Applied Mathematics: A Very Short Introduction

Description

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