Math 201-NYB-05 Integral Calculus

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```					                                                                             Math 201-NYB-05
Integral Calculus
Ponderation: 3-2-3            Credits: 2 2
3

Fall 2001
Periods:    B: 14 - 24 - 34 - 44 - 54                Gottfried Wilhelm von
Leibniz

Instructor:                               Steve Hardy                                            Telephone:                    656-6921 (ext. 272)
Office:                                   Room 334                                               Email:                        shardy@slc.qc.ca

Prerequisite:                             Differential Calculus (Math 201-NYA-05)

Textbook (optional):                      Stewart, James              Single Variable Calculus, 4th Ed.                  Brooks Cole Publishing Co. 1999
ISBN: 0-534-35563-3

Additional References:                    Larson & Hostetler                    Calculus
Anton, Howard                         Calculus with Analytic Geometry, 5 th Ed.
Swokowski, Earl W.                    Calculus of a Single Variable

Programme Objectives:                     In this course you will use the methods of integral calculus to study functions and problem solving (partially
satisfying objective 00UP for the Science Program). You will also apply what has been learned to one or
more subject in the sciences (partially satisfying objective 00UU for the Science Program).
More generally, you will learn
1) to solve problems systematically;
2) to reason logically;
3) to communicate in a clear and precise fashion;
4) to use previously acquired knowledge when dealing with new situations;
5) to use the appropriate information technologies;
6) to work autonomously;
7) the historical context of the concepts taught;
8) appropriate attitudes.

Course Objectives:                        The calculus courses introduce the student to that branch of mathematics called analysis. In this course the
student will learn to apply integral calculus methods to the study of functions and to problem solving. To
meet this objective, the student will learn:
1) to calculate the indefinite integral of a function
2) to calculate the definite integral over an interval as well as improper integrals
3) to represent concrete situations as differential equations and to solve simple differential equations
(separable variables)
4) to calculate areas, volumes and lengths as well as construct graphic representations of objects in
#2 and # 3
5)     Analyse the convergence of series

Course Description:                       The course will follow the lecture method with frequent problem solving interludes during which the
teacher will be available for individual help.
Student should feel free and are welcome to ask questions at any point during the lecture.

Integrative Activity:                     The integrative activity this semester is a multi-disciplinary study of the science of Working Out. This
course will, in conjunction with the other science disciplines, cover the calculus techniques needed for this
study. The assessment of this study will be done in the other science courses.

Absences:                                 Attendance is mandatory and a maximum of 7 absences will be tolerated (explained and/or unexplained).
More than the 7 absences may mean failure in the course.

Rules & Regulations:                      St. Lawrence Campus has definite regulations concerning cheating, plagiarism and the quality of written
English which are clearly indicated in the Student Handbook and the St. Lawrence Campus Prospectus. It
will be assumed that all students have read and understood these rules and regulations.
Course Content:
1. THE DEFINITE INTEGRAL:                               3. APPLICATIONS:
a) Antiderivatives and Substitution (U-sub.)            a) Differential Equations.
b) Sigma Notation and Area.                             b) Areas between curves.
c) The Definite Integral and “The Fundamental           c) Volumes of Solids of Revolution.
Theorem of Calculus”.                                d) Arc Length.
e) Area of Surface of Revolution. 1
f) Moments and Center of Mass. 1
g) Work. 1

2. TECHNIQUES OF INTEGRATION:                           4. INFINITE SEQUENCES AND SERIES:
a) Integration by Parts.                                a) Sequences.
b) Trigonometric Integrals.                             b) Series (general, telescoping, arithmetic,
c) Trigonometric Substitution. (trig-sub.)                 geometric, harmonic, p)
d) Inverse Trigonometric Substitution. (Z-sub.) 1       c) Tests for Convergence (Divergence,
d) Long Division and Partial Fractions.                    Comparison, Integral, Ratio, Root, Limit
e) Rationalizing Substitution. (V-sub.)                    Comparison, Alternating).
1                                 f) Using Table of Integrals. 1                          d) Power Series and Radius of Convergence.
These topics will only
g) Improper Integrals.                                  e) McLaurin and Taylor Series.
be covered if time
h) Numerical Integration. 1                             f) Taylor Polynomials and their Remainders.
allows.

Evaluation:
Criteria:             The evaluation in this course will verify that students have learned:
1) to use the appropriate concepts
2) to adequately represent surfaces in #2 and # 3
3)    to choose and apply the correct rules and integration techniques
4)    to manipulate algebraic expressions correctly
5)    to arrive at exact answers
6)    to arrive at correct interpretations of results
7)    to be able to justify their reasoning in the steps they take
8)    to use the appropriate terminology (notation)
In order to do so, there will be
Exercises:          Exercise problems will be given regularly; these will be neither collected nor graded but will be essential to
your progression. It will be imperative that you attempt some, if not all, of the assigned problems.
Gifts:              Regular "Gifts" (i.e. homework) will be given. Students will be expected to submit their "Gift" the
following school day in a NEAT and LEGIBLE way, LATE "Gifts" will not be accepted
Quizzes:            Regular (weekly, ~10 minutes) quizzes will be given during the semester on the topic(s) covered during the
week. A student missing a quiz will automatically be given the result “0” for that quiz.
Tests:              • There will be 3 class tests during the semester which are compulsory. A student missing a test will
automatically be given the result “0” for that test.
• Students are responsible for knowing when a test will be given. Ignorance of a test date will not be
considered a valid excuse.
• In the event that the college closes or the teacher is absent on an assignment due date or a scheduled test
date, the due date or test is moved to the next school day automatically.
Final Exam:         There will be a three hours comprehensive final examination at the end of the semester.

Scheme: