Text: Introduction to Real Analysis, William
F. Trench
Pearson Education, 2002
Instructor: Dr. M. Kulenovic, Tyler 216, X44436, email:
kulenm@math.uri.edu
Online information: www.math.uri.edu/courses or www.math.uri.edu/~kulenm
Office hours: MW: 12, F:1112.
Time:
MW: 34:15
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 R^{n}, 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 58 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 

