Notesale: Turn your study into money

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LECTURE 1 - INTRODUCTION TO THE COURSE
Oh, the leaves began to fallin’
And the seas began to part!
And the people that confronted him were many
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Introduction
Welcome to Newcastle and congratulations on getting the grades to be admitted
during two extremely challenging years - this cannot have been easy for you and it
is my sincere hope that better times are coming
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e
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This lecture serves as an introduction to the course
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What is the course about?
At A-level, calculus concerns the study of functions such as polynomials, for example f (x) = 3x5 + 3x − 10; trigonometric functions such as f (x) = sin(x) or
f (x) = cos(5x); exponential and logarithmic functions such as f (x) = e−x and
f (x) = log(3x)
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In this course we will be developing what you have done at A Level and start
to ask more broad and slightly deeper questions about functions in general e
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‘is
every function differentiable?’ or ‘is it always possible to integrate any function?’
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Thus one theme in the course will be
the development of mathematical language and vocabulary
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How the course will run
3
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Lectures
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In the lectures I will explain some of the theory and give examples of how it
is used to answer questions and solve problems
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It is still a very good idea for you to make your own notes though as this helps
enormously with learning the material
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I’m very friendly and welcome people
asking questions and pointing out any typos or things that are not clear
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If you are able to, please wear a mask when the University requires that you
do so (at the moment that includes during lectures and classes)
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2
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On Friday at 16:00-17:00 there will be an online session
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This session is recorded
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Every other week (even teaching weeks for Calculus), on Wednesday morning, you will have a small tutorial lead by a postgraduate researcher or
possibly another member of staff
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The activities are designed to help you deepen your understanding of the material
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You will be told
which group to attend
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3
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Lecture notes and online material
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It will not contain all the details of the examples
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As mentioned already, I will provide a list of non-assessed problems that will
form the basis of the discussion in the online session and I provide tutorial activity sheets every fortnight
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You will be required to upload a scan of your written work to Canvas
• Assignment A will be released on DATE and is due DATE
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• Assignment B will be released on DATE and is due DATE
The questions in the non-assessed problem sheets and some of the items discussed
in the tutorial will be good preparation for these assignments
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1
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My office is 2
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I am
almost directly underneath Kate Henderson’s office on the third floor if that helps
find me
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However, I do (metaphorically) operate an open-door policy and so if you would
like to talk about mathematics at another time and I’m in my office, please do
knock
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2
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My main mode of virtual communication is by email and my email
address is:
stuart
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ac
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ac
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Please do not use the Canvas site to send messages to me as these also get marked as spam
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It is fine to address me as ‘Stuart’ (or if you want to be formal ‘Dr Hall’ but
I prefer Stuart)
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if they are a professor) as this is polite
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5
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Transition Sessions
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My transition drop-ins are:
Tuesday 10:00-11:00 in the Barbara Strang Centre TG34
Thursday 10:00-11:00 in the Herschel TR4 on the 4th floor
We can talk about any of the 1st year courses in these sessions including calculus
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These are: Mondays
at 10:00-11:00 and Thursday 17:00-18:00
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There are many excellent books on the subject and here are a few
to think about dipping in to
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P
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• Principles of Mathematical Analysis by W
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• Guide to Analysis by F
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Hart - Another nice book, less advanced than
Rudin so a bit more accessible

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