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Physical Modeling in MATLAB^®

Allen B. Downey Version 2 Contributor: W. Craig Scratchley

Version 2.1.0

Copyright 2014 Allen B. Downey

Permission is granted to copy, distribute, and/or modify this document under the terms of the Creative Commons Attribution-NonCommercial 3.0 Unported License, which is available at http://creativecommons.org/licenses/by-nc/3.0/.

• Preface to Version 2
• Preface
  • Contributor’s list
• Contents
• Variables and Values
  • A glorified calculator
  • Math functions
  • Documentation
  • Variables
  • Assignment statements
  • Why variables?
  • Errors
  • Floating-point arithmetic
  • Comments
  • Glossary
  • Exercises
• Scripts
  • M-files
  • Why scripts?
  • The workspace
  • More errors
  • Pre- and post-conditions
  • Assignment and equality
  • Incremental development
  • Unit testing
  • Glossary
  • Exercises
• Loops
  • Updating variables
  • Kinds of error
  • Absolute and relative error
  • for loops
  • plotting
  • Sequences
  • Series
  • Generalization
  • Glossary
  • Exercises
• Vectors
  • Checking preconditions
  • if
  • Relational operators
  • Logical operators
  • Vectors
  • Vector arithmetic
  • Everything is a matrix
  • Indices
  • Indexing errors
  • Vectors and sequences
  • Plotting vectors
  • Reduce
  • Apply
  • Search
  • Spoiling the fun
  • Glossary
  • Exercises
• Functions
  • Name Collisions
  • Functions
  • Documentation
  • Function names
  • Multiple input variables
  • Logical functions
  • An incremental development example
  • Nested loops
  • Conditions and flags
  • Encapsulation and generalization
  • A misstep
  • continue
  • Mechanism and leap of faith
  • Glossary
  • Exercises
• Zero-finding
  • Why functions?
  • Maps
  • A note on notation
  • Nonlinear equations
  • Zero-finding
  • fzero
  • What could go wrong?
  • Finding an initial guess
  • More name collisions
  • Debugging in four acts
  • Glossary
  • Exercises
• Functions of Vectors
  • Functions and files
  • Physical modeling
  • Vectors as input variables
  • Vectors as output variables
  • Vectorizing your functions
  • Sums and differences
  • Products and ratios
  • Existential quantification
  • Universal quantification
  • Logical vectors
  • Glossary
• Ordinary Differential Equations
  • Differential equations
  • Euler’s method
  • Another note on notation
  • ode45
  • Multiple output variables
  • Analytic or numerical?
  • What could go wrong?
  • Stiffness
  • Glossary
  • Exercises
• Systems of ODEs
  • Matrices
  • Row and column vectors
  • The transpose operator
  • Lotka-Volterra
  • What could go wrong?
  • Output matrices
  • Glossary
  • Exercises
• Second-order Systems
  • Spatial vectors
  • Newtonian motion
  • Freefall
  • Air resistance
  • Two dimensions
  • Spacial vectors revisited
  • Putting it all together
  • What could go wrong?
  • ODE Events
  • Glossary
  • Exercises
• Optimization and Interpolation
  • Optimization
  • Golden section search
  • Discrete and continuous maps
  • Interpolation
  • Interpolating the inverse function
  • Field mice
  • Glossary
  • Exercises
• Celestial Mechanics
  • Celestial mechanics
  • Animation
  • Conservation of Energy
• Final Thoughts
  • Dot and cross products
  • What is a model for?
  • Glossary
  • Exercises
• The Nine Theorems of Debugging
• Nested Functions
• Index