Course Syllabus
Lectures will be from 12:00 - 12:50 P.M. in L11 on Monday and Thursday; in EEM117 on Tuesday and Wednesday.
Course Text
Real Analysis by Carothers published by Cambridge University Press.
Some of the homework problems will be assigned from the Text. Please make sure you have the correct edition.
Course Content
Real number system and set theory : Completeness property, Archimedian
property, Denseness of rationals and irrationals, Countable and uncountable,
Cardinality, Zorn's lemma, Axiom of choice. Metric spaces: Open sets, Closed
sets, Continuous functions, Completeness, Cantor intersection theorem, Baire
category theorem, Compactness, Totally boundedness, Finite intersection property.
Functions of several variables: Differentiation, inverse and implicit function
theorems. Rlemann-Stieitjes integral: Definition and existence of the integral,
Properties of the integral, Differentiation and integration. Sequence and Series
of functions: Uniform convergence, Uniform convergence and continuity, Uniform
convergence and integration, Uniform convergence and differentiation.
Equicontinuity, Ascoli's Theorem.
Prerequisite: This course assumes knowledge of MTH 101.
Grading
| Homeworks/Quizzes | : 35% |
| Midterm Exam | : 25% |
| Final | : 40% |
Homeworks
Homeworks will be assigned reguarly and will be due in class.
Homeworks are meant to help you learn the material regularly and unless you do them by yourself, you will not be able to do well on the tests. Its also good to do as many practice problems as possible.
Quizzes
There will be announced Quizzes during the semester. There will be no make up quizzes or homeworks.
Exams
There will be one midterm exam and one final exam. Dates will be specified once the timetable it out.
Always bring your Identity Card to the exam.
Make up exams will be offered only when you have a valid excuse.