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EDSML Presessional Material
Welcome to EDSML 2023
Python Presessional Reading
Intro to Python
Printing and formatting statements
Variables
If statement
While loops
Lists
For loops
List comprehensions
Nested lists
Handling errors
Importing in Python
Creating custom functions
Tuples
File handling
Dictionaries
Flow control statements
Sets
Plotting data with Matplotlib
Assert
Python classes
Lambdas
Python Intro for MATLAB Users
Python Intro for R users
Python Intro for C/C++ Users
Additional Python Tips and Techniques
Intro to the Command Line
Intro to Git & Github
The
git
version control system
The Github.com Website
Mathematics
Linear algebra
Basic definitions and operations
Systems of linear equations
Theory
Eigenvalues and eigenvectors
Linear Algebra in Python
Calculus
Differential Calculus
Integral Calculus
Vector calculus (MM3)
Series and sequences
Taylor series
Fourier series
Fourier transforms
Differential equations
Introduction to differential equations
Linear Differential Equations
First-order ODEs
Higher order Linear ODEs
Series ODE
Introductory definitions and concepts
First-order linear PDEs
Canonical form of second-order linear PDEs
Poisson’s and Laplace’s equation
Heat (diffusion) equation
Solving PDEs with fourier methods
Wave equation
Self-similar solutions
Numerical methods
Interpolation and curve fitting
Numerical differentiation
Solving or timestepping an ODE
Heun’s method
Runge-Kutta method
Successive over-relaxation method
FTCS scheme
BTCS scheme
Numerical integration
Roots of equations
Linear algebra introduction
Gaussian elimination
LU decomposition
Ill-conditioning and roundoff errors
Iterative methods to solve a matrix
Statistics
Linear regression
Introduction to statistics for Geoscientists
Software Installation
Reading list
Index
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
L
|
M
|
N
|
O
|
P
|
Q
|
R
|
S
|
T
|
V
|
W
A
Algebraic multiplicity
Assert (Python)
Auxiliary condition
B
Basis
Bisection method
Break statement (Python)
BTCS scheme
C
Canonical form (2nd order PDE)
Central difference
Class (Python)
Coefficient of determination
command line
Continue statement (Python)
Convolution
Curl of a vector field
Curve fitting
D
D'Alembert's formula
Delta function
Determinant
Dictionary (Python)
Differential equation
Divergence of a vector field
E
Eigenvalue
Eigenvector
Elliptic PDE
Explicit form (DE)
Explicit scheme
F
File handling (Python)
Finding roots of equations numerically
For (Python)
Forward difference
Forward Euler scheme
Fourier series
Fourier series: coefficients
Fourier transform method
Fourier transforms
Frobenius method
FTCS scheme
Function (Python)
G
Gauss-Jordan elimination
,
[1]
Gauss-Seidel's method
Gaussian elimination
,
[1]
Gaussian function
Geometric multiplicity
Gibbs Phenomenon
Gibbs phenomenon
Gradient of a scalar field
H
Handling errors (Python)
Heat (diffusion) equation
Heun's method
Hyperbolic PDE
I
If (Python)
Implicit form (DE)
Implicit scheme
Importing modules (Python)
Inner product
Interpolation
Interpolation and curve fitting
Invariants
Inverse of a matrix
Iterative methods to solve a matrix
J
Jacobi's method
L
Lambda (Python)
Laplace operator
Laplace's equation
Laplacian for scalar/vector fields
Linear combination
Linear Differential Equation
Linear regression
Linear system
Linear transformation
List (Python)
List comprehension (Python)
LU decomposition
M
Matplotlib (Python)
Matrix norm
Matrix norms
Matrix operations
Matrix-matrix multiplication
Matrix-vector multiplication
Method of characteristics
N
Nested list (Python)
Norm
Null space
Numerical 2nd derivative
Numerical differentiation
Numerical integration
O
Odd and even functions
Outer product
P
Parabolic PDE
Partial differentiation
Pass statement (Python)
Permutations
Picard's method
Plots: 3D
Plots: Animations
Plots: histogram
Plots: image
Poisson's equation
Power series method
Printing (Python)
Q
Quiver plot
R
Range (Linear Algebra)
Rank
Root bracketing
Root-mean-square error
Roundoff errors
Runge-Kutta method
S
Scalar field
Secant method of root finding
Self-similar solution
Separation of variables
Series solution of ODEs
Set (Python)
Similar matrix
SOR algorithm
Spanning set
Sparse matrices
Statistics: basics
Streamline plot
String formating (Python)
SymPy: curl
SymPy: differentiation
SymPy: divergence
SymPy: gradient
T
Taylor series
Timestepping an ODE
Trace
Tuple (Python)
V
Variable (Python)
Vector calculus
Vector differentiation
Vector field
Vector function
Vector norms
Vector space
W
Wave equation
Well-posedness
While (Python)
Wronskian