• Prologue
  • Why Python?
  • Acknowledgements
• Lecture 1 - Getting Started
  • Overview, Objectives, and Key Terms
  • Overview of Python
  • Python Distributions
  • Accessing Python
  • Basic Types
  • On Naming Variables
  • Further Reading
• Lecture 2 - Basic Operators and Built-In Functions
  • Overview, Objectives, and Key Terms
  • Python Operators
  • Exploring Built-In Functions
  • A First Program
  • Further Reading
• Lecture 3 - Basic Data Processing with NumPy and Matplotlib
  • Overview, Objectives, and Key Terms
  • NumPy and One-Dimensional Arrays
  • Diving into pyplot
  • Data Input and Output via NumPy
  • Further Reading
• Lecture 4 - More on NumPy Arrays: Slicing and `np.linalg`
  • Overview, Objectives, and Key Terms
  • Making Two-Dimensional Arrays
  • Visualizing 2-D Arrays
  • Slicing
  • Matrix-Vector and Matrix-Matrix Operations
  • Further Reading
• Lecture 5 - Algorithms, Flowcharts, and Pseudocode
  • Overview, Objectives, and Key Terms
  • Algorithms
  • Sequence by Example: Computing Grades
  • Selection
  • Iteration
  • Practice Problems
  • Further Reading
• Lecture 7 - Conditional Statements and the Structure of Python Code
  • Overview, Objectives, and Key Terms
  • The Simplest if
  • The else Clause
  • The elif Clause
  • Other Tidbits
  • Further Reading
• Lecture 8 - More on Conditionals
  • Overview, Objectives, and Key Terms
  • Motivating Nested Conditionals - Life Insurance
  • But Do We Need Them?
  • Debugging
  • Further Reading
• Lecture 9 - Loops in Python
  • Overview, Objectives, and Key Terms
  • A Motivating Problem
  • The break Clause
  • Numerical Convergence
  • Further Reading
• Lecture 10 - More on Loops
  • Overview, Objectives, and Key Terms
  • The for Loop
  • A Pythonic Quirk
  • Nested for loops
  • One Last Tidbit: continue
  • Further Reading
• Lecture 11 - Pythonic Containers
  • Overview, Objectives, and Key Terms
  • What is a sequential type?
  • The list Type
  • Mutability
  • The tuple Type
  • The dict Type
  • Further Reading
• Lecture 12 - Processing Text Data
  • Overview, Objectives, and Key Terms
  • Reading Text Files
  • Parsing Strings
  • Putting It All Together: Processing data.txt
  • Writing to File
  • Further Reading
• Lecture 13 - Basics of Functions
  • Overview, Objectives, and Key Terms
  • What is a Function?
  • Functions with Multiple Return Values
  • Functions with Multiple Arguments
  • Function Documentation
  • Functions and Flowcharts
  • Further Reading
• Lecture 14 - More on Functions
  • Overview, Objectives, and Key Terms
  • *args and **kwargs
  • Anonymous Functions
  • Recursive Functions
  • Further Reading
• Lecture 15 - Recursive Functions
  • Overview, Objectives, and Key Terms
• Lecture 16 - Algorithm Complexity and Numerical Experiments
  • Overview, Objectives, and Key Terms
• Lecture 17 - Searching
  • Overview, Objectives, and Key Terms
  • The Basic, Linear Search
  • A Bit About Order
  • Binary Search
  • A Comment on Built-In Functions
  • Further Reading
• Lecture 18 - Sorting
  • Overview, Objectives, and Key Terms
  • Sorting is Hard Work
  • Quantifying that Hard Work
  • Better Sorting for Bigger Data
  • Built-in Sorting
  • Further Reading
• Lecture 19 - Numerical Differentiation
  • Overview, Objectives, and Key Terms
  • If, in the beginning, \(\Delta\) didn’t go to 0...
  • Back to Order
  • Approximating the Second Derivative
  • Finite-Difference Approximations of Arbitrary Order
  • Further Reading
• Lecture 20 - Numerical Integration
  • Overview, Objectives, and Key Terms
  • Riemann Sums in Practice
  • Beyond the One-Side Sums
  • What About Accuracy?
  • Using scipy.integrate
  • Further Reading
• Lecture 21 - Linear Systems
  • Overview, Objectives, and Key Terms
  • What Is A Linear System, and When Can It Be Solved?
  • Solving Linear Systems by Elimination
  • Elimination via NumPy and SciPy
  • Further Reading
• Lecture 22 - Root Finding
  • Overview, Objectives, and Key Terms
  • Nonlinear Equations
  • Determining Roots Numerically
  • Solving Systems of Nonlinear Equations Numerically
  • Further Reading
• Lecture 23 - Optimization
  • Overview, Objectives, and Key Terms
  • Some Nomenclature
  • Finding Extrema
  • The Connection To Nonlinear Functions
  • Solving Unconstrained Optimization Problems
  • Solving Constrained Optimization Problems
  • Further Reading
• Lecture 24 - Modeling Data with Least Squares Fitting
  • Overview, Objectives, and Key Terms
  • Noisy Data and \(y = at + b\)
  • What “Best” Means
  • Beyond Linear Models
  • Beyond Polynomial Models
  • Further Reading
• Lecture 25 - Modeling Data with Interpolation
  • Overview, Objectives, and Key Terms
  • Simple Linear Interpolation
  • Interpolation In Two Dimensions
  • Higher-Order Interpolation
  • Further Reading
• Lecture 26 - Euler’s Method for IVPs
  • Overview, Objectives, and Key Terms
  • Differential Equations
  • Whence Comes \(y'+py=q\)?
  • The General Problem \(y' = f(y(t), t)\)
  • There Once was a Man Named Euler
  • Chopping Up Time
  • A Look at Errors and Stability (Optional)
  • Further Reading
• Lecture 27 - Systems of IVPs
  • Overview, Objectives, and Key Terms
  • A Coupled System and Its Numerical Solution
  • When the Equations are “Stiff”
  • SciPy’s odeint
  • Further Reading
• Lecture 28 - Numerical Solution of BVPs
  • Overview, Objectives, and Key Terms
  • Chopping Up the BVP
  • A Simple Example
  • Eigenvalue Problems
  • Comment on FDM and Alternatives
  • Further Reading
• Appendix A - Modules and Packages
  • Overview, Objectives, and Key Terms
  • Creating Modules
  • Running Modules as Scripts
  • Using Modules on the Moon
  • Packages
  • Further Reading
• Appendix B - Unit Tests and Defensive Programming
  • Overview, Objectives, and Key Terms
  • Be on the Defensive
  • Testing, 1-2-3
  • Further Reading