Calculus

Mathematics 69.102 (Fall 2001 - Winter 2002)

Website URL: http://www.carleton.ca/~angelo/calculus/cal102.html

Office Hours:
Monday, April 15, 12:00 - 4:00 p.m., Herzberg 4250.
Friday, April 26, 2:00 - 5:00 p.m., Herzberg 4250.

EXTRA CLASS: Monday, April 8, 2:00 p.m. in Herzberg 4351 (the Colloquium Room).

Revised: April 23, 2002
New Classroom: Loeb C264 (as of Jan. 3)

INSTRUCTOR:
Angelo B. Mingarelli, Professor
Office: Herzberg Physics  #4250
Tel/Fax: (613) 520 3534
Electronic mail : angelo@math.carleton.ca
Office Hours: TBA. when not lecturing or by appointment.

TEXTBOOK(S):
Mainly Chapter 6 of my Calculus by Angelo B. Mingarelli (Solutions Manual on this web site), cost: $59.95 +GST; available from the Bookstore or from the Instructor.

UPDATED PDF FILES to SOLUTIONS MANUAL!!

Solutions Manual August, 2001 edition only) Chapters1-6 only (*.PDF file, needs Adobe Acrobat or recent version of Netscape)
Solutions Manual    Solutions to Sections 7.1 and 7.2 ONLY (*.PDF file, needs Adobe Acrobat or recent version of Netscape)
Solutions Manual Solutions to Sections 7.3-end (Also as a PDF file)

TOPICS COVERED:
Mostly topics from the 69.104 outline but with proofs. However, see the Detailed Class Oultine below for an extensive list of topics from the Calendar.

PREREQUISITES:
(i)  A pre-university calculus course with a grade of 65 percent or better; and
(ii) An OAC in Algebra and Geometry, or Mathematics 69.017*, or permission of the School. (See Prerequisites for First-year Calculus and Algebra Courses in the Calendar)
Note: Although the main prerequisite for Mathematics 69.102 is a grade of 65 percent or better in a pre-university calculus course, past experience indicates that students with less than 75 percent in their prerequisite calculus have only a small chance of success in Mathematics 69.102.

EVALUATION
Your grade will be calculated as:
(i) Term Mark 60%;
(ii) Christmas Examination 20% and Final Examination, 20%
OR
Christmas Final 50 % and final exam 50%, whichever of the two gives you the highest grade.

TERM MARK:
This will be derived from:
1) 8 term tests (best 6 chosen) for a total of 30% of your term mark.
2) Routine problems using WebCT will be assigned weekly for practice purposes: Use your Chat account name for login and your student number for your password.
3) Around 14 weekly quizzes over the two terms (best 10 chosen) will be given for the remaining 30%.
4) 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 listed in the Calendat. 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 6, 2001

LECTURE SCHEDULE:
Mondays, Loeb C264, 9:30 a.m.
Wednesdays, Loeb C264,  8:30 a.m.
Thursdays, Loeb C264, 10:30 a.m.
 

TUTORIALS:
All tutorials are held on Tuesdays at 12:30 p.m. (and will begin Tuesday, Sept. 18) in  either Rooms 501 or 505 Southam Bldg.
Tuesdays 12:30 p.m. - 1:30 p.m.

1A       Family name: A - Mc: 501 SA  (SA=Southam Bldg) Yanjuan Cheng ycheng@math.carleton.ca :  Tue. 13:30--14:30   HP4367
2A       Family name: Me - Z: 505 SA  Esteban Gomez-Rivière , egrivier@chat.carleton.ca: Mr. Gomez-Rivière's office hours are Wed. from 2:30 to 3:30.
 

STATUTORY HOLIDAY:
The University is closed October 5 and October 8. As well, there are no UNDERGRADUATE CLASSES on University Day.
WINTER BREAK: Feb 18-22, 2002

CLASSES END:
Monday, early December 2001.

TUTORIAL CENTRE:
Please note that the mathematics TUTORIAL CENTRE , in Herzberg Physics Building, Room 4385, will be opening around Sept. 21, 2001
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

Mathematics 69.102 (Calculus)

This course is strongly recommended for students intending to specialize in mathematics, statistics, physics, or related areas. Limits, differentiation, the definite integral, elementary functions, techniques of integration, parametric equations and polar coordinates. Improper integrals, L'Hôpital's rules, sequences and series, Taylor's formulae, introduction to differential equations. Precludes additional credit for Mathematics 69.104*, 69.105*, 69.107*, 69.109*, 69.207*, and for 69.201, 69.202.
 
