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Lecture times and places

Tutorial feedback classes times and places

Students are expected to register for one of the tutorial classes and to attend each week. Please do not attend more than one class each week. If you need additional help then contact me. It is essential to work at the problems sheets provided and assistance in doing this will be provided in the tutorial classes.

Additional problems are discussed in the feedback classes to help students with the Problem sheets. I will post here a brief record of the problems discussed.

• Week 1: Limits
  
• Week 2: Limits


• Week 3: Directional Derivatives


• Week 4: The Fréchet Derivative


• Week 5: Differentials and 1-Forms


• Week 6: Differentiating Vector-Valued Function


• Week 7: The Chain Rule and the Inverse Function Theorem


• Week 8: The Implicit Function Theorem


• Week 9: Lagrange Multipliers


• Week 10: Critical Points


• Week 11: Differential Forms


• Week 12: Exterior Differential and Surface Integrals

Queries

Any queries or comments about this course can be emailed to me at pjeccles@manchester.ac.uk. I will try to reply within 48 hours.

Office Hours

Students are welcome to call on me in my office (Alan Turing 1.111) at any time. If I am busy I will ask you to come back at another time and if possible arrange one. If I am not in my office then leave a not under my door or send me an email saying when you will return. I will try to make a point of being in my office available to students at the following time.

However, sometimes I will have other commitments at this time.

Week 3 questionnaire feedback

I distributed week 3 feedback forms during the tutorials on 12 and 13 February. Here is some feedback from me on the forms.

Books

See reading lists for more information.

It appears difficult to find a book which covers the material in this course at a similar level. The most comprehensive book is the following which can be accessed electronically via the the above link to the University Library reading list.

• Wendell Fleming, Functions of Several Variables

The following free book on the internet may be useful (the file is quite large and so takes a few seconds to load).

• William Trench, Introduction to Real Analysis

A slightly less advanced book which covers some of the material in the course is the following.

• Seán Dineen, Multivariate Calculus and Geometry

Course notes

Background material

This lecture course builds on material from several previous courses in particular MATH20101/20111 Real Analysis, MATH10202/10212 Linear Algebra and MATH10122/10232 Calculus and Vectors. For convenience most background material which is used is summarized in background notes posted on this website. Some of this material will be referred to in lectures, usually displayed by overhead projector. This material is not examinable except when it forms a part of results discussed in the lectures.

• A. Continuity of Real-Valued Functions of One Variable
  
• B. Differentiation of Real-Valued Functions of One Variable
  
• C. Linear Algebra

Lecture notes

I will aim to post these prior to the lectures but may sometimes post revised versions after the lectures in the light of student feedback. I will refer to these on-line notes in the lectures and it is useful to have them available to annotate in the lectures.

• 1. Continuous Functions of Several Variables


• 2. Differentiation of Real-Valued Functions of Several Variables


• 3. Differentiation of Vector-Valued Functions of Several Variables


• 4. Extreme Values, Critical Points and Higher Partial Derivatives


• 5. Differential Forms and the Integration of Differential Forms

Problem sheets

• 1. Limits and Continuity
  
• 2. The Directional Derivative


• 3. The Fréchet Derivative


• 4. Calculating the Derivative


• 5. Differentiating Vector-Valued Functions and the Chain Rule


• 6. The Inverse Function Theorem and the Implicit Function Theorem


• 7. Finding Extrema Subject to a Constraint


• 8. Critical Points and Higher Derivatives


• 9. Differential Forms and Integration

Solution sheets

Solution sheets will be posted after students have had time to work at the problems.

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• 9.

Mid-semester coursework

15% of the marks fork this course unit come from an in-class test which will took place during the usual lecture hour on Tuesday 16 April, immediately after the Easter Break.

Here are some solutions to the coursework test.

Examination

The remaining 85% of the marks come from the end of semester examination. The rubric in 2013 will be the same as in 2010, 2011 and 2012 as follows.

• Answer all four questions in Section A (40 marks in all) and three of the four questions in Section B (15 marks each). If all four questions from Section B are attempted then credit will be given for the three best answers only. The total number of marks on the paper is 85. A further 15 marks are available from work during the semester making a total of 100.

Here are some solutions to the June 2010 examination.

Here are some solutions to the June 2011 examination.

Here is some feedback on the June 2012 examination.

Diary of amendments to and additions to this webpage