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