Course objectives: (from the departmental syllabus): One of the main objectives of the course is to bridge the gap between undergraduate calculus to graduate courses by giving rigorous treatment of topics like real number system, sequences and series, continuity, differentiation, integration in one and higher dimensions, and uniform convergence.

Textbook: Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill; 3rd edition, 1976.
Recommended web site: http://www.math.ucdavis.edu/~emsilvia/math127/math127.html

Topics: The Real and Complex Number System, Basic Topology, Numerical Sequences and Series, Continuity, Differentiation, The Riemann-Stieltjes Integral.

MATH 4510, Advanced Mathematics for Engineers
MWF: 2:30pm - 3:25pm, BR 306

Prerequisite: "C" or better in MATH 2110 and MATH 2120

Course objectives (from the departmental syllabus): This course is designed to introduce the student to Fourier Series, the method of solution of partial differential equations by separation of variables, and the application of these techniques to certain problems of mathematical physics and engineering.

Textbook: Zill, Differential Equations with Boundary Value Problems, 6th Edition, Brooks/Cole, 2005

Topics: Series solutions of linear differential equations, orthogonal functions and Fourier series, partial differential equations and boundary-value problems, integral transform method.

MATH 6010, Functional Analysis I
MWF: 1:25am - 2:20pm, BR 420

Prerequisite: "C" or better in MATH 4120 or MATH 5120.

Course objectives (from the departmental syllabus): One of the main objectives of the course is to familiarize the students with the basic concepts, principles and methods of functional analysis and its applications. Main topics include Normed spaces, Banach spaces, Dual spaces, Hilbert spaces, Hahn- Banach Theorem, Operator theory on Hilbert spaces, and Spectral theory of linear operators.

Textbook: Ervin Kreyszig, Introductory Functional Analysis with Applications, Wiley (1989)
Recommended web sites:
        http://www.math.umn.edu/~garrett/m/fun/
        http://www.mth.uea.ac.uk/~h720/teaching/functionalanalysis/materials/FAnotes.pdf

Topics: Metric spaces, normed spaces, Banach spaces, inner product spaces, Hilbert spaces, fundamental theorems for normed and Banach soaces, Further applications: Banach fixed point theorem.