Advanced Calculus

FALL 2017

10:30 - 11:45 am M,W,F MB 124

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Catalogue Description:

MATH 514 ADVANCED CALCULUS (4-0-4)(F). Introduction to fundamental elements of Analysis on Euclidean spaces including the basic differential and integral calculus. Topics include: Infinite series, sequences and series of function, uniform convergence, theory of integration, implicit function theorem and applications. PREREQ: MATH 275, MATH 301, and MATH 314.

Course background:
This is a proof based course, designed as a mathematical introduction to fundamental concepts underlying in Analysis in several real variables.  Students are assumed to have a background in Multivariable Calculus, Linear Algebra and in Real Analysis andto be comfortable with proof techniques in Mathematics. Students are expected to rigorously apply the mathematical method in this course.  

Course objectives:
1. Increase the sophistication of the student's skill in using the mathematical method in clever ways to create mathematics,
2. Enrich the student's mathematical culture by attention to historical context,
3. Prime the student's professional etiquette by giving attention to proper written presentation, exposition and attribution of mathematical work,
4. Inspire the student's taste for searching for aesthetically pleasing mathematics, 

Text Books:

The text book for the course is

Walter RudinPrinciples of Mathematical Analysis, McGraw-Hill Publishing Company

Evaluated work in the course:

Homework (150),
Test (125)
Final Examination (125)
MATH 514 specific (TBA)

Calendar:
Aug.  21:     First day of classes - Solar Eclipse 2017
Aug.  25:     Last day to add without a permission number.
Sept. 01:     Last day to add, or to drop without a "W".
Sept. 04:    Labor day - no classes.
Oct. 20:     Midterm exam
Oct. 27:     Last day to drop.
Nov. 20:    Thanksgiving Break from Nov. 20 until Nov. 26.
Dec 08:     Last day of classes.
Dec 13:     10:00 am - 12:00 pm Final Exam.