Lecture plan
MA30287: Mathematics of Planet Earth
Preface
Lecture plan
Introduction
1
What does Mathematics of Planet Earth mean?
2
Conservation laws
3
Dimensional scaling analysis
4
Basic energy models
Practical applied mathematics
5
Asymptotic approximations I
6
Asymptotic approximations II
7
Numerical solutions of IVPs
8
Asymptotic approximations III
9
Nonlinear root finding
10
Numerical solutions of PDEs
11
The wine cellar problem
Energy balance models
12
EBM with nonlinear albedo
13
EBM with latitude I
14
EBM with latitude II
15
EBM with latitude III
16
EBM with latitude IV
Fast-slow dynamics
17
Ice ages I: an introduction
18
Ice ages II: a model for fast-slow dynamics
19
Ice ages III: analysis of the van der Pol equation
20
Fast-slow dynamics for higher-order systems
Box models of the ocean and environment
21
Basic models of the ocean
22
Stommel’s box model
23
Box models for flood estimation
Exercises
24
Problem set 1
25
Problem set 2
26
Problem set 3
27
Problem set 4
28
Problem set 5
29
Problem set 6
30
Problem set 7
31
Problem set 1 solutions
32
Problem set 2 solutions
33
Problem set 3 solutions
34
Problem set 4 solutions
35
Problem set 5 solutions
36
Problem set 6 solutions
37
Problem set 7 solutions
Problem classes
38
Problem class 1: an introduction to Noteable
39
Problem class 2: dimensional analysis
40
Problem class 3: BVPs
41
Problem class 4: PDEs and numerical stability
42
Problem class 5
43
Problem class 6
Appendices
44
Differential equations
45
Dynamical systems
46
Vector calculus
47
Modelling
48
Finite difference approximations
49
Coding
50
An example of ChatGPT going wrong
References
Lecture plan
A lecture plan can be found at
this link
.
Preface
Introduction