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News | Details | Course notes | Exam Advice | Assignments | Weekly problems | Links and FAQ |

Welcome to MA180/186/190 Calculus/Analysis, Semester 2 2018-19.

- Our first lecture will be at 1.00 on Monday January 14, in IT250.

Course codes: |
MA180 (Science), MA186 (Arts) and MA190 (Computer Science and Information Technology). | ||

Lecturer: |
Dr Rachel Quinlan, Room
ADB-G007, Arás de Brún.
Email: rachel.quinlan@nuigalway.ie |
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Lectures: |
Monday 13:00--14:00 in IT250
Tuesday 10:00--11:00 in the Anderson lecture theatre |
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First Lecture: |
Monday, January 14 2019. | ||

Tutorials: |
TBA | ||

Course Content: |
Integral calculus, the real numbers, sequences and convergence. | ||

Recommended texts: |
"Calculus" by James Stewart (for Chapters 1 and 3 in particular), and the lecture notes. | ||

Course website: |
Information and course documents will be posted to this site, which is linked from the Blackboard pages for MA180, MA186 and MA190. Blackboard will also be used for announcements and for posting grades. | ||

Assessment: |
There will be 6 online homeworks (covering algebra and calculus) during the semester, as well as a 2-hour exam at the end of the semester. |

The course notes are divided into three Chapters:

- Chapter 1:
*Integral Calculus* - Section 1.1: Areas under curves.
- Section 1.2: The definite integral.
- Section 1.3: The Fundamental Theorem of Calculus.
- Section 1.4: Techniques of Integration. Section 1.5: Improper Integrals.
- Section 1.6: Exam advice for Chapter 1.
- Chapter 2:
*The Real Numbers* - Section 2.1: The set of real numbers
- Section 2.2: Subsets of R
- Section 2.3: Infinite sets and cardinality
- Section 2.4: Uncountability of the real numbers
- Section 2.5: The completeness axiom
- Section 2.6: Exam advice for Chapter 2
- Chapter 3:
*Sequences and Convergence*- Section 3.1: Introduction to sequences and series
- Section 3.2: Sequences
- Section 3.3: Introduction to infinite series
- Section 3.4: Introduction to power series
- Section 3.5: Exam advice for Chapter 3.

These lecture notes constitute the primary text for this course.

In addition, below you'll find the slides used in lectures. You should think of these as abbreviated versions of the full notes. It is important to be aware that the lecture notes constitute an essential part of this course and that they contain more detailed information than these slides.

NoteIn the module feedback in Week 7, one student indicated that they would prefer these in a one slide per page format rather than four per page. Both are provided below from Lecture 11 onward (I'll add the ones from Chapter 1 later). Please note that you do not have to wait for the feedback exercise to communicate a request like this - if you'd like the material in a different format, just tell me and I'll make it available if I can.

> -->1. | Monday 14/01/19 | Introduction | Introduction to the course. | |

2. | Monday 14/01/19 | Lecture 1 | Areas under curves | |

3. | Tuesday 15/01/19 | Lecture 2 | The definite integral. | |

4. | Tuesday 22/01/19 | Lecture 3 | The Fundamental Theorem of Calculus. | |

5. | Wednesday 23/01/19 and Monday 28/01/19 | Lecture 4 and 5 | Techniques of Integration - basic examples. | |

6. | Tuesday 29/01/19 | Lecture 6 | Techniques of Integration - substitution. | |

7. | Monday 4/02/19 | Lecture 7 | Techniques of Integration - integration by parts. | |

8. | Tuesday 5/02/19 and Monday 11/02/19 | Lecture 8 and 9 | Techniques of Integration - partial fraction expansions. | |

9. | Monday 12/02/19 | Lecture 10 | Improper integrals. | |

10. | Monday 18/02/19 | Lecture 11 | The set of real numbers. | One pp |

11. | Tuesday 19/02/19 | Lecture 12 | Subsets of the set of real numbers. | One pp |

12. | Monday 25/02/19 and Tuesday 26/02/19 | Lectures 13 and 14 | Infinite sets and cardinality. | One pp |

13. | Monday 4/03/19 | Lecture 15 | The set of real numbers is uncountable. | One pp |

14. | Monday 05/03/19 | Lecture 16 | The axiom of completeness. | One pp |

15. | Monday 11/03/19 | Lecture 17 | Introduction to sequences and series. | One pp |

16. | Tuesday 12/03/19 and Tuesday 19/03/19 | Lecture 18 | Sequences and Convergence. | One pp |

17. | Monday 25/03/19 and Tuesday 26/03/19 | Lecture 21 and 22 | Introduction to Infinite Series. | One pp |

18. | Monday 1/04/19 | Lecture 23 | Introduction to Power Series. | One pp |

19. | Tuesday 2/04/19 | Lecture 24 | Exam Advice | One pp |

- Weekly Problem 1
- Weekly Problem 2
- Weekly Problem 3
- Weekly Problem 4
- Weekly Problem 5
- Weekly Problem 6
- Weekly Problem 7
- Weekly Problem 8
- Weekly Problem 9
- Weekly Problem 10
- Weekly Problem 11
- Weekly Problem 12

- SUMS: Support for Undergraduate Mathematics Students is a free drop-in support centre for all NUI Galway students who are taking any mathematics course. It is located on the ground floor of Aras de Brun, ADB-G023, and is open Monday-Thursday, 2pm-5pm. Students are strongly advised to make consistent use of the SUMS service.
- Many questions frequently asked by Science students are answered in the First Year Information Handbook
- A mathematical theorem explained through the medium of interpretive dance.

School of Mathematics, Statistics and Applied Mathematics

National University of Ireland, Galway, University Road, Galway, Ireland.

Phone: +353 (0)91 492332 (direct) , +353 (0)91 524411 x2332 (switchboard)

Fax: +353 (0)91 494542 Email: Mary.Kelly@nuigalway.ie

This page was last updated Thursday, May 02

National University of Ireland, Galway, University Road, Galway, Ireland.

Phone: +353 (0)91 492332 (direct) , +353 (0)91 524411 x2332 (switchboard)

Fax: +353 (0)91 494542 Email: Mary.Kelly@nuigalway.ie

This page was last updated Thursday, May 02