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Contents

• Chapter 0  Preface to Version 2
• Chapter 1  Preface
• Chapter 2  Variables and Values
  • 2.1  A glorified calculator
  • 2.2  Math functions
  • 2.3  Documentation
  • 2.4  Variables
  • 2.5  Assignment statements
  • 2.6  Why variables?
  • 2.7  Errors
  • 2.8  Floating-point arithmetic
  • 2.9  Comments
  • 2.10  Glossary
  • 2.11  Exercises
• Chapter 3  Scripts
  • 3.1  M-files
  • 3.2  Why scripts?
  • 3.3  The workspace
  • 3.4  More errors
  • 3.5  Pre- and post-conditions
  • 3.6  Assignment and equality
  • 3.7  Incremental development
  • 3.8  Unit testing
  • 3.9  Glossary
  • 3.10  Exercises
• Chapter 4  Loops
  • 4.1  Updating variables
  • 4.2  Kinds of error
  • 4.3  Absolute and relative error
  • 4.4  for loops
  • 4.5  plotting
  • 4.6  Sequences
  • 4.7  Series
  • 4.8  Generalization
  • 4.9  Glossary
  • 4.10  Exercises
• Chapter 5  Vectors
  • 5.1  Checking preconditions
  • 5.2  if
  • 5.3  Relational operators
  • 5.4  Logical operators
  • 5.5  Vectors
  • 5.6  Vector arithmetic
  • 5.7  Everything is a matrix
  • 5.8  Indices
  • 5.9  Indexing errors
  • 5.10  Vectors and sequences
  • 5.11  Plotting vectors
  • 5.12  Reduce
  • 5.13  Apply
  • 5.14  Search
  • 5.15  Spoiling the fun
  • 5.16  Glossary
  • 5.17  Exercises
• Chapter 6  Functions
  • 6.1  Name Collisions
  • 6.2  Functions
  • 6.3  Documentation
  • 6.4  Function names
  • 6.5  Multiple input variables
  • 6.6  Logical functions
  • 6.7  An incremental development example
  • 6.8  Nested loops
  • 6.9  Conditions and flags
  • 6.10  Encapsulation and generalization
  • 6.11  A misstep
  • 6.12  continue
  • 6.13  Mechanism and leap of faith
  • 6.14  Glossary
  • 6.15  Exercises
• Chapter 7  Zero-finding
  • 7.1  Why functions?
  • 7.2  Maps
  • 7.3  A note on notation
  • 7.4  Nonlinear equations
  • 7.5  Zero-finding
  • 7.6  fzero
  • 7.7  What could go wrong?
  • 7.8  Finding an initial guess
  • 7.9  More name collisions
  • 7.10  Debugging in four acts
  • 7.11  Glossary
  • 7.12  Exercises
• Chapter 8  Functions of Vectors
  • 8.1  Functions and files
  • 8.2  Physical modeling
  • 8.3  Vectors as input variables
  • 8.4  Vectors as output variables
  • 8.5  Vectorizing your functions
  • 8.6  Sums and differences
  • 8.7  Products and ratios
  • 8.8  Existential quantification
  • 8.9  Universal quantification
  • 8.10  Logical vectors
  • 8.11  Glossary
• Chapter 9  Ordinary Differential Equations
  • 9.1  Differential equations
  • 9.2  Euler’s method
  • 9.3  Another note on notation
  • 9.4  ode45
  • 9.5  Multiple output variables
  • 9.6  Analytic or numerical?
  • 9.7  What could go wrong?
  • 9.8  Stiffness
  • 9.9  Glossary
  • 9.10  Exercises
• Chapter 10  Systems of ODEs
  • 10.1  Matrices
  • 10.2  Row and column vectors
  • 10.3  The transpose operator
  • 10.4  Lotka-Volterra
  • 10.5  What could go wrong?
  • 10.6  Output matrices
  • 10.7  Glossary
  • 10.8  Exercises
• Chapter 11  Second-order Systems
  • 11.1  Spatial vectors
  • 11.2  Newtonian motion
  • 11.3  Freefall
  • 11.4  Air resistance
  • 11.5  Two dimensions
  • 11.6  Spacial vectors revisited
  • 11.7  Putting it all together
  • 11.8  What could go wrong?
  • 11.9  ODE Events
  • 11.10  Glossary
  • 11.11  Exercises
• Chapter 12  Optimization and Interpolation
  • 12.1  Optimization
  • 12.2  Golden section search
  • 12.3  Discrete and continuous maps
  • 12.4  Interpolation
  • 12.5  Interpolating the inverse function
  • 12.6  Field mice
  • 12.7  Glossary
  • 12.8  Exercises
• Chapter 13  Celestial Mechanics
  • 13.1  Celestial mechanics
  • 13.2  Animation
  • 13.3  Conservation of Energy
• Chapter 14  Final Thoughts
  • 14.1  Dot and cross products
  • 14.2  What is a model for?
  • 14.3  Glossary
  • 14.4  Exercises
• Chapter 15  The Nine Theorems of Debugging
• Chapter 16  Nested Functions

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