Learn Physics with Functional Programming

Informationen zum Autor Scott Walck has a PhD in Physics from Lehigh University and has been a professor of physics, including computational physics, to undergraduates for over 20 years at Lebanon Valley College. He has also written academic articles and given talks on the use of functional programming in teaching physics. Klappentext "This book shows how to solve physics problems using Haskell, a functional programming language. Source code, equations, and diagrams throughout demonstrate how physics enthusiasts and functional programmers can use Haskell and its mathematical structures to solve problems from Newtonian mechanics and electromagnetics"-- Zusammenfassung Deepen your understanding of physics by learning to use the Haskell functional programming language. Learn Physics with Functional Programming is your key to unlocking the mysteries of theoretical physics by coding the underlying math in Haskell. You'll use Haskell's type system to check that your code makes sense as you deepen your understanding of Newtonian mechanics and electromagnetic theory, including how to describe and calculate electric and magnetic fields. As you work your way through the book's numerous examples and exercises, you'll learn how to: Encode vectors, derivatives, integrals, scalar fields, vector fields, and differential equations Express fundamental physical principles using the logic of Haskell's type system to clarify Newton's second law, Coulomb's law, the Biot-Savart law, and the Maxwell equations Use higher-order functions to express numerical integration and approximation methods, such as the Euler method and the finite-difference time-domain (FDTD) method Create graphs, models, and animations of physical scenarios like colliding billiard balls, waves in a guitar string, and a proton in a magnetic field Whether you're using this book as a core textbook for a computational physics course or for self-study, Learn Physics with Functional Programming will teach you how to use the power of functional programming to explore the beautiful ideas of theoretical physics. Inhaltsverzeichnis Acknowledgments Introduction Part I: A Haskell Primer for Physicists Chapter 1: Calculating with Haskell Chapter 2: Writing Basic Functions Chapter 3: Types and Entities Chapter 4: Describing Motion Chapter 5: Working with Lists Chapter 6: Higher-Order Functions Chapter 7: Graphing Functions Chapter 8: Type Classes Chapter 9: Tuples and Type Constructors Chapter 10: Describing Motion in Three Dimensions Chapter 11: Creating Graphs Chapter 12: Creating Stand-Alone Programs Chapter 13: Creating 2D and 3D Animations Part II: Expressing Newtonian Mechanics and Solving Problems Chapter 14: Newton's Second Law and Differential Equations Chapter 15: Mechanics in One Dimension Chapter 16: Mechanics in Three Dimensions Chapter 17: Satellite, Projectile, and Proton Motion Chapter 18: A Very Short Primer on Relativity Chapter 19: Interacting Particles Chapter 20: Springs, Billiard Balls, and a Guitar String Part III: Expressing Electromagnetic Theory and Solving Problems Chapter 21: Electricity Chapter 22: Coordinate Systems and Fields Chapter 23: Curves, Surfaces, and Volumes Chapter 24: Electric Charge Chapter 25: Electric Field Chapter 26: Electric Current Chapter 27: Magnetic Field Chapter 28: The Lorentz Force Law Chapter 29: The Maxwell Equations Appendix: Installing Haskell Bibliography Index...

Klappentext

Deepen your understanding of physics by learning to use the Haskell functional programming language.

Learn Physics with Functional Programming is your key to unlocking the mysteries of theoretical physics by coding the underlying math in Haskell.

You’ll use Haskell’s type system to check that your code makes sense as you deepen your understanding of Newtonian mechanics and electromagnetic theory, including how to describe and calculate electric and magnetic fields.

As you work your way through the book’s numerous examples and exercises, you’ll learn how to:

• Encode vectors, derivatives, integrals, scalar fields, vector fields, and differential equations
• Express fundamental physical principles using the logic of Haskell’s type system to clarify Newton’s second law, Coulomb’s law, the Biot-Savart law, and the Maxwell equations
• Use higher-order functions to express numerical integration and approximation methods, such as the Euler method and the finite-difference time-domain (FDTD) method

• Create graphs, models, and animations of physical scenarios like colliding billiard balls, waves in a guitar string, and a proton in a magnetic field
  Whether you’re using this book as a core textbook for a computational physics course or for self-study, Learn Physics with Functional Programming will teach you how to use the power of functional programming to explore the beautiful ideas of theoretical physics.

  Inhalt
  Acknowledgments 
  Introduction
  Part I: A Haskell Primer for Physicists
  Chapter 1: Calculating with Haskell
  Chapter 2: Writing Basic Functions
  Chapter 3: Types and Entities
  Chapter 4: Describing Motion
  Chapter 5: Working with Lists
  Chapter 6: Higher-Order Functions
  Chapter 7: Graphing Functions
  Chapter 8: Type Classes
  Chapter 9: Tuples and Type Constructors
  Chapter 10: Describing Motion in Three Dimensions
  Chapter 11: Creating Graphs
  Chapter 12: Creating Stand-Alone Programs
  Chapter 13: Creating 2D and 3D Animations 
  Part II: Expressing Newtonian Mechanics and Solving Problems
  Chapter 14: Newton’s Second Law and Differential Equations
  Chapter 15: Mechanics in One Dimension
  Chapter 16: Mechanics in Three Dimensions
  Chapter 17: Satellite, Projectile, and Proton Motion
  Chapter 18: A Very Short Primer on Relativity 
  Chapter 19: Interacting Particles
  Chapter 20: Springs, Billiard Balls, and a Guitar String
  Part III: Expressing Electromagnetic Theory and Solving Problems
  Chapter 21: Electricity
  Chapter 22: Coordinate Systems and Fields
  Chapter 23: Curves, Surfaces, and Volumes
  Chapter 24: Electric Charge
  Chapter 25: Electric Field
  Chapter 26: Electric Current
  Chapter 27: Magnetic Field
  Chapter 28: The Lorentz Force Law
  Chapter 29: The Maxwell Equations
  Appendix: Installing Haskell
  Bibliography
  Index