# ANALYSIS OF REAL NUMBERS AND FUNCTIONS

MAT2ANA

Not currently offered

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.

SchoolEngineering and Mathematical Sciences

Credit points15

Subject Co-ordinatorYuri Nikolayevsky

Subject year levelYear Level 2 - UG

Available as ElectiveNo

Learning ActivitiesN/A

Capstone subjectNo

## Subject particulars

### Subject rules

PrerequisitesMAT1CLA OR (MAT1NLA AND MAT1CDE)

Co-requisitesN/A

Incompatible subjectsN/A

Equivalent subjectsN/A

Quota Management StrategyN/A

Quota-conditions or rulesN/A

Special conditionsN/A

Minimum credit point requirementN/A

Assumed knowledgeN/A

## Learning resources

### Printed subject text available from University Bookshop

Resource TypeBook

Resource RequirementPrescribed

AuthorDepart of Mathematics and Statistics

Year2015

Edition/VolumeN/A

PublisherLa Trobe University

ISBNN/A

Chapter/article titleN/A

Chapter/issueN/A

URLN/A

Other descriptionN/A

Source locationN/A

Career-focusedNo

Work-based learningNo

Self sourced or Uni sourcedN/A

Entire subject or partial subjectN/A

Total hours/days requiredN/A

Location of WBL activity (region)N/A

## Graduate capabilities & intended learning outcomes

### Intended Learning Outcomes

01. Calculate limits of certain sequences and functions and justify these calculations.
02. Prove the convergence or otherwise of certain series by applying appropriate tests.
03. Manipulate bounds and least upper bounds
04. Perform calculations involving function and metric spaces.
05. Apply the contraction map theorem in various situations.
06. Communicate your understanding of analysis using both words and precise mathematical symbolism.

## Subject options

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