The lecture refers to the following chapters in the textbook:
1. Introduction: Chapter 1
2. Mathematical Foundations: Appendix A
3. Probability Theory: Appendix B
4. Estimation and Hypothesis Testing:
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MATH1116 Analysis
Lecture 18, 2016
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Directional Derivatives
Definition
Let v Rn with kvk = 1, and f : Rn R. We say that f admits a derivative in
th
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MATH1014 Calculus
September 19, 2016
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Justifying the formula for the length of a curve
We have used the
Math1116 Analysis Lecture Notes
Australian National University, Semester 2, 2016
Pierre Portal and Gri Ware
(last update: 15 June 2016)
Preface
These notes provide a summary of the material that will
Solution to Analysis Questions 7 and 8
7. Suppose, in order to gain a contradiction, that the desired result is not true, that is:
8n 2 N 9x 2 I
8a 2 I
1
,x
n
(x
+ n1 ) 6 (a
Use this to choose a seque
Solution to Problem 6 on the Week 3 and Week 4 Tutorial Worksheets
MATH1116, Semester 2, 2016
What condition must nonnegative integers m, n, and p satisfy so that
xm y n
lim
(x,y)!(0,0) (x2 + y 2 )p
e
Advanced Mathematics and Applications
Series of Real Numbers Module
Dr Griffith Ware
Mathematical Sciences Institute
c 2015
Any application of the ANU logo on
a coloured background is subject
to appro
Advanced Mathematics and Applications
Series of Real Numbers Module
Dr Griffith Ware
Mathematical Sciences Institute
c 2015
Any application of the ANU logo on
a coloured background is subject
to appro
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Griff Ware (ANU)
MATH1116 Analysis
Lecture 2, 2016
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Tutorials
If you have emailed me about t
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Griff Ware (ANU)
MATH1116 Analysis
Lecture 3, 2016
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Norms and Metrics
In the previous lecture we introduced two abstract ideas, concerning (a) th
41
5.3. Dierentiability
References: Adams 12.6, Trench 5.3.
5.3.1. Remark. Let f : R2 ! R be given by
(
xy
, if (x, y) 6= (0, 0)
x2 +y 2
f (x, y) =
0,
if (x, y) = (0, 0) .
We have previously seen that