Applied Mathematics: A Very Short Introduction

Halftitle page
Series page
Title page
Copyright page
Dedication page
Contents
Preface
Reading playlist
Acknowledgements
List of illustrations
1 What’s so funny ‘bout applied mathematics? Modelling, theory, and methods
Mathematics
A Study in Contrast
Burning Candles
Reflection
2 Do you want to know a secret? Turkeys, giants, and atomic bombs
Cooking a turkey
A digression about scales, dimensions, and units
Back to the kitchen
The giants who did not walk among us
Dr Taylor or: How I learned to love the bomb
A word of caution from Lord Rayleigh
Reflections
3 Do you believe in models? Simplicity and complexity
Becoming rich
Throwing a ball
Model complexity
The physics paradigm
A modern view of mathematical modelling
4 Do you know the way to solve equations? Spinning tops and chaotic rabbits
Equations we cannot solve
Solving differential equations
Tautologies: the tale of rabbits and wolves
Numerical solutions
Chaotic rabbits
Reflections
5 What’s the frequency, Kenneth? Waves, quakes, and solitons
Linear waves on a string
Earthquakes
Nonlinear waves: the remarkable soliton
Reflection: Pandora’s box
6 Can you picture that? X‐rays, DNA, and photos
Computer tomography and Radon transform
The discovery of the structure of DNA
Digital images and compression
Modern developments
Reflection
7 Mathematics, what is it good for? Quaternions, knots, and more DNA
Quaternions
Knots and DNA
Reflection
8 Where are we going? Networks and the brain
Networks
The mathematical brain
Reflection
Epilogue
Further reading
Index
Social Media