ANALYSIS OF REAL NUMBERS AND FUNCTIONS

MAT2ANA

2020

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: Engineering and Mathematical Sciences (Pre 2022)

Credit points: 15

Subject Co-ordinator: Yuri Nikolayevsky

Available to Study Abroad/Exchange Students: Yes

Subject year level: Year Level 2 - UG

Available as Elective: No

Learning Activities: N/A

Capstone subject: No

Subject particulars

Subject rules

Prerequisites: MAT1CLA OR (MAT1NLA AND MAT1CDE)

Co-requisites: N/A

Incompatible subjects: N/A

Equivalent subjects: N/A

Quota Management Strategy: N/A

Quota-conditions or rules: N/A

Special conditions: N/A

Minimum credit point requirement: N/A

Assumed knowledge: N/A

Learning resources

Printed subject text available from University Bookshop

Resource Type: Book

Resource Requirement: Prescribed

Author: Depart of Mathematics and Statistics

Year: 2015

Edition/Volume: N/A

Publisher: La Trobe University

ISBN: N/A

Chapter/article title: N/A

Chapter/issue: N/A

URL: N/A

Other description: N/A

Source location: N/A

Career Ready

Career-focused: No

Work-based learning: No

Self sourced or Uni sourced: N/A

Entire subject or partial subject: N/A

Total hours/days required: N/A

Location of WBL activity (region): N/A

WBL addtional requirements: N/A

Graduate capabilities & intended learning outcomes

Graduate Capabilities

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.

Melbourne (Bundoora), 2020, Semester 1, Day

Overview

Online enrolment: Yes

Maximum enrolment size: N/A

Subject Instance Co-ordinator: Yuri Nikolayevsky

Class requirements

LectureWeek: 10 - 22
Two 1.00 hour lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

PracticalWeek: 10 - 22
Two 1.00 hour practical per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

Assessments

Assessment elementCommentsCategoryContributionHurdle%ILO*

Fortnightly assignments (1500 words equivalent total)

N/AN/AN/ANo30SILO1, SILO2, SILO3, SILO4, SILO5, SILO6

One 3-hour examination

N/AN/AN/ANo70SILO1, SILO2, SILO3, SILO4, SILO5, SILO6