MAT3004: Introduction to Function Spaces

Lecturer

Sergey Zelik

E-mail: S.zelik@surrey.ac.uk

Class Details

Day	Time	Room	weeks
Tuesday	11:00-13:00	24AA04	0 – 12
Thursday	14:00-16:00	22AA04	0--12
Tutorial Thursday	During Lecture	22AA04	0--11

Assessment

MAT3004: There will be two class tests and an examination.

Class tests: Two class tests counts for 13% (Tuesday, November 5^th) and 12% (Tuesday, December 17^th) of the semester marks respectively. Examination counts for 75% of semester marks

Unassessed Assignments

There will be two unassessed MOCK-tests (one-week prior the Assessed ones for MAT3004)

Course material (hand-outs/assignments)

• Handwritten and scanned lecture notes (which are the same for the current year)  pdf
• ClassNotes split by topics:

Metrics and norms, convergence and continuity pdf

Open and closed sets, topology pdf

Completeness and completion pdf

Compactness, Hausdorff and Arzela theorems pdf

Banach Contraction Theorem and applications to ODEs pdf

Hilbert spaces and abstract Fourier series pdf

Classical Fourier series pdf

• More ClassNotes (thanks to Henk) pdf (notes for years 2005-2006, no one-to-one correspondence with current lectures, but nice for the additional reading!) see also here ps
• Questions for self-control pdf
• Additional Exercises (first part) pdf
• Additional Exercises (second part) pdf
• Hints for Additional Exercises pdf (now opened)
• Some Exercises thanks to Henk Bruin pdf

Current year (2019):

Mock-Test I with solutions  pdf

Class-Test I with solutions pdf

Mock-Test II with solutions pdf

Previous years:

2018

Mock-Test 1 with solutions pdf

Assessed Test 1 with solutions pdf

Mock-Test 2 with solutions pdf

Assessed Test 2 with solutions pdf

Final Exam with informal solutions pdf

2017

Mock-Test 1 with solutions pdf

Assessed Test 1 with solutions pdf

Mock-Test 2 with solutions pdf

Assessed-Test 2 with solutions pdf NEW!!

Previous year exam paper pdf with INFORMAL solutions pdf NEW!!

2016

• Coursework I (2016) with solutions pdf
• ClassTest I (2016) with solutions pdf
• Coursework II (2016) pdf
• ClassTest II(2016) with solutions pdf

2013

• CourseWork I with solutions pdf
• CourseWork II with solutions pdf
• Test I with solutions pdf
• Test II with solutions pdf

2012

• Coursework I (2012) with solutions pdf
• Test I (2012) with solutions pdf
• CourseWork II (2012) with solutions pdf
• Test II (2012) with solutions pdf

2011

• CourseWork I(2011) with solutions pdf
• ClassTest 1(2011) with solutions pdf
• ClassTest 2(2011) with solutions pdf
• CourseWork 2(2011, coincides with Q1 and Q4 of the previous exam paper) pdf with solutions pdf

2010

Coursework 1 (2010) MMath and BsC with solutions

Test with solutions (2010) pdf

Coursework 2 (2010) MMAth and BsC

2009

• Coursework 1 (2009) with solutions:   MMath  and   BsC
• ClassTest (2009) with solutions pdf
• Coursework 2(2009):  MMath  and BSc with solutions

2008

• CourseWork 2 (year 2008) with solutions  MMath and BsC
• CourseWork 1 (year 2008) with solutions:  MMath and BsC
• ClassTest (2008) with solutions  MMath and BsC pdf
• Exam 2008 MMath pdf with solutions pdf
• Exam 2008 BsC pdf with solutions pdf
• Coursework 1 of year 2007 + Solutions in pdf
• Test Year 2006 pdf

Past Exam papers

2009 2010 2011 2012 2013

Additional reading

• Karen Saxe, "Beginning functional analysis", Springer, ISBN 0-387-95224

Further texts can be found in the library. For example:

• E. Kreyszig, Introductory Functional Analysis with Applications, Wiley 1978.
• N. Young, An introduction to Hilbert space, Cambridge University Press, 2001.
• W. Rudin, Principles of mathematical analysis, McGraw-Hill 3rd ed. 1976, ISBN 0-07-085613-3 (or any other edition).

External links

http://www.wolframalpha.com/

A brilliant engine for the online computing of partial derivatives, integrals, solving min-max problems and for doing many other things!