**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 |