Advanced Calculus

Mathematics 70.200 ( Fall, 1999 - Winter, 2000)

Website URL: http://www.carleton.ca/~amingare/calculus/cal200.html

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.
 

CLASSES BEGIN:

Thursday, September 9, 1999
 

LECTURE SCHEDULE:

Mondays, 306 Dunton Tower, 8:30 a.m.
Thursdays, 306 Dunton Tower, 10:00 a.m.
 

TUTORIALS:

All tutorials are held on Thursdays at 1:30 p.m. and will begin the week of Sept. 21 in  Room 506 Southam Bldg.
 

STATUTORY HOLIDAY:

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

TUTORIAL CENTRE:

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

Detailed Class Outline

Winter, 1998

WEEK  DATES  TESTS  SECTIONS  TOPICS 
Sept. 9  None  Chapter 5.1-2 Point Sets, Review of Limits and Continuity
Sept.13 
Sept.16 
None  Chapter 5.3, 
Chapter 6.0-1-2
Continuity,  Functions of several variables, 
Partial derivatives, Implicit functions 
Sept. 20 
Sept. 23
None  Chapter 6.3 
Chapter 6.4 -5
Maxima and Minima, 
Differentials and The Chain Rule
Sept. 27 
Sept.30
TEST 1 
Tutorial room 
Chapter 6.52, 6.6 
Chapter 6.8
Second order partials, Implicit differentiation, Lagrange's Method
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
Oct. 14  None  Chapter 7.6 Relative extrema: Second Derivative Test
Oct. 18 
Oct. 21
TEST 2 
Tutorial Room 
Chapter 8.1 
Chapter 9.1
Implicit Function Theorem 
Inverse Function Theorem
Oct. 25 
Oct. 28
None  Chapter 12.1-2 
Chapter 12.3
Differentials and Differentiability 
Newton's Method
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 
 Chapter 13.3
Chapter 13.6-7
General iterated integrals 
Triple integrals, Application to volume and centroids
13  Nov. 29  None 
 Chapter 13.8-9 
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 
 Chapter 21.4
Chapter 21.5
Abel's Theorem and applications of series 
Inferior and Superior Limits
26  Mar. 26
Mar. 30
None 
 Chapter 21.6 
Real Analytic Functions
REVIEW