ANALYSIS OF REAL NUMBERS AND FUNCTIONS
MAT2ANA
2017
Credit points: 15
Subject outline
The limits of sequences and limits of functions are studied in this subject. Initially we study them in one-dimensional space and then in higher dimensions. We also study series and various tests are derived to determine the convergence or otherwise of these series. We then extend the basic idea of limit to include sequences of functions and sequences of sets in metric spaces. A powerful theorem called The Contraction Mapping Theorem will be derived. This theorem plays a fundamental role in analysis and its applications. We will use it to establish the existence and uniqueness of solutions to certain differential equations.
School: School Engineering&Mathematical Sciences
Credit points: 15
Subject Co-ordinator: Yuri Nikolayevsky
Available to Study Abroad Students: Yes
Subject year level: Year Level 2 - UG
Exchange Students: Yes
Subject particulars
Subject rules
Prerequisites: MAT1CLA or (MAT1NLA and MAT1CDE)
Co-requisites: N/A
Incompatible subjects: N/A
Equivalent subjects: N/A
Special conditions: N/A
Learning resources
Readings
| Resource Type | Title | Resource Requirement | Author and Year | Publisher |
|---|---|---|---|---|
| Readings | Printed subject text available from University Bookshop | Prescribed | Depart of Mathematics and Statistics 2015 | La Trobe University |
Graduate capabilities & intended learning outcomes
01. Calculate limits of certain sequences and functions and justify these calculations.
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
- Related graduate capabilities and elements:
- Creative Problem-solving(Creative Problem-solving)
- Critical Thinking(Critical Thinking)
- Writing(Writing)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
- Discipline-specific GCs(Discipline-specific GCs)
02. Prove the convergence or otherwise of certain series by applying appropriate tests.
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
- Related graduate capabilities and elements:
- Inquiry/ Research(Inquiry/ Research)
- Critical Thinking(Critical Thinking)
- Discipline-specific GCs(Discipline-specific GCs)
- Creative Problem-solving(Creative Problem-solving)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
- Writing(Writing)
03. Manipulate bounds and least upper bounds
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
- Related graduate capabilities and elements:
- Creative Problem-solving(Creative Problem-solving)
- Discipline-specific GCs(Discipline-specific GCs)
- Critical Thinking(Critical Thinking)
- Writing(Writing)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
04. Perform calculations involving function and metric spaces.
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
- Related graduate capabilities and elements:
- Critical Thinking(Critical Thinking)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
- Writing(Writing)
- Creative Problem-solving(Creative Problem-solving)
- Discipline-specific GCs(Discipline-specific GCs)
05. Apply the contraction map theorem in various situations.
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
- Related graduate capabilities and elements:
- Discipline-specific GCs(Discipline-specific GCs)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
- Creative Problem-solving(Creative Problem-solving)
- Writing(Writing)
- Inquiry/ Research(Inquiry/ Research)
- Critical Thinking(Critical Thinking)
06. Communicate your understanding of analysis using both words and precise mathematical symbolism.
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
- Related graduate capabilities and elements:
- Discipline-specific GCs(Discipline-specific GCs)
- Writing(Writing)
Melbourne, 2017, Semester 1, Day
Overview
Online enrolment: Yes
Maximum enrolment size: N/A
Enrolment information:
Subject Instance Co-ordinator: Yuri Nikolayevsky
Class requirements
PracticalWeek: 10 - 22
Two 1.0 hours practical per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.
LectureWeek: 10 - 22
Two 1.0 hours lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.
Assessments
| Assessment element | Comments | % | ILO* |
|---|---|---|---|
| fortnightly assignments | 30 | 01, 02, 03, 04, 05, 06 | |
| one 3-hour examination | 70 | 01, 02, 03, 04, 05, 06 |