Math and Science Department
College of Arts and Sciences
Course Code: MTHM365
Course Title: Advanced
Calculus
Credit: 3
units
Prerequisite(s): Mathematical
Analysis III (MTHM355)
Term:
Second Semester
School Year: 2004
– 2005
Schedule: 9:00
A.M. – 12:00 Noon (F)
Instructor: Bernardo
R. Marquez, Ph.D.
E-mail: bernard@adnu.edu.ph
Consultation Hours: 2:00
P.M. – 3:00 P.M. (TTh)
6:00 P.M. – 9:00 P.M. (Th)
2:00 P.M. – 4:30 P.M. (F)
Consultation Venue: P219
One of the unique characteristics of mathematics is
the development of its concepts that cover various cases and situations. The
limit of a function, for instance, is equipped with a variety of rules to
facilitate its computation in different cases. Another example is the concept
of the definite integral which can be extended to deal with situations that are
not embraced by its basic definition. Indeterminate forms, improper integrals,
sequences, and series are few of the many topics in calculus that illustrate
that fundamental tendency of mathematics for a wider coverage of its ideas and
methods.
This course deals with special cases on finding limits
and evaluating integrals that are not covered by the basic definitions or
theorems learned in the series of Mathematical Analysis subjects. In addition,
the course also studies how to approximate functions using polynomials and
power series. Approximation of functions in this way is then shown to have
applications in computing the values of algebraic and transcendental functions
and the values of certain integrals. Students are expected to recall much of
the material they have taken in their previous calculus subjects.
At the end of the semester,
the students are expected to:
|
1. |
Explain
the concepts of an indeterminate form, an improper integral, a sequence, and
a series and illustrate them in different cases. |
|
2. |
Compute limits involving
indeterminate forms, evaluate improper integrals, and solve a variety of
problems on sequences and series. |
|
3. |
Manifest appreciation of
and interest in the various mathematical concepts and recognize their
significance in higher branches of mathematics and in other technical
sciences. |
|
Topics/Content Area |
Time frame (in hrs.) |
|
I.
Indeterminate forms and improper integrals A. The indeterminate form 0/0 B. Other indeterminate forms C. Improper integrals with infinite limits of integration D. Other improper integrals |
18 |
|
II.
Polynomial approximations, sequences, and infinite series A. Polynomial approximations by Taylor’s formula B. Sequences C. Infinite series of constant terms D. Infinite series of positive terms E. Infinite series of positive and negative terms F. A summary of tests for convergence or divergence
of an infinite series G. Power series H. Differentiation and integration of power series I. Taylor
series J. Power
series for natural logarithms and the binomial series |
30 |
Note: (1) Four meetings are
allotted to the four major examinations.
(2) Some topics may be deleted or added depending on the
available time.
Boardwork,
Seatwork, Quizzes, Preliminary Examination, Mid-term Examination, Pre-final
Examination,
and Final Examination
CFRS = 40%CS + 10%PE + 20%ME + 10%PF + 20%FE
CS = 60%Q +
40%BS
|
where: |
CFRS |
= |
Total Converted Final Raw
Score |
|
|
CS |
= |
Class Standing |
|
|
PE |
= |
Preliminary Examination Raw
Score over the Perfect Score |
|
|
ME |
= |
Mid-term Examination Raw
Score over the Perfect Score |
|
|
PF |
= |
Pre-final Examination Raw
Score over the Perfect Score |
|
|
FE |
= |
Final Examination Raw Score
over the Perfect Score |
|
|
Q |
= |
Total Raw Score in the
Quizzes over the Total Perfect Score |
|
|
BS |
= |
Boardwork\Seatwork Grade |
Textbook
Leithold,
Louis. The Calculus. 7th ed. New York: Harper Collins College
Publishers, 1996.
Books
Anton, Howard. Calculus with Analytic
Geometry. 2nd ed. New York: Anton Textbooks, Inc., 1984.
Ash, Carol, and Ash, Robert B. The
Calculus Tutoring Book. New York: The Institute of Electrical and
Electronics Engineers, Inc., 1986.
Auslander, Louis. Calculus: A First
Course. Glenview, Illinois: Scott, Foresman, and Company, 1971.
Baumslag, Gilbert, and Baumslag,
Benjamin.Calculus. New York: Quantum Publishers, Inc., 1976.
Don Allen, G.; Chui, Charles; and Perry,
Bill. Elements of Calculus. Belmont, California: Wadsworth, Inc., 1983.
integrals.wolfram.com
www.calculus.net
www.ihatecalculus.com
www.ima.umn.edu/~arnold/graphics.html
www.karlscalculus.org
Abridged
Version
11-11-04