A Mezze of Mathematical Methods is Volume 1 of Science by Simulation. It is a recipe book of mathematical models that can be enlivened by the transmutation of equations into computer code. In this volume, the examples chosen are an eclectic mix of systems and stories rooted in common experience, rather than those normally associated with constrained courses on Physics, Chemistry or Biology which are taught in isolation and susceptible to going out of date in a few years.

Rather than a 'what' of Science, this book is aimed at the 'how', readily applied to projects by students and professionals. Written in a friendly style based upon the author's expertise in teaching and pedagogy, this mathematically rigorous book is designed for readers to follow arguments step-by-step with stand-alone chapters which can be read independently. This approach will provide a tangible and readily accessible context for the development of a wide range of interconnected mathematical ideas and computing methods that underpin the practice of Science.

Contents:

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  Introduction

  
  


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  The Epidemiology of Eyam

  
  


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  Holmes and Watson Meet Bayes

  
  


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  May's Chaotic Bunnies

  
  


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  Pendulums, Poincaré Diagrams and Strange Attractors

  
  


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  A Standard Atmosphere

  
  


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  The Subtlety of Rainbows

  
  


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  Exploring Julia's Fractals

  
  


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  Radar, Chirps and Phased Arrays

  
  


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  Navigating the Sphere

  
  


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  Modelling Money and Mortgages

  
  


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  Power to the People

  
  


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  Appendices:

  
  
  
  
  • Linear Regression — Determining Lines of Best Fit
  
  
  • Using the Runge–Kutta Method to Solve the Pendulum Problem
  
  
  
  

Readership: A book for early undergraduate and keen high school students of Mathematics, Physics, Economics, Chemistry, Engineering, Computer Science, and Biology. Teachers and lecturers should consider using this to assist with teaching STEM subjects. Also valuable as a general interest textbook for the professional mathematical modelling community.

Key Features:

• An eclectic mix of fully realised mathematical models with contexts ranging from epidemiology to elections, and chaos to calculus. Generally applicable, and not constrained by syllabus and course content that may become out of date in a few years


• Sufficient detail is provided to turn mathematics into code, and the supporting code itself is available to download from http://www.eclecticon.info/scibysim_vol1.htm


• Mathematically rigorous, with many more steps left in compared to most books at this level. Designed for readers to follow arguments step-by-step


• Aimed to help address the erosion of mathematical content in many secondary school Science courses (e.g., A-Level Physics and Chemistry), and help STEM students better prepare for university study


• High quality technical illustrations throughout. Nearly all illustrations have been created programmatically by the author, using the methods described in the book