06/27/2005 - 08/10/2005
Monday & Wednesday 09:30 AM - 12:00 PM
Public Affairs Center 125
This is a course in the calculus of functions of several variables; but the material will be taught by combining linear algebra with multivariable calculus to emphasize the interconnectedness of these two subjects.
Each topic in the calculus will be introduced for functions of a single variable and then extended to functions of several variables: limits, continuity, derivatives, integrals, and the Fundamental Theorem of Calculus. Topics in linear algebra will be introduced as needed to understand the calculus for functions of several variables: vectors, matrices, linear independence, basis, and dimension. Major goals of the course are to understand the Inverse Function Theorem, the Implicit Function Theorem, and Green's Theorem, which is a multidimensional analogue the Fundamental Theorem of Calculus.
Our text will be Theodore Shifrin, Multivariable Mathematics/Linear Algebra, Multivariable Calculus, and Manifolds.
Grades will be based on regularly assigned problem sets that will be roughly an equal mixture of computational problems and theoretical problems.
There are no specific prerequisites for the course; all the essential topics will be introduced in the course itself, and the course should be accessible to any student with a modest background in mathematics.
Irene Mulvey (B.A., Stonehill College; Ph.D., Wesleyan University) is professor of mathematics at Fairfield University. Her recent publications include "Symbolic Representation for a Class of Unimodal Cycles," Topology and Its Applications (2002), and "Multi-modal Cycles with Linear Map Having Exactly One Fixed Point," International Journal of Mathematics and Mathematical Sciences (2001). Click here for more information about Irene Mulvey.
Consent of Instructor Required: No
|Level: GLSP||Credits: 3||Enrollment Limit: 18|
Texts to purchase for this course:
Theodore Shifrin, MULTIVARIABLE MATHEMATICS: LINEAR ALGEBRA, MULTIVARIABLE CALCULUS, AND MANIFOLDS (John Wiley & Sons), Paperback
READING MATERIALS AVAILABLE AT BROAD STREET BOOKS, 45 BROAD STREET, MIDDLETOWN, 860-685-7323
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