Outline of differential equations. Similar to the popular book series with the same name. In chapters 01, 03, 04, and 05, Python is used for calculations and matplotlib for plotting. In subsequent chapters, (until Chapter 31), Wolfram Alpha (and also Maxima) are used for calculations, and matplotlib for plotting. Chapter 31 is a 16-part tour of Partial Differential Equations, in which both Python and Octave are used.
Notebook versions in both classic Jupyter notebook and PDF formats are available. Github can now render Jupiter notebooks, but the default code font may be of poor quality. In Firefox this can be fixed in settings by setting all three font family choices (in the advanced menu) to the same desired font (such as Monaco), while allowing the "allow pages to choose ..." checkbox to remain checked. If using Chrome, a congenial solution can be obtained by using the browser extension "Github Refined".
The markdown cells were created with the Bookerly font, which for the purpose of fidelity should be on the system.
Contents:
Chapter01 Basic Concepts
Chapter03 Classifications of 1st Order
Chapter04 Separable 1st Order
Chapter05 Exact 1st Order
Chapter06 Linear 1st Order
Chapter07 Applications of 1st Order ODEs
Chapter08 Linear ODEs: Theory of Solutions
Chapter09 2nd Order Linear Homogeneous w Constant Coeff
Chapter10 nth Order Linear Homogeneous w Constant Coeff
Chapter11 Method of Undetermined Coefficients
Chapter12 Method of Variation of Parameters
Chapter13 Initial Value Problems for Linear ODEs
Chapter14 Applications of 2nd Order Linear ODEs
Chapter15 Matrices
Chapter16 e^At
Chapter17 Reduction of Linear Differential Equations
Chapter18 Graphical and Numerical Methods for 1st Order
Chapter19 Further Numerical Methods for Solving 1st Order
Chapter20 Numerical Methods for Solving 2nd Order via Systems
Chapter21 The Laplace Transform
Chapter22 Inverse Laplace Transform
Chapter23 Convolution and the Unit Step Function
Chapter24 Solutions of Linear ODEs by Laplace Transforms
Chapter25 Solutions of Linear Systems by Laplace Transforms
Chapter26 Solutions of Linear ODEs by Matrix Methods
Chapter27 Power Series Solns of Linear Equations with Variable Coefficients
Chapter28 Series Solutions Near a Regular Singular Point
Chapter29 Some Classical Differential Equations
Chapter31-1 Boundary Element Method
Chapter31-2 Differential Quadrature
Chapter31-3 Domain Decomposition
Chapter31-4 Elliptic Case--Finite Differences
Chapter31-5 Elliptic Case--Monte Carlo Method
Chapter31-6 Elliptic Case--Relaxation
Chapter31-7 Hyperbolic Case--Finite Differences
Chapter31-8 Hyperbolic Case--Method of Characteristics
Chapter31-9 Lattice Gas Dynamics
Chapter31-10 Method of Lines
Chapter31-11 Parabolic Case--Explicit Method
Chapter31-12 Parabolic Case--Implicit Method
Chapter31-13 Parabolic Case--Monte Carlo Method
Chapter31-14 Pseudo-Spectral Method
Chapter31-15 Reduced Finite Element Method
Chapter31-16 PDE Solvers Using Neural Network Methods