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# Analysis I

Math 3150, Section 001 - Analysis I, Spring 2019 [Course Syllabus]

**Lectures:** MWF 11:15 - 12:05 at MONT 314

**Office hours:** MW 1pm-2pm at MONT 304

**Required Text Book:** Elementary Analysis: The Theory of Calculus
by Kenneth A. Ross. ISBN 978-1-4614-6270-5, Springer; 2nd ed. 2013 edition (April 17, 2013).

** Exam Dates**:

Exam 1: March 1, Friday.

Exam 2: April 5, Friday.

Final Exam: May 8, Wednesday.

** Grading policy**: Quiz: %20, Homework: %10, 1st Exam: %20, 2nd Exam: %20, Final Exam:%30.

Exam 1: March 1, Friday.

Exam 2: April 5, Friday.

Final Exam: May 8, Wednesday.

### Exams

### Homework

- HW1: Assigned problems for sections 1.1 to 1.5. Due date: Monday, February 4 before the class.
- HW2: Assigned problems for sections from 2.7 to 2.9. Due date:
~~Friday, February 8~~Monday, February 11 before the class. - HW3: Assigned problems for 2.9 (if you did not sovle in HW2) and problems in this old exam. Due date: Monday, February 18 before the class.
- HW4: Assigned problems for 2.10,
~~2.11~~, and problems in this old exam. Due date: Monday, February 25 before the class. - HW5: Assigned Problems for 2.11 and 2.12. Due date: Monday, March 11.
- HW6: Assigned Problems for 3.17, 3.18, 3.19. Due date: Wednesday, March 27.
- HW7: Assigned Problems for 3.20 and problems in these two old exams Old Exam 1 [You can skip problem 4] and Old Exam 2 [You can skip problem 5]. Due date: Monday, April 1.
- HW8: Assigned Problems for 5.28, 5.29, and 5.30. Due date: Monday, April 15.
### Quizzes

### Lecture and Assignment Schedule

### Important Links

- Please log-on HuskyCT for the course announcements and grades.
- Academic Calendar for this semester https://registrar.uconn.edu/academic-calendar/fall-2018/.
- Exam rescheduling https://guide.uconn.edu/student-interactions/rescheduling-exams/.
- Academic Integrity Policy https://community.uconn.edu/academic-integrity-faculty-faq/.

Section | Covered on | Topics | Assigned Problems |
---|---|---|---|

1.1 | 01/23 | The Set $\mathbb{N}$ of Natural Numbers | Page 5, Exercises 1.4, 1.7, 1.11. |

1.2 | 01/23 and 01/25 | The Set $\mathbb{Q}$ of Rational Numbers | Page 13, Exercises 2.3, 2.8. |

1.3 | 01/25 | The Set $\mathbb{R}$ of Real Numbers | Page 19, Exercises 3.6, 3.7. |

1.4 | 01/30 | The Completeness Axiom | Pages 27-28, Exercises 4.1,4.3, 4.14. |

1.5 | 02/01 | The Symbols $+\infty$ and $-\infty$ | Page 30, Exercise 5.6. |

2.7 and 2.8 | 02/01 and 02/04 and 02/06 | Limits of Sequences and A discussion about Proofs | Page 44, Exercises 8.2 (b) (d) (e), 8.4, 8.6. |

2.9 | 02/06 and 02/08 and 02/11 and 02/13 | Limit theorems for sequences | Page 54, Exercises 9.1 (a) (c), 9.2 (a) (b), 9.3, 9.4, 9.5. |

2.10 | 02/15 and 02/18 and 02/20 | Monotone sequences and Cauchy sequences | Pages 64-65-66, Exercises 10.1 (a) (c) (e), 10.2, 10.4, 10.6 (a) (b), 10.7, 10.10, 10.12. |

2.11 | 02/22 and 02/25 | Subsequences | Pages 76-77-78, Exercises 11.4, 11.10, 11.11 |

Exam 1 Review | 02/27 | We will talk about problems from the old exams | |

Exam 1 | 03/01 | Exam 1 Covers 1.1-1.5 and 2.7-2.11. | |

2.11 and 2.12 | 03/06 | Subsequences and lim sup's and lim inf's | Page 82, Exercise 12.3 |

3.17 | 03/08 | Continuous functions | Pages 130-131-132, Exercises 17.2, 17.9, 17.12, 17.13. |

3.18 | 03/11 | Properties of continuous functions | Page 139, Exercises 18.4, 18.5, 18.6, 18.8, 18,9, 18.10. |

3.19 | 03/13 and 03/15 | Uniform continuity | Pages 151-152, Exercises 19.2 (b), 19.5 (d) (e) (f), 19.8, 19.9 |

3.20 | 03/27 and 03/29 and 04/01 | Limits of Functions | Pages 162-163, Exercises 20.1, 20.2, 20.5, 20.6, 20.11, 20.12 |

Exam 2 Review | 04/03 | We will talk about problems from the old exams | |

Exam 2 | 04/05 | Exam 2 Covers 2.11-2.12 and 3.17, 3.18. 3.19, and 3.20 | |

5.28 | 04/08 | Basic Properties of the Derivative | Pages 230-231-232, Exercises 28.1 (a), 28.2 (a), 28.3(a), 28.7(a)(b)(c)(d), 28.14(a)(b), 28.16. |

5.29 | 04/10 | The Mean Value Theorem | Pages 239-240, Exercises 29.1 (a)(c), 29.3, 29.4, 29.5, 29.7, 29.9. |

5.30 | 04/12 | L'Hospital's Rule | Pages 248, Exercises 30.1, 30.3, 30.5. |

6.32 | 04/15 and 04/17 and 04/19 | The Riemann Integral | Page 279, Exercises 32,1, 32.2, 32.3 |

6.33 | 04/22 and 04/24 | Properties of the Riemann Integral | Page 289, Exercises 33.4, 33.7, 33.8 |

6.34 | 04/26 and 04/29 | Fundamental Theorem of Calculus | Page 296, Exercises 34.2, 34.3 |

Final Exam Review | 05/01 and 05/03 | We will talk about problems from the old final exams |