MTH 435/URI
Introduction to Mathematical Analysis I
Course Information and Syllabus, Fall 2003

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

Prerequisites: MTH 243

Exams and Grading: There will be two exams and some homework assignments and quizzes. The exams will be in part of open book type.

TWO HOUR TESTS:                             40 percent

QUIZZES AND HOMEWORK:            30 percent

FINAL EXAM:                                      30 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, continuity and uniform continuity, derivatives, the Riemann integral, improper integrals. Detailed proofs emphasized.

Course Outline by Topical Areas:

The Real Number System. Basic Properties of the Derivative, the Mean Value Theorem, L'Hospital's Rule, Taylor's Theorem, Applications,
The Riemann Integral,  Properties of the Riemann Integral,  Fundamental Theorem of Calculus, Improper Integrals, Applications. Infinite Series and Sequences, Sequences of  Real Numbers and Infinite Series of  Real Numbers.

We will cover Chapters 1-3 and 4.1-4.3. 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.

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:

 Chapter Homework Problems 1 1.1:  10,11 1.2:   3, 5, 7, 89, 16-18, 22 1.3:    7, 10, 16, 22 2 2.1:  4, 5, 8, 23, 32, 36, 37, 2.2:  3, 6, 20, 22, 27, 28, 30 2.3:   12, 18, 21, 25, 26 2.4:   8-20, 37, 38, 42, 44 2.5:   4, 7, 8, 11, 16-19, 22 3 3.1:  4, 5, 8, 16 3.2:  2, 3, 7, 9 3.3:  5, 6, 9, 12 3.4:  4, 7, 8,11, 18, 25-28 3.4:  2, 3, 7, 8 4 4.1:  11,12, 18, 22, 33, 34 4.2:  5, 8, 9,12 4.3:  4, 7,10, 14, 15, 18, 31