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
John Bukardt's
collection
of Python codes.