SCIENCE BY SIMULATION (V2)

Models of Classical Physics is the second volume 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 represent the standard canon of Classical Physics (Mechanics, Thermodynamics, Waves and Optics, Electromagnetism) and are based upon paradigm problems and systems that all pre-university and undergraduate STEM students should have the opportunity to experience and, in time, master.

Rather than the 'what' of Science, this book is aimed at the 'how', providing guidance that can be 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 (and indeed sections) which can be read independently. This approach will provide a tangible and accessible context for the development of a wide range of interconnected mathematical ideas and computing methods that underpin the practice of Science, and Physics in particular.

Contents:

• Introduction:
  • Problem-Solving, Practical Experiments and Computer Simulations
  • The Style and Structure of Science by Simulation (Volume 2)
  • Mathematics: The Language of Physics
• Mechanics:
  • Beginning with Classical Mechanics
  • Bouncing Balls
  • Projectiles and Constant Acceleration Motion
  • The Ladder Problem
  • The Drawbridge Problem
  • The Three Barrels Problem
  • Weebles Wobble But Don't Fall Down
  • The Inclined Plane
  • Rolling Down a Slope
  • Slide and Roll the Loop
  • Atwood Machine
  • A Swinging Door
  • Lagrangian Mechanics, the Brachistochrone and Asymmetric Catenary
  • A Selection of Mechanics Books
• Thermodynamics:
  • Heat Engines
  • Newtonian Cooling
  • Kinetic Theory and Random Walks
  • Boltzmann's Exponential Statistics
  • A Selection of Thermodynamics Books and Resources
• Waves and Ray Optics:
  • An Anatomy of Waves
  • Standing Waves on Guitar Strings and in Organ Pipes
  • Wave Impedance, Reflection and Transmission
  • Ray Optics: Refraction, Reflection, Lenses and Mirrors
  • Fraunhofer and Fresnel Diffraction
  • Doppler and Mach
  • Water Waves and the Kelvin Wedge
  • Simple Harmonic Motion and Resonance in a Driven Mass–Spring System
  • A Selection of Books on Waves
• Electromagnetism:
  • Power Cables and Continued Fraction Resistor Networks
  • The Maximum Power Theorem
  • Modelling Electric Fields
  • Electric and Magnetic Dipoles
  • Capacitors
  • Curie, Ising and Ferromagnetism
  • Ampère's Theorem and a Toroidal Inductor
  • The Hall Probe
  • The Mass Spectrometer, the Velocity Selector and the Cyclotron
  • The Frequency Response of a Transformer
  • Resonance in an LCR Circuit
  • The Fresnel Equations
  • Maxwell's Equations of Electromagnetism
  • A Selection of Electromagnetism Books
• Appendix A. The Calculus of Variations:
  • The Beltrami Identity
  • LagrangianMechanics
• Appendix B. Dispersion Relationship for Waves on the Interface Between Two Fluids

Readership: This textbook is suitable for pre-university and undergraduate students of Physics, Engineering, Applied Mathematics, Computer Science, Materials Science and other related STEM subjects, as well as teachers of these courses. The book will also be of interest to professionals working in STEM industries, particularly those involving the creation of mathematical models of physical systems.