic career, to formally withdraw from the course
than to simply ignore it and get an F.
Thursday, September 9, 1999
Mondays, 306 Dunton Tower, 8:30 a.m.
Thursdays, 306 Dunton Tower, 10:00 a.m.
All tutorials are held on Thursdays at 1:30 p.m. and will begin the
week of Sept. 21 in Room 506 Southam Bldg.
The University is closed October 11. As well, there are no UNDERGRADUATE
CLASSES on October
8 as this is University Day
WINTER BREAK: Feb., 2000
CLASSES END:
Monday, December 6, 1999
Please note that the mathematics TUTORIAL CENTRE,
in Herzberg Physics Building, Room 4385, will be opening around Sept.
27, 1999
Tutors advertise frequently on the Notice Boards
around the Centre.
Hours for the center are as follows:
MONDAYS TO THURSDAYS: 10 AM TO 4 PM
FRIDAYS: CLOSED
| WEEK | DATES | TESTS | SECTIONS | TOPICS |
| 1 | Sept. 9 | None | Chapter 5.1-2 | Point Sets, Review of Limits and Continuity |
| 2 | Sept.13
Sept.16 |
None | Chapter 5.3,
Chapter 6.0-1-2 |
Continuity, Functions of several variables,
Partial derivatives, Implicit functions |
| 3 | Sept. 20
Sept. 23 |
None | Chapter 6.3
Chapter 6.4 -5 |
Maxima and Minima,
Differentials and The Chain Rule |
| 4 | Sept. 27
Sept.30 |
TEST 1
Tutorial room |
Chapter 6.52, 6.6
Chapter 6.8 |
Second order partials, Implicit differentiation, Lagrange's Method |
| 5 | Oct. 4
Oct. 7 |
None | Chapter 7.1-2-3
Chapter 7.4-5 |
Differentiability, Changing the order of diff'n.
Mean Value Theorem, Taylor's Theorem |
| 6 | Oct. 14 | None | Chapter 7.6 | Relative extrema: Second Derivative Test |
| 7 | Oct. 18
Oct. 21 |
TEST 2
Tutorial Room |
Chapter 8.1
Chapter 9.1 |
Implicit Function Theorem
Inverse Function Theorem |
| 8 | Oct. 25
Oct. 28 |
None | Chapter 12.1-2
Chapter 12.3 |
Differentials and Differentiability
Newton's Method |
| 9 | Nov. 1
Nov. 4 |
None | Chapter 16.6, 17.4
Chapter 18.1(11-12) |
Heine-Borel Th. and Uniform continuity
Riemann Integrability, Upper and lower sums |
| 10 | Nov. 8
Nov. 11 |
TEST 3
Tutorial Room |
Chapter 18.2
Chapter 18.6 |
The Integral as a limit of Riemann sums
Double integrals and Outer content of sets |
| 11 | Nov.15
Nov. 18 |
None | Chapter 18.61
Chapter 13.2 |
Double & Iterated integrals over rectangles
Integration over general regions |
| 12 | Nov. 22
Nov. 25 |
TEST 4
Tutorial Room |
|
General iterated integrals
Triple integrals, Application to volume and centroids |
| 13 | Nov. 29 | None |
|
Triple integrals in cylindrical and spherical coordinates |
| TERM 2 | DATES | TESTS | SECTIONS | TOPICS |
| 14 | Jan.6,
|
None | Chapter 15.1-2 | Point functions on curves and surfaces, Line integrals
|
| 15 | Jan. 10
Jan. 13 |
None | Chapter 15.51
Chapter 15.6, 15.61 |
Surface Integrals,
Divergence Theorem, Green's Identities |
| 16 | Jan. 17
Jan 20 |
None | Chapter 15.7
Chapter 15.3, 15.4, 15.41 Chapter 6.4 -5 |
Stokes' Theorem
Green's Theorem, Exact Differentials, Path Independence of a Line Integral Differentials and The Chain Rule |
| 17 | Jan. 24
Jan. 27 |
TEST 5
Tutorial room |
Chapter 16.31, 4, 41, 5
Chapter 19, 19.1, 11 |
Topics in Convergence: Convergent sequences in Euclidean
space
Cauchy's convergence criterion Series: Taylor series and a series for the arctan function |
| 18 | Jan. 31
Feb. 3 |
None | Chapter 19.2
Chapter 19.21, 22 |
Series with non-negative terms
The Integral and Ratio Tests |
| 19 | Feb. 7
Feb. 10 |
None | Chapter 19.3
Chapter 19.31, 32 Chapter 19.7 |
Absolute and conditional convergence
Rearrangement of terms in a series, Alternating series Dirichlet Test for convergence |
| 20 | Feb 14
Feb. 17 |
TEST 6
Tutorial Room |
Chapter 19.4
Chapter 19.5, 6 |
Tests for absolute convergence: Raabe, Gauss and Cauchy
Tests
Binomial Series, Multiplication of Series |
| 21 | Feb. 21
Feb. 24 |
WINTER BREAK | ||
| 22 | Feb. 28
Mar. 2 |
None | Chapter 20.0, 1
Chapter 20.2, 3 |
Uniform Convergence of Sequences and Series
Comparison Test for uniform convergence, Continuity of the Limit Function |
| 23 | Mar. 6
Mar. 9 |
TEST 7
Tutorial Room |
Chapter 20.4, 5
Chapter 21.0, 1 |
Integration and Differentiation of Sequences and Series
Power Series, Interval of Convergence |
| 24 | Mar. 13
Mar. 16 |
None | Chapter 21.2
Chapter 21.3 |
Differentiation of Power Series
Division of Power Series |
| 25 | Mar. 20
Mar. 23 |
TEST 8
Tutorial Room |
|
Abel's Theorem and applications of series
Inferior and Superior Limits |
| 26 | Mar. 26
Mar. 30 |
None |
|
Real Analytic Functions
REVIEW |