**Text**: **Introduction to Real Analysis**, William
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.

**Interesting Links**

**
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 |