mat2ana analysis real numbers and func
ANALYSIS OF REAL NUMBERS AND FUNCTIONS
MAT2ANA
2018
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.
SchoolSchool Engineering&Mathematical Sciences
Credit points15
Subject Co-ordinatorYuri Nikolayevsky
Available to Study Abroad StudentsYes
Subject year levelYear Level 2 - UG
Exchange StudentsYes
Subject particulars
Subject rules
Prerequisites MAT1CLA or (MAT1NLA and MAT1CDE)
Co-requisitesN/A
Incompatible subjectsN/A
Equivalent subjectsN/A
Special conditionsN/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.
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.
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.
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.
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.
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.
Subject options
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Melbourne, 2018, Semester 1, Day
Overview
Online enrolmentYes
Maximum enrolment sizeN/A
Enrolment information
Subject Instance Co-ordinatorYuri Nikolayevsky
Class requirements
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.
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.
Assessments
| Assessment element | Comments | % | ILO* |
|---|---|---|---|
| Fortnightly assignments (1500 words equivalent total) | 30 | 01, 02, 03, 04, 05, 06 | |
| One 3-hour examination | 70 | 01, 02, 03, 04, 05, 06 |