INTRODUCTION TO ANALYSIS

Course Code

MA 2005

Credit Points

15

Course Coordinator

Professor Michael Weiss

Pre-requisites

MA 1005 or, with the permission of the Head of Mathematical Sciences, both MA 1007 and MA 1507.

Overview

• Fundamental properties of real numbers: field operations, order, completeness.


• Sequences and limits: convergence, basic examples, decimal representation of real numbers.


• Functions of one real variable: limits and continuity, elementary functions, basic results on continuous functions.


• Differentiation of functions of one variable: basic definitions and properties, chain rule, first examples of Taylor polynomials and series


• Integration of functions of one variable: basic definitions and properties, the fundamental theorem of calculus, application to arc lengths of plane curves.

Structure

3 one-hour lectures and 1 one-hour tutorial per week (to be arranged).

Assessment

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%).

Resit: 1 two-hour written examination paper. The CAS mark awarded will be the maximum of 100% resit and 80% resit with 20% in-course assessment.

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact Course Coordinator for feedback on the final examination.