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M2AA1 Differential Equations 2016
Tuesday, 2 February 2016
Small revision model answer 5 of problem sheet nr1
Some asked me how I concluded so quickly in the previously posted model answer for this question that in case c=0 the sequence was Cauchy and thus converged, and I decided to expand the explanation.
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Lecture notes
Chapter 0 - Introduction
Chapter 1 - Contractions
Chapter 2 - Existence and uniqueness
Chapter 3 - Linear autonomous ODEs
Chapter 4 -The flow near an equilibrium
Chapter 5 - Poincare-Bendixson Theorem
(+
appendix
)
Chapter 6 - Biological applications
Chapter 7 - Calculus of Variations
(
Liquid mirror example
)
Scanned notes from lectures
28/01/16
;
29/01/16
;
02/02/16
;
04/02/16
;
05/02/16
;
09/02/16
;
11/02/16
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12/02/16
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16/02/16
;
18/02/16
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19/02/16
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23/02/16
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25/02/16
;
26/02/16
;
01/03/16
;
03/03/16
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04/03/16
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08/03/16
;
10/03/16
;
11/03/16
;
15/03/16
;
17/03/16
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18/03/16
;
Videos
Inverse Function Theorem in R:
proof
+
proof of formula for derivative
Higher dimensional derivatives
Implicit Function Theorem in R^n:
proof
+
proof of formula for derivative
Proof of Lemma 4.1.1
(
notes
)
Problem sheets
Nr 1
(
Solns
)
Nr 2
(
Solns
)
Nr 3
(
Solns
)
Nr 4
(
Solns
)
Nr 5
(
Solns
)
Nr 6
(
Solns
)
Nr 7
(
Solns
)
Nr 8
(
Solns
)
Progress tests (and solns)
Test 1 (11/02/2016)
Test 2 (10/03/2016)
How to study for the 2016 exam?
2016 Exam preparation notes
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Typos Chapter 4
Problem sheet 5
Lecture notes Chapter 5
Lectures, office hour and tuesday problem class th...
Lecture notes Chapter 4
Model answers first progress test
Update Lecture Notes Chapter 3
Jordan normal form notes
Videos online
Inner product in \(\mathbb{C}^n\)
Videos proof of Inverse and Implicit Function Theo...
Jordan-Chevalley Decomposition
Small revision model answer 5 of problem sheet nr1
How to prepare for the class test of 11 Feb?
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Jeroen Lamb
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