 

Fall-Winter, 2001-2002. TENTATIVE OUTLINE


 
WEEK DATES TESTS SECTIONS TOPICS
  Sept. 6  None  See Notes Introduction and History of the Calculus
Sept.10 
Sept.12 
Sept. 13

WebCT quiz
try it out!
Chapter 1 and 
See Notes
Review of basic Calculus: Absolute values, the Box Method (for composition of functions), Inequalities
 Sept. 17 
Sept. 19 
Sept. 20
WebCT quiz 
Tutorial Quiz

See Notes
Point sets and their properties, Topology of the real line: neighborhoods, open sets and their properties
Sept. 24 
Sept. 26 
Sept. 27
TEST 1
Tutorial room 

See Notes
Closed sets, Formal language and quantifiers
Oct. 1 
Oct. 2 
Oct. 4 
Oct. 5

Tutorial Quiz

Notes

Formal language and quantifiers (continued), Methods of mathematical proof (direct, by contradiction, contrapositive, case by case, induction, etc.) 
Oct. 8
Oct. 10 
Oct. 11
WebCT quiz 
Tutorial quiz
Chapter 2 and 
Chapter 6

Limits and Continuity (formal definitions)
Oct. 15 
Oct. 17 
Oct. 18
WebCT quiz 
TEST 2
Tutorial Room 

Chapter 6

Limits and Continuity (continued),  Axiom of Continuity, Dedekind sections, Least Upper Bound Theorem, Limits of sequences
Oct. 22 
Oct. 24 
Oct. 25

Tutorial quiz

Notes

Points of accumulation, Bolzano-Weierstrass Theorem, Heine-Borel Theorem, Uniform continuity
8 Oct. 29 
Oct. 31 
Nov. 1
WebCT quiz 
TEST 3
Tutorial Room 

Chapter 3 
Notes

Differentiability (Product and Quotient Rules, The Chain Rule and its applications, Mean Value Theorem, Rolle's Theorem), 
9 Nov. 5 
Nov. 7 
Nov. 8

WebCT quiz 
Tutorial quiz

Chapter 3

L'Hospital's Rule, Implicit Function Theorem (and implicit differentiation)
10   Nov. 12 
 Nov. 14 
Nov.15
WebCT quiz 
TEST 4
Tutorial Room 

Chapter 3 
Chapter 4

Euler's Exponential function and its derivative, The natural logarithm
11  Nov. 19 
Nov. 21 
Nov. 22
WebCT quiz 
Tutorial quiz
    Chapter 7 
      Notes

The Integral and techniques of integration: Substitution
12   Nov. 26 
Nov. 28 
Nov. 29
WebCT quiz 
Tutorial quiz 
Final 2000 Exam in
69.104
Chapter 8 
Notes 

Integration by parts, Taylor's formula with remainder, Integration by partial fractions 
Final 2000 Exam in 69.104 (PDF file)
TERM 2 DATES TESTS SECTIONS TOPICS
13  Jan.3, WebCT quiz  Chapter 8  Trigonometric substitutions, Improper integrals
14 Jan. 7 
Jan. 9 
Jan. 10
WebCT quiz 
Tutorial quiz

Chapter 9 

Applications of the integral: Area between two curves, Volume of a solid of revolution,
15  Jan. 14 
Jan 16 
 Jan. 17

WebCT quiz 
Tutorial quiz

Chapter 5

Review of curve sketching in Cartesian coordinates (maxima, minima, inflection points, etc.), 
16  Jan. 21 
Jan. 23 
Jan. 24
WebCT quiz 
TEST 5
Tutorial room 

Notes

Polar coordinates, Curve sketching in polar coordinates 
Notes on polar coordinates
Exercises on plots in polar coordinates
17  Jan. 28 
Jan. 30 
Jan. 31
WebCT quiz 
Tutorial quiz

Notes

Curve sketching in polar coordinates 
Notes for weeks 15-16-17
Exercises on describing regions in polar and cartesian coordinates
18  Feb. 4 
Feb. 6 
Feb. 7
WebCT quiz 
Tutorial quiz

Notes

Sequences and series 
Notes for week 18
Exercises on sequences and series
19  Feb. 11 
Feb. 13 
Feb. 14
WebCT quiz
TEST 6
Tutorial Room 

Notes

Convergent sequences in Euclidean space, Series with non-negative terms, The Comparison Test, Telescoping series 
Exercises on series
20 Feb. 18
Feb. 20
Feb. 21
 
WINTER BREAK
21 Feb. 25 
Feb. 27 
Feb. 28

Tutorial quiz

Notes
Cauchy's convergence criterion, Inferior and Superior Limits, 
More exercises on Sequences
The Ratio Test,
22 Mar. 4 
 Mar. 6 
Mar. 7
WebCT quiz
TEST 7
Tutorial Room 

Notes
Taylor series and a series for the arctan function, The Integral Test 
More exercises on Series
Alternating series: Dirichlet Test for convergence, Absolute and conditional convergence
23 Mar. 11 
Mar. 13 
Mar. 14

Tutorial quiz 

Notes

Differential equations (an existence and uniqueness theorem) 
Exercises on Differential Equations
24 Mar.18 
Mar. 20 
Mar. 21
WebCT quiz 
TEST 8
Tutorial Room 
Chapter 10 

Applications of differential equations
25 Mar. 25 
Mar. 27 
Mar. 28 
Mar. 29
Apr. 4
None 
 
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