Module Catalogues, Xi'an Jiaotong-Liverpool University   
 
Module Code: MTH118
Module Title: Analysis 2
Module Level: Level 1
Module Credits: 5.00
Academic Year: 2019/20
Semester: SEM2
Originating Department: Mathematical Sciences
Pre-requisites: MTH013ANDMTH117MTH008
   
Aims
To provide a basic understanding of the principles of Real Analysis.

Learning outcomes 
A. State definitions and theorems in real analysis.

B. Present proofs of the main theorems.

C. Apply these definitions and theorems to simple examples.

D. Construct their own proofs of simple unseen results.



Method of teaching and learning 
This module will be delivered by a combination of formal lectures and tutorials.
Syllabus 
Differentiation. Existence and continuity of derivatives. Mean value Theorems. Taylor’s Theorem.

Riemann integral. Integration of continuous functions. Integration of functions with discontinuities. Improper integrals.

Fundamental Theorem of calculus.

Convergence of sequences of functions. Point-wise and uniform convergence. Uniform convergence and continuity. Uniform convergence and integration/differentiation.

Fourier Series

Fourier Series: Calculation of Fourier series; point-wise and uniform convergence; the Fourier series theorem; even and odd functions; integration and differentiation of Fourier series; Parseval's theorem; Gibbs phenomenon.


Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester 39    13      98  150 

Assessment

Sequence Method % of Final Mark
1 Final Exam 70.00
2 Class Test1 15.00
4 Class Test2 15.00

Module Catalogue generated from SITS CUT-OFF: 8/20/2019 6:20:58 PM