Exercises
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
Exercises
Exercises and problem sets to be released as the term progresses.
25
Box models for flood estimation
26
Problem set 1