MTH 436/URI
Introduction to Mathematical Analysis II
Course Information and Syllabus, Spring 2004

Text: Introduction to Real AnalysisWilliam F. Trench    Pearson Education, 2002

Instructor: Dr. M. Kulenovic, Tyler 216, X44436, e-mail: kulenm@math.uri.edu

Online information: www.math.uri.edu/courses or www.math.uri.edu/~kulenm

Office hours: MW:  1-2,  F:11-12.                    Time: MW: 3-4:15                 Room: Wales 224

Prerequisites
: MTH 243, MTH 435

Exams and Grading: There will be two exams and some homework assignments and quizzes.

TWO HOUR TESTS:                             40 percent

QUIZZES AND HOMEWORK:            35 percent

FINAL EXAM:                                      25 percent

Course Objectives:
To develop the theoretical foundations of calculus; Preparation for advanced courses in probability, statistics, real analysis,  and applied mathematics.

Course Description:
Sets and functions, real topology in Rn, continuity and uniform continuity of real valued functions of several variables., derivatives, the Riemann integral, metric spaces. Detailed proofs emphasized.

Course Outline by Topical Areas:
Infinite Series of  Real Numbers. Infinite Series of  Functions. Real Valued Functions of Several Variables. Continuity and Partial Derivatives. Taylor's Formula. Vector Valued Functions of Several Variables. The Inverse Function Theorem. The Implicit Function Theorem. Jacobian and Hessian. Integrals of Functions of Several Variables. Introduction to Metric Spaces. Compact Sets and Continuous Functions in Metric Spaces.

We will cover Chapters 5-8 and 4.4, 4.5. This course emphasizes the theory of calculus, which means that it crosses the bridge from the original formulation of calculus by Newton and Leibniz to the full introduction of logical rigor, carried out over the course of the nineteenth century, which laid the basis for the branch of mathematics now known as analysis. Thus, the emphasis will be on the rigorous development of the theoretical basis of calculus. Most proofs will be given and required for the exams.

Computer Requirements
The use of CAS (computer algebra systems) packages such as  such as MATHEMATICA, Maple or Scientific Notebook is strongly encouraged. Some computer lectures in Scientific Notebook and Maple packages will be presented, and provided.

Interesting Links           Interactive Real Analysis             Analysis WebNotes

 Chapter Homework Problems 4 4.4:   1, 2, 5, 8, 12, 14, 17, 27 4.5:   2, 5, 8, 10, 16, 26, 29 5 5.1:   7, 12, 15, 18, 22, 24, 25 5.2:   3, 5, 8, 12 5.3:   3, 12, 14, 23, 24 5.4:   3, 5, 7, 8, 11, 15, 21, 25 6 6.1:  16, 19 6.2:   5, 7, 9, 19, 11, 13, 14, 20 6.3:   7, 10, 12 , 17, 20 6.4:   4, 10, 12, 14, 16 7 7.1:   6, 7, 10, 11 7.2:   3, 5, 7, 11,17, 20, 22, 24 7.3:   3, 4, 9,10, 15, 19, 23, 25 8 8.1   3, 4, 15, 18, 25 8.2   3, 5, 7, 12 8.3   2, 4