MTH 438/URI
Advanced Calculus with Applications II

Course Information and Syllabus, Spring 1999

Text: Advanced Calculus, Patrick M. Fitzpatrick 
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:
Functions of several variables, multiple integrals, space curves, line integrals, surface integrals, Green's theorem, Stokes' theorem, sequences and series of functions, metric spaces, contraction principle.

Course Outline by Topical Areas:
The Euclidean Space, Metric Space, Partial Differentiability of Real-Valued Functions of Several Variables, Approximating Nonlinear Mapping by Linear Mapping, The Inverse Function Theorem,  The Implicit Function Theorem and Its Applications,  Integration for Functions of Several Variables, Line and Surface Integrals, Applications

We will mainly cover Chapters 10-19. 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 and twentieth 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 some of these systems will be presented, and provided. Most of the problems can be solved by using the graphing calculator.

Instructor: Dr. M. Kulenovic, Tyler 219, X7636, e-mail:kulenm@math.uri.edu
Online information: www.math.uri.edu/courses  or  www.math.uri.edu/~kulenm

Office hours: MWF:  11-12. 

Time: MWF: 9-10               Room:   Washburn 111
 
Chapter Homework Problems
10 10.1:   4,5,9
10.2:   3,5,8
10.3:   2,5,7 
11 11.1:   1,3,6,11
11.2:   2,5,9
11.3:   5,7,8
12 12.1:   3,4,8
12.2:   1,2,3,11 
12.3:   1,6,10
12.4:   1,2
12.5:   1,2,5,7
13 13.1:   3,4,9,11
13.2:   4,5,8,11
13.3:   1,4,6,10
14 14.1:   2,4,8,11
14.2:   1,4,7,11
14.3:   4,5,7,11
15 15.2:  2,4,5,8
15.3:  3,4,7
16 16.1:  2,5,7,9
16.3:  1,7
17 17.1:  4,5,11
17.2:  1,4,5
17.4:  4,7,11
18 18.1:  1,7,10,14
18.2:  2,4,5,11
18.3:  1,3,6
18.4:  1,3,7
19 19.1:  2,6,10
19.2:  1,4,6,10
19.3:  3,7,11,12