• Python Tutorial
    for APMA 0330
  • Preface
  • Links
    • Computing for APMA0330
    • Computing for APMA0340
    • Python tutorial for APMA0340
    • SymPy tutorial for APMA0330
    • SymPy tutorial for APMA0340
  • An Introduction to Python
    • Python Download
    • Installation
    • Anaconda
    • Python Distributions
    • IDEs - Spyder
    • IDEs - Jupyter
    • Hello, world!
    • Basic Operations
    • Data Types
    • Containers
    • Control Flow
    • Python Keywords
    • Variables and Data Types
    • Classes and Objects
    • Functions
    • Numerical Computing
    • Symbolic Manipulation
    • Derivative
    • Existence
    • Uniqueness
    • Picard iterations
    • Adomian iterations
  • Part I: Plotting
    • Basic Matplotlib
    • Plotting solutions to ODEs
    • Discontinuous functions
    • Direction fields
    • Implicit plot
    • Parametric plots
    • Labeling figures
    • Figures with arrows
    • Electric circuits
    • Plotting with filling
    • Polar plot
    • Some famous curves
    • Cycloids
    • Miscellany
  • Part 2: First Order ODEs
    • Motivating examples
    • Solving ODEs
    • Singular solutions
    • Solving ODEs
    • Plotting Solutions to ODEs
    • Direction fields
    • Separable equations
    • Autonomous equations
    • Equations reducible to separable equations
    • Equations with linear fractions
    • Exact equations
    • Integrating factors+
      • Function of x
      • Function of y
      • Function of xy
      • Function of x/y
      • Function of x&su./?/p2; + y&su./?/p2;
      • Common factors
      • Homogeneous factors
      • Special factors
      • Approximation of integrating factors
    • Linear equations
    • RC Circuits
    • Bernoulli equations
    • Riccati equations
    • Clairaut equations
    • Qualitative analysis +
      • Bifurcations
      • Landau theory
      • Validity interval
    • Orthogonal trajectories
    • Population models
    • Pursuit
    • Applications
  • Part 3: Numerical Methods and Applications
    • Numerical solutions
    • Fixed point iteration
    • Bracketing methods
    • Open methods
    • Homotopy method
    • Comperisons
    • Padé approximations
    • Euler's methods +
      • Backward method
      • Heun's methods
      • Modified Euler method
    • Runge—Kutta methods +
      • Runge—Kutta methods of order 2
      • Runge—Kutta methods of order 3
      • Runge—Kutta methods of order 4
    • Polynomial approximations
    • Error estimates
    • Adomian Decomposition Method
    • Finite Difference Schemes
    • Variational iteration method
    • Multistep methods +
      • Multistep methods of order 3
      • Multistep methods of order 4
      • Milne method
      • Hamming method
    • Applications
  • Part 4: Second and Higher Order Differential Equations
    • Differential equations of higher order
    • Canonical forms
    • Reduction higher order ODEs
    • Linear operators
    • Fundamental set of solutions
    • Linear ODEs
    • Constant coefficient ODEs
    • Complex roots
    • Reduction of order
    • Annihilator operators
    • Method of undetermined coefficients
    • Variation of parameters
    • Factorization
    • Inhomogeneous ODEs
    • Euler equations +
      • Factorization
      • Inhomogeneous Euler equations
  • Part 4 N: Nonlinear ODEs
    • Numerical solutions
    • Boundedness of solutions
    • Spring problems +
      • Free vibrations
      • Damped vibrations
      • Forced vibrations
      • Resonance
      • Nonlinear models
      • Driven models
    • Pendulum +
      • Simple pendulum
      • Solution of pendulum equation
      • Period of pendulum
      • Real pendulum
      • Driven pendulum
      • Rocking pendilum
      • Pumping swing
    • Dyer model
    • Electric circuits
    • Adomian Decomposition Method
    • Applications
  • Part 5: Series and Recurrences
    • Recurrences
    • Discrete logistic recurrence
    • Generating functions
    • Lagrange Inversion Theorem
    • Series convergence
    • Review of power series
    • Convergence acceleration
    • Taylor's method
    • Picard iterations
    • Iteration
    • Series solutions for the first order equations
    • Examples for the first order equations
    • Series solutions for the second order equations
    • Series solutions for the first order equations
    • Examples for the second order equations
    • Euler equations
    • Regular singular points +
      • Distinct exponents
      • Equal exponents
      • Integer difference
      • Complex exponents
    • Polynomial solutions
    • Bessel's equations
    • Modified Decomposition Method
    • MDM for first order ODEs
    • MDM for second order ODEs
    • Applications
  • Part 6: Laplace Transformation
    • Definition of Laplace transform
    • Heaviside and Dirac functions
    • Laplace transform of discontinuous functions
    • Table of Laplace transforms
    • Inverse Laplace transforms
    • Convolution integral
    • Residue method
    • Solving IVPs with Laplace transforms
    • ODEs with discontinuous input
    • Nonconstant coefficient IVPs
    • Bessel functions
    • MLDM
    • Elzaki transform
    • Mechanical and electrical applications
  • Part 7: Boundary Value Problems
    • Boundary Value Problems
    • Green functions
    • Picard iterations
    • Finite difference schemes
    • Shooting methods
    • Tridiagonal linear systems
    • Numerov method
    • Adomian decomposition
    • Variational iteration methpod
    • Block discretization
    • Blasius layer
    • Falkner--Skan layer
    • Heat transfer
    • Singular BVPs
    • Applications
  • Glossory
    • Under the terms of GNU General
    Public License GPL