# 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

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

Resource TypeTitleResource RequirementAuthor and YearPublisher
ReadingsPrinted subject text available from University BookshopPrescribedDepart of Mathematics and Statistics 2015La 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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Start date between: and    Key dates

## Melbourne, 2018, Semester 1, Day

### Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorYuri Nikolayevsky

### Class requirements

Lecture Week: 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.

Practical Week: 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.