MA2321 - Analysis in Several Real Variables Dr. David R. Wilkins

Lecture Material for Michaelmas Term 2018

Course notes:—

• MA2321 Course Notes, Michaelmas Term 2018, Part I (Sections 1 to 4)
• MA2321 Course Notes, Michaelmas Term 2018, Part II (Sections 5 and 6)
• MA2321 Course Notes, Michaelmas Term 2018, Part III (Section 7)
• MA2321 Course Notes, Michaelmas Term 2018, Part IV (Sections 8 to 10) [Corrected 19/11/2018]

Slide presentations:—

• MA2321 slide presentations in Michaelmas Term 2018.

Assignments:—

• MA2321, Michaelmas Term 2018, Assignment 1 (due Thursday, November 1, 2018)
• MA2321, Michaelmas Term 2018, Solutions to Assignment 1
• MA2321, Michaelmas Term 2018, Assignment 2 (due Monday, November 19, 2018)
• MA2321, Michaelmas Term 2018, Solutions to Assignment 2

Further resources

• MA2321 miscellaneous resources for Michaelmas Term 2018.

Examination Syllabus for the Examination concluding Michaelmas Term 2018

• MA2321, Michaelmas Term Examination 2018, Syllabus of Examinable Material

Lecture Material for Michaelmas Term 2017

Course notes:—

• MA2321 Course Notes, Michaelmas Term 2017, Part I (Sections 1 to 4)
• MA2321 Course Notes, Michaelmas Term 2017, Part II (Sections 5 and 6)
• MA2321 Course Notes, Michaelmas Term 2017, Part III (Sections 7 to 10)
• MA2321 Course Notes, Michaelmas Term 2017, Part IV (Section 11)

Lecture slides:—

• MA2321 lecture material in Michaelmas Term 2017, including slides where available.

Assignments:—

• MA2321, Michaelmas Term 2017, Assignment 1 (due Thursday, November 23, 2017)
• MA2321, Michaelmas Term 2017, Solutions to Assignment 1
• MA2321, Michaelmas Term 2017, Assignment 2 (due Friday, January 26, 2018)
• MA2321, Michaelmas Term 2017, Solutions to Assignment 2

Examination Syllabus for the Annual Examination in Hilary Term 2018

• MA2321, Annual Examination 2018, Syllabus of Examinable Material

Course Material from the Academic Year 2016/17

Available from a separate webpage is course material for MA2321 from the Academic Year 2016/17.

Course Material from the Academic Year 2015/16

Available from a separate webpage is course material for MA2321 from the Academic Year 2015/16.

Courses notes for 211, 221 and 224 as originally taught by Prof. David Simms, together with some later MA2321 Material

Course 211 (Linear Algebra and Differential Forms) — Prof. David Simms (transcribed by Brendan Griffin, further edited by Geoff Bradley)

Course 221 (Real and Complex Analysis) — Prof. David Simms (transcribed by Eoin Curran)

Chapter 4 (Differentiation, pp. 71—88) has substantial overlap with Section 8 of the MA2321 notes for 2016—17. Similarly Chapter 6 (Further Calculus, pp. 107--114) has substantial overlap with Section 9 of the MA2321 notes for 2016—17.

Course 224: Geometry---Continuity and Differentiability (Lecture Notes by Prof. David Simms, LaTeXed by Chris Blair)

MA224 Geometry (Based on the Lectures of Prof. Simms, typeset by Josh Tobin

Module Webpage for MA2321 in Michaelmas Term 2014 (Prof. David Simms)

Exercise sets relevant to MA2321 in 2016—17 include MA2321 Exercises I; 2014, MA2321 Exercises II; 2014 and MA2321 Exercises III; 2014. Note however that (i) these exercises were never set as homework problems to be marked and contribute to the final grade. They were discussed in class, and some of the exercises constituted the basis for regular examination questions. Also the essential content of many of the “exercies” has been incorporated into the course content for MA2321 in 2015—16 and 2016—17.

Correspondences with MA2223 in Michaelmas Term 2015

There were a number of correspondence between the content of modules MA2223 and MA2321 summarized here.

Material to aid Preparation for the Annual Examination 2016

• Syllabus for Examination 2016
• Sample Examination Paper for MA2321

Resources available on the Internet

See http://www.maths.tcd.ie/~dwilkins/Courses/MA2321/resources.php.

Course Material from Previous Years in Related Modules

The lecture courses taught by the lecturer at TCD in previous years that overlap most closely with the current MA2321 module are lecture courses (or modules) MA121, MA221, MA223 and MA212.

• Module MA121: Analysis (Academic year 2003/04)
• Module MA221: General Topology and Analysis (Michaelmas Term 2007, and Academic Year 2006/07)
• Module MA212: Topology (Academic Year 2000/01)
• Module MA223: Analysis in Several Real Variables (Academic Year 1987/88)
• Module MA3429: Differential Geometry (Michaelmas Term 2010)
• Course 425: A Course in Riemannian Geometry (based on lecture notes for courses taught at Trinity College Dublin in the academic years 1987/88 and 1990/91)

(N.B., the version of Sophister module MA3429 Differential Geometry taught in Michaelmas Term 2010 would be significantly different from what is currently taught, and from what has been taught in previous years.)

Back to D.R. Wilkins: Lecture Notes

Dr. David R. Wilkins, School of Mathematics, Trinity College Dublin